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Loaded questions: the prevalence, causes, and consequences of teacher salary schedule frontloading

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Loaded questions: the prevalence, causes, and consequences of teacher salary schedule frontloading

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Content Loaded Questions: The Prevalence, Causes, and Consequences of Teacher Salary Schedule Frontloading Copyright 2020 by Paul Bruno A Dissertation Presented to the FACULTY OF THE USC GRADUA TE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY URBAN EDUCATION POLICY August 2020 Paul Bruno Acknowledgements This dissertation would not have been possible with the support of many individuals, most of whom will necessarily go unnamed. Among those to whom I am most grateful are my parents, who for as long as I can remember emphasized the importance of education, including my own education. My ability to continue my education to this point is a direct result of the continuous support of my wife, Colleen. I count myself very fortunate to have found in Katharine Strunk an advisor with whom I could do good work and who has gone to great lengths to help me do my own. I also appreciate the rest of my committee - Morgan Polikoff, TJ McCarthy, and Dan Goldhaber- for their support on this project in particular. 11 Table of Contents Acknowledgements ........................................................................................................................ .ii Table of Contents ........................................................................................................................... .iii List of Tables ................................................................................................................................... v List of Figures ................................................................................................................................ vi Abstract ......................................................................................................................................... vii Introduction ..................................................................................................................................... 1 Conceptual Framework ............................................................................................................... 3 Previous Literature .......................................................................................................................... 5 The Prevalence of Frontloaded Teacher Salary Schedules ......................................................... 6 Labor Market Factors Related to Frontloading Compensation ................................................... 8 Competition for teachers in the labor market. ........................................................................ 8 Imperfect information about teachers . .................................................................................. 13 Union Influence ........................................................................................................................ 16 Summary ................................................................................................................................... 20 Research Questions ....................................................................................................................... 21 RQ 1: The Prevalence of Frontloading ...................................................................................... 22 RQ2: The Causes of Frontloading ............................................................................................ 22 RQ3: The Consequences of Frontloading ................................................................................. 23 Data ............................................................................................................................................... 24 Salary Schedules ....................................................................................................................... 24 Operationalizing salary schedule frontloading . .................................................................... 25 Staff Data .................................................................................................................................. 32 Student Achievement Data ........................................................................................................ 33 Financial Data ........................................................................................................................... 33 Collective Bargaining Agreement Data .................................................................................... 35 Other Data ................................................................................................................................. 36 Methods ......................................................................................................................................... 36 111 RQl: The Prevalence of Frontloading ...................................................................................... 36 RQ2: The Causes of Frontloading ............................................................................................ 37 2.a: Is the shape of the salary schedule the result of teachers' union influence? .................. 37 2.b: Is the shape of the salary schedule a result of district responses to labor market factors? .................................................................................................................................. 38 Approaches assessing both union influence and competition for teachers .. ......................... 42 RQ3: The Consequences of Frontloading ................................................................................. 48 3 .a: District hiring outcomes .. ............................................................................................... 48 3. b and 3.c: Student achievement and district spending patterns . ........................................ 50 Results ........................................................................................................................................... 51 RQl: The Prevalence of Frontloading ...................................................................................... 51 RQ2: The Causes of Frontloading ............................................................................................ 57 2.a: Is the shape of the salary schedule the result of teachers' union influence? .................. 57 2.b: Is the shape of the salary schedule the result of district responses to labor market factors? .................................................................................................................................. 61 Approaches assessing both union influence and competition for teachers .. ......................... 67 RQ3: The Consequences of Frontloading ................................................................................. 77 3 .a: District hiring outcomes .. ............................................................................................... 77 3.b: Student achievement. ..................................................................................................... 82 3.c: District spending patterns ............................................................................................... 85 Discussion ..................................................................................................................................... 88 References ..................................................................................................................................... 95 Tables ........................................................................................................................................... 111 Figures ......................................................................................................................................... 133 Appendix ..................................................................................................................................... 147 IV List of Tables Table 1 - Research Questions, Hypotheses, Methods, and Results ............................................. 111 Table 2 - Measures of Salary Schedule Frontloading ................................................................. 112 Table 3 - Correlations Between Frontloading Measures ............................................................. 113 Table 4 - Standardized Account Code Structure Codes Defining Expenditure Variables ........... 114 Table 5 - CBA Items Used to Estimate Overall Restrictiveness ................................................. 114 Table 6 - Items used in Evaluation Subarea Contract Restrictiveness Measure ......................... 115 Table 7 - Summary Statistics ....................................................................................................... 117 Table 8 -A bsolute Changes in Frontloading ............................................................................... 11 8 Table 9 - Salary Schedule Structure as a Function of CBA Restrictiveness and Teacher Experience .................................................................................................................................... 119 Table 10 - Salary Schedule Structure as a Function of CBA Restrictiveness and Teacher Experience, by Outcome Level ................................................................................................... 120 Table 11 - Salary Schedule Structure as a Function of Monitoring Intensity ............................ 121 Table 12 - Salary Schedule Structure as a Function of Monitoring Intensity by District Type . 122 Table 13 - Salary Schedule Differences Between High School and Elementary Districts ........ 123 Table 14 - Salary Levels with Spatial Spillovers ....................................................................... 124 Table 15 - Frontloading (Standardized) with Spatial Spillovers ................................................ 125 Table 16 - Parametric Regression Discontinuity Estimates of Salary Schedule Features ......... 126 Table 17 -P redicting the Percentage of Newly Hired Teachers without a Full Credential.. ...... 127 Table 18 -P redicting New Teacher Hires' Experience .............................................................. 12 8 Table 19 -P redicting the Percentage of Newly Hired Teachers without a Full Credential, Quadratic Models ........................................................................................................................ 129 Table 20 - Student Achievement as a Function of Salary Schedule Structure (District FE Models) ....................................................................................................................................... 130 Table 21 - Standardized Student Achievement as a Function of Salary Schedule Structure, by Student Achievement Level (District FE Models) ................................................................. 131 Table 22 - Resource Allocation Measures as a Function of Salary Schedule Structure (District FE Models) ................................................................................................................... 132 V List of Figures Figure 1 - Example Salary Schedule Lanes ............................................................................... 130 Figure 2 - Conceptual Framework ............................................................................................. 131 Figure 3 - CTA Service Centers ................................................................................................. 132 Figure 4 -Av erage Teacher Salary by Step ................................................................................ 133 Figure 5 - The Distribution of Salary Schedule Frontloading .................................................... 134 Figure 6 - The Distribution of Salary Schedule Frontloading (Standardized) ........................... 135 Figure 7 - Changes in Average Salaries at Various Steps ........................................................... 136 Figure 8 - Frontloading over Time ............................................................................................. 137 Figure 9 - Changes in Frontloading between 2003-2004 and 2016-2017 .................................. 138 Figure 10 - Distribution of Unduplicated Pupil Percentages ..................................................... 139 Figure 11 - Teacher Salaries and District Unduplicated Pupil Percentages ............................... 140 Figure 12 - Frontloading and Unduplicated Pupil Percentages .................................................. 141 Figure 13 - Regression Discontinuity Estimates of Salary Levels Over Time ........................... 142 Figure 14 - Regression Discontinuity Estimates of Frontloading Over Time ............................ 143 Vl Abstract Most teachers are paid according to salary schedules in which teachers are placed in "lanes" based on their education level and advance up "steps" of their lane as they accumulate experience. In theory salary schedules that are "frontloaded," letting teachers attain the highest salaries quickly, allow districts to more effectively recruit and retain teachers. However, little empirical evidence supports that proposition and it is unclear why, if frontloaded schedules are more effective, backloaded schedules remain common. I extend this literature using a 14-years of district-level data from California, including detailed data on the contents of districts' contracts with their teachers' unions and the composition of their salary schedules. These data allow me to (i) assess the prevalence of teacher salary schedule frontloading, (ii) test theoretical explanations for salary frontloadedness, and (iii) evaluate the relationship between salary frontloadedness and districts' hiring outcomes, student achievement, and spending patterns. While teacher salary schedules in California are heavily frontloaded in how they distribute annual raises, they vary substantially in their degree of frontloadedness. I find no evidence supporting common theoretical arguments that backloaded salary schedules are the result of teachers' union influence or administrators' inability to monitor teacher performance effectively. Instead, frontloading appears to be driven at least in part by competition for new teachers. Indeed, frontloaded salary schedules appear to be helpful in recruiting better-credentialed teachers, though they also appear costly for districts and are not associated with improved student achievement. These findings contribute to our understanding of teacher labor markets and of administrative dynamics in districts. Given their ubiquity, understanding the economics and politics of teacher salary schedules is important to effective policymaking. Keywords: teacher compensation, teacher labor markets, teachers' unions Vll Introduction Given the fundamental importance of teachers for school operations (Goldhaber, 2016) and evidence that teachers are sensitive to financial incentives (Clotfelter, Glennie, Ladd, & Vigdor, 200 8; Feng & Sass, 2017), the question of how best to compensate teachers has received a great deal of policy attention. Much of this attention has focused on the possibility of differentiating teacher compensation based on supply (i.e., for difficult-to-staff positions) or performance, and both approaches have shown some promise (Hough & Loeb, 2013; Pham, Nguyen, & Springer, 2017). However, in other cases results have been more mixed (Liu, Johnson, & Peske, 2004; Springer, Swain, & Rodriguez, 2016). Additionally, these kinds of reforms can be costly to implement (Turque, 2012) and are often controversial, especially in in the case of performance pay (Goldhaber, Dearmond, & Deburgomaster, 2011; Postal, 2018). Despite these and similar efforts to reform teacher compensation, the large majority of teachers continue to be paid on the basis of salary schedules in which teachers are placed in "lanes" based on their education level and advance up "steps" of their lane as they accumulate experience (Gray, Bitterman, & Goldring, 2013). Despite their apparent rigidity, the design of these salary schedules may offer opportunities for improving the way teachers are paid through changes to the ways that salary increments are distributed within and across lanes. Of interest for the present study is that salary schedules can differ in the way they distribute raises for additional teaching experience, "frontloading" schedules such that new teachers attain high salaries quickly or "backloading" them so that salaries increase more rapidly for more veteran teachers. Figure 1 illustrates these ideas using two lanes from two different salary schedules in the 2016-2017 school year. Each lane indicates the salary received by teachers with a bachelor 's degree and 60 additional graduate credits of education (BA+60) at each step (i.e., level of 1 experience) on their respective districts' salary schedules. Despite offering nearly identical starting and ending salaries to teachers in their first and thirtieth years in the classroom, respectively, these salary profiles have noticeably different shapes. In particular, the salaries offered to teachers in the Ramona City Unified School District are more frontloaded than those offered in the Paradise Unified School District. Despite beginning their careers (i.e., at step 1) with essentially the same salaries as their counterparts in Paradise, teachers in Ramona City earn approximately $5,000 more in their fifth year in the classroom, and almost $16,200 more by step 10. By their 15 th year teachers at this level of education in Ramona City earn 85% of their maximum possible (i.e., step 30) salaries, a feat not achieved by teachers in Paradise until their 24 th year. Changes within a salary schedule framework may be more feasible politically than other, more radical compensation reforms that depart from the step-and-lane paradigm altogether. And given their ubiquity, improving the design of these salary schedules may be a powerful lever to improve teacher quality. However, little evidence exists to guide policymakers looking to improve teacher salary schedules. I therefore use detailed salary schedule data available for the large majority of California districts over 14 years to answer three questions. First, how frontloaded are teacher salary schedules, and have they become more or lessfrontloaded over time? Second, why do districts frontload their salary schedules to different degrees? Third, is salary schedule frontloading associated with districts ' staffing outcomes, student achievement, and spending patterns? I find that salary schedules in California are heavily frontloaded in how they distribute raises to teachers, and have been so for many years, though many individual districts have made their salary schedules considerably more or less frontloaded over time. These changes do not appear to be explained by the activity of teachers' unions or how districts monitor their employees. 2 Rather, frontloading appears to be driven at least in part by competition for new teachers. I also find some evidence that more heavily frontloaded salary schedules are associated with districts hiring better-credentialed teachers, suggesting that frontloaded compensation can help districts recruit and retain teachers more effectively. However, I find little evidence that more frontloaded salary schedules are associated with improved student achievement, and some evidence that frontloading salary schedules more heavily can be costly for districts if they do not also reduce salaries for veteran teachers. In what follows I consider the extant literature on teacher salary schedules, paying special attention to the evidence on salary schedule frontloading and its likely implications for relatively novice teachers. I then revisit my research questions in light of that literature and describe the data and methods I use to answer those questions. I then present my results and conclude with a discussion of implications. Conceptual Framework Before considering the existing literature on the structure of teacher compensation in detail, it will be helpful to first outline a basic conceptual framework bringing together the theories most commonly used to explain why districts frontload salaries for teachers to different degrees. This will help both to organize the relevant previous literature and to preview the hypotheses associated with my research questions. This framework is illustrated in Figure 2. Explanations of the frontloadedness of salary schedules, represented by the circles in Figure 2, generally fall into two broad categories. First, districts might frontload their salary schedules to different degrees as they respond to labor market factors. One of these factors is imperfect information about teacher quality. If discerning teacher skill or effort takes time, districts will be reluctant to award high salaries to teachers immediately, 3 before their quality can be assessed. This results in deferred (i.e., backloaded) compensation (Lazear, 1981 ; Prendergast, 19 99; Salop & Salop, 197 6). Working in the other direction is competition for teachers in the labor market. Because frontloaded compensation is attractive to teachers, and especially novice teachers, districts will tend to offer more rapid salary increases when they want to ensure that they can hire and retain an adequate number of strong teachers (Ballou & Podgursky, 2002; Lankford & Wyckoff, 199 7). Second, the frontloadedness of salary schedules might be the result of union influence. Whether teachers' unions will tend to advocate for compensation that is more frontloaded (to maximize overall compensation levels) or more backloaded (to benefit more senior members) is a matter of some dispute in the literature (Grissom & Strunk, 2012; Gustman & Segal, 1977; Lankford & Wyckoff, 19 97; Monk & Jacobson, 1985; West & Mykerezi, 2011). Previous literature highlights an important similarity between labor market factors and union influence: namely, that they operate at least in part through relationships that districts have to one another. For example, school districts have to offer attractive compensation packages to attract and retain teachers because teachers may otherwise prefer to work in other nearby districts. These kinds of interactions between districts are sometimes called spatial relationships and are represented by the dashed circle in Figure 2, but they are not limited to interactions that arise only because districts are physically close to one another. For instance, local teachers' unions that are members of the same supra-local union organization may have similar outcomes because they are close to one another institutionally (e.g., sharing union administrators), and those connecting institutions allow bargaining strategies to travel between districts (Goldhaber, Lavery, & Theobald, 2014). However, an important difference between these labor market and union forces is that 4 district responses to the former are generally thought to be beneficial for district operations, while district responses the latter may not be. This is because when districts frontload their salary schedules in response to labor market factors, they will also more effectively recruit and retain teachers and a stronger teaching staff will benefit students. This will be true even if frontloaded salary schedules increase salary costs for the district, and higher salary costs may be at least partially offset by savings associated with improved teacher retention (e.g., lower hiring costs). Conversely, when districts' salary schedules change to reflect greater union influence, this may result in increased salary expenditures without a commensurate benefit for students, for example if unions prefer to allocate experience-based raises in ways unrelated to teacher effectiveness. These consequences of frontloading are illustrated by the squares in Figure 2. This framework is not inclusive of every possible factor that might contribute to the frontloadedness of districts' salary schedules, nor of every possible consequence of that frontloadedness. Rather, Figure 2 illustrates the forces most commonly emphasized in the previous literature, which I discuss in greater detail below. Additionally, the relationships illustrated in Figure 2 begin to highlight the hypotheses I will test in the analyses that follow my review of the literature; the portions of the framework corresponding to each of my research questions are labeled at the top of Figure 2. Previous Literature While an extensive literature examines teacher compensation, this work typically focuses on overall salary levels (e.g., Akiba, Chiu, Shimizu, & Liang, 2012; Figlio, 1997; Hanushek & Rivkin, 2007; Imazeki, 2005) or differentiating compensation on the basis of teacher supply (e.g., Feng & Sass, 2017; Strunk & Zeehandelaar, 2011) or performance (e.g., Pham et al., in press). Comparatively few studies consider the shape of teacher salary schedules or the extent to which 5 they are frontloaded. However, extant work is generally in agreement on two questions. First, that teacher salary schedules are often backloaded, in some cases significantly so (Grissom & Strunk, 2012; Lankford & Wyckoff, 1997; Monk & Jacobson, 1985; Vigdor, 20 08), and, second, that both theory and evidence suggest that frontloaded salary schedules allow schools to attract and retain teachers more effectively (Grissom & Strunk, 2012; Hendricks, 2014, 2015; Murnane, Singer, Willett, Kemple, & Olsen, 1991 ). Here I consider the research on each of these two questions in turn. Th e Prevalence of Frontloaded Teacher Salary Schedules Taken as a whole, prior work suggests that there is considerable variation in the extent to which teacher salary schedules are frontloaded. Early work on the subject suggested that backloading was the norm for teacher salaries. Monk and Jacobson (1985) consider salary schedules in a sample of school districts in New Yo rk state, and find that between 1973 and 1983 districts increased veteran teachers' salaries more rapidly in percentage terms than novices' , a form of backloading across time, with a similar pattern apparent in a sample of contracts collected nationwide. They also observe more backloading in teacher compensation than for workers in other occupations, including civil servants, scientists, and engineers. Lankford and Wyckoff (1997) consider a larger sample of districts in New Yo rk and a longer time period - 1970 to 199 4 - and use observed teacher salaries to estimate salary schedule parameters. They find that 85% of districts backloaded salary increases during this period, increasing veteran teachers' salaries more in percentage terms than those of novices, and observe only modestly less backloading in a sample of districts from elsewhere in the country. Rather than looking at changes to salary schedules longitudinally to identify frontloading and backloading, more recent work considers the distribution of salary increments within salary 6 schedules. This might better capture expected wage profiles as they are perceived by teachers as they make labor market decisions, since anticipating future changes to salary schedules may be difficult. For example, Vigdor (200 8) uses as an example the 2007-2008 statewide salary schedule in North Carolina and shows that it is substantially backloaded; teachers with two years of experience receive salaries that are only 2% higher than those for beginners. Salaries grow faster at higher levels of experience, but he emphasizes that that is precisely when teacher productivity gains have leveled off. He then uses data from the American Community Survey to show that teachers' compensation is heavily backloaded relative to that of doctors and lawyers; workers in those professions approach their peak lifetime earnings before they are 45 years old on average, a feat that is not achieved by teachers until they are over 50 . However, other recent work finds that frontloaded salary schedules, if not the norm, are nevertheless common. Grissom and Strunk (2012) use a nationally representative sample of districts from the 1999 -2000 administration of the Schools and Staffing Survey (SASS) and define backloading as the receipt of larger average annual salary increases (in dollar terms) for teachers during their second decade of teaching than for teachers in their first 10 years. They find more frontloading than previous studies, with the median district in their sample using a salary schedule that is very slightly frontloaded (i.e., having slightly larger salary increments for less experienced teachers). Some of the variation in salary schedule frontloading appears to be regional. Of particular interest for present purposes are several studies finding that teacher salary schedules are generally frontloaded in California school districts. Though it is not an explicit focus of their research, Rose and Sonstelie (2010) show descriptively that at several levels of education salary schedules in California in 1999 -2000 on average gave substantially larger step raises to teachers between the 7 first and eleventh steps of the schedule than between the eleventh and twenty-first steps. Other work has borne this out in more recent years. Rose and Sengupta (2007) find that in 2003-2004, of total raises granted to teachers between the first and twentieth steps, on average California districts awarded 68% to 81 % by step 10, depending on the lane (i.e., education level). Most recently, Goldhaber et al. (2018) find that in 2014-2015 only 7% of California districts backloaded their salary schedules by giving larger average annual raises to teachers in their second decade than in the first decade. On average, they find that average step raises received by teachers were 134% larger in the first five years than in the fifteenth to twentieth years and were 453 % larger in the first ten years than in the second ten years. Notably, they also find considerable variation in the degree of frontloading within California; the standard deviations of those figures are each slightly larger than average itself. These studies are not without their limitations. Perhaps most notably, the work discussed above focuses primarily on the first 20 steps of the salary schedule; as I discuss below, subsequent steps may be important. Nevertheless, taken as a whole, existing work suggests that while it is not unusual for teacher salary schedules to be backloaded, nor is it uncommon for schedules to be frontloaded. Indeed, in some places, such as California, frontloading appears to be the norm. Labor Market Factors Related to Frontloading Compensation Competition for teachers in the labor market. Existing research offers two theoretical arguments for why frontloaded salaries - whether higher starting salaries or rapid early-career salary increases - are attractive to teachers and will thus allow districts to better compete for teachers in the labor market. Both theoretical arguments can also claim some empirical support, though the empirical literature is limited. Productivity returns to experience. As with many workers, the productivity returns to 8 experience for teachers appear to be largest during the early years of teachers' careers ( Clotfelter et al., 200 8; Rockoff, 2004). Even recent evidence showing that teachers continue to improve well into their careers finds that these gains nevertheless appear to be diminishing in experience (Ladd & Sorensen, 2016; Papay & Kraft, 2015; Wiswall, 2013). Workers who are more productive are not only more valuable to their employers, but more valuable to other potential employers; if a teacher's compensation does not keep pace with her productivity, she may leave for an employer ( e.g., another district) offering a higher wage. Districts should therefore offer a wage profile that is steeply increasing in early career experience so as not to lose its newer teachers as they become more effective, and can offer smaller (if any) raises for more experienced teachers (Ballou & Podgursky, 2002; Lankford & Wyckoff, 199 7). Sensitivity to compensation by experience. Another possibility is that workers later in their careers may be less sensitive to changes in wages than their less experienced counterparts. As Lankford and Wyckoff (1997) point out, prospective teachers are still in many cases uncommitted to any particular profession as they begin their careers, the productivity of later career teachers may tend to be more job-specific as their tenure increases, and many districts pay teachers on the basis of their in-district experience and so will not pay veterans for the entirety of their experience acquired elsewhere. An additional increase in salary for a relatively novice teacher should therefore have greater force as an incentive than an increase of the same magnitude for a veteran. Empirical evidence. Several studies find that districts appear to establish salary schedules that are sensitive to competition for teacher labor and teachers' potential labor market opportunities, though few consider frontloading explicitly or implicitly ( e.g., by distinguishing between salaries at higher and lower steps of the schedule). For example, Rose and Sengupta (2007), find in 9 California that districts in regions with higher non-teacher wages or lower rates of new teacher credentials issued per K-12 student offer higher salaries to teachers. While these higher salaries are found at all steps of the schedule, the results are suggestive of additional frontloading. Specifically, higher regional non-teacher wages are associated with particularly large differences in average annual raises across the first 10 steps of the schedule compared to the second 10 steps, and a lower supply of new teacher candidates is significantly related to salary levels at steps 1 and 10 of the schedule, but not step 20. 1 This is consistent with the theoretical rationales for frontloading discussed above, as a more competitive market for teacher labor will tend to make both novice teachers' skill acquisition and novices' relatively greater sensitivity to compensation more salient. However, because their data are cross-sectional, they cannot rule out unobserved district heterogeneity as a source of differences between salary schedules. In a similar vein, several studies assess the extent to which nearby districts affect one another 's salary schedules using spatial econometric methods (Greenbaum, 2002; Millimet & Rangaprasad, 2007; Wagner & Porter, 2000; Winters, 2011 ). These studies differ somewhat in how they operationalize proximity between districts, but consistently find spatial salary spillovers. That is, districts tend to offer higher salaries when nearby districts offer higher salaries, and this is true for average teacher salaries (Millimet & Rangaprasad, 2007) and salaries for both novices (Wagner & Porter, 2000; Winters, 2011) and more veteran teachers (Greenbaum, 2002; Winters, 2011). Only Winters (2011) considers salary spillovers for both more and less experienced teachers; he finds that these spillovers are roughly 27% larger in magnitude for starting salaries than for salaries for 1 I infer patterns of frontloading from si mple comparisons of coef fic ients across regr ession models predicting salary levels or annual rai ses at different step s of the salary schedule; Rose and Sengupta (2007) do not te st whether the se coeffic ients are significantly diff erent from one another. Additionally, they assume that teachers at higher st eps in the schedule have also accumulated additional education, and thus occupy higher -pa yi ng lanes. This confla tes to some extent salary returns to experience with salary returns to education . 10 20-year veterans. These results are again consistent with districts not only competing with one another for teachers on the basis of salary level but competing more aggressively for less- experienced teachers. However, these studies are again cross-sectional, making causal inference difficult. 2 It is perhaps significant that the only longitudinal study of the determinants of salary schedule structure of which I am aware arrives at a contrary conclusion. Ballou and Podgursky (2002) use data on more than 1,400 districts nationwide observed three times in the SASS between the 1987 - 198 8 and 199 3-1994 school years. They find no relationship between staffing difficulties in the base year - as measured by districts' teacher certification or vacancy rates - and starting salaries for new teachers in subsequent years. However, they do find that districts with more unfilled positions in 19 87- 198 8 made larger increases than other districts in salaries for teachers with 20 years of experience and a master's degree by 199 3-1994 (though not by 199 0-1991). This is suggestive of, if anything, greater backloading in districts with greater staffing difficulties, though they have no information about other step-and-lane cells in districts' salary schedules and find evidence that measurement error is a problem in the SASS data. One complication when interpreting evidence on districts' use of frontloaded salary schedules is that cost constraints may limit the ability of districts to adopt such schedules, even when they are effective for recruiting and retaining teachers. If wages increase monotonically in experience, then for any given maximum wage the more rapidly workers gain in salary the costlier their aggregate wages are to the employer (West & Mykerezi, 2011). These costs may be more difficult for school districts to manage than they are for private firms since teacher productivity gains do not directly increase districts' revenues or profits. Districts may therefore face more acute 2 Additionally, spatial relation ship s, even if causal, admit of explanations other than competition between di stricts, such as pattern bargaining (Goldhaber, Lavery, & Theobald, 2014; Greenbaum, 2002) . 11 trade-offs between larger raises for early career teachers and other priorities, such as maximum salary levels or employee benefits. For example, Vigdor (200 8) proposes a more heavily frontloaded, but cost-neutral and thus presumably more efficient, salary schedule for North Carolina districts that achieves budget neutrality by reducing not only raises for veteran teachers, but maximum salaries. 3 Similarly, Lankford and Wyckoff (1997) find descriptive evidence that backloading is more common in times of relative financial strain, consistent with frontloading being costly for districts. Even if districts use frontloaded compensation to attract and retain teachers, whether that effort is effective is a separate question. Few studies link features of salary schedules to district outcomes of any kind. Those that do suggest that salary schedule design may matter a great deal and may matter in particular for novice teachers. In early work on these issues, Murnane et al. (19 91) find that among teachers in Michigan and North Carolina the relationship between salary and retention was particularly positive for teachers with less experience, though they do not adjust teacher turnover rates for other factors. More recently, Hendricks (2014) uses teacher-level panel data from Texas and finds that higher levels of base pay are associated with lower rates of teacher turnover. Consistent with the theory that novice teachers will be particularly sensitive to salary and with Murnane et al. (1991), this relationship is largest in magnitude for the least experienced teachers, for whom a 1 % increase in salary is associated with a 0.25 percentage point drop in turnover, a relationship that decreases with experience. In subsequent work, Hendricks (2015) uses variation in the statewide minimum 3 As I discuss below, Lankford and Wyckoff (1997) point out that there might be little poli tical incentive for districts to reduce maximum salarie s. For example, admini strator salari es might be imp lici tly tied to maximum teacher salaries - say, because it is assumed that every principal should be paid more than every teacher - and the highe st salary offered might be more salient to local voters than th e distribution of salary incremen ts . Higher salaries for newer teachers may therefore be likely to come from else where in the budget, though they may also produce cost savings (e.g., on hiring costs if turnover of new teachers is reduced) . 12 salary schedule as a source of plausibly exogenous variation in district salary schedules. He finds that a one percent increase in salary offered to teachers with a given experience level increases the proportion of teachers hired with that experience level of 0.04 to 0. 08 percentage points. Again, the magnitude of this relationship is generally decreasing in experience, though he finds no relationship among teachers with zero to one year of prior experience; he interprets this as evidence that school administrators may prefer not to hire the most novice teachers. Similar to Vigdor (200 8), Hendricks argues that if novice teachers' hiring and turnover rates are particularly sensitive to salary, and given apparently diminishing skill returns to experience, many districts could staff their schools more effectively or efficiently by moving to salary schedules that are increasing and concave in experience (i.e., frontloaded). Only two studies test this hypothesis directly. Grissom and Strunk (2012), using SASS data on a national sample of districts and controlling for a range of district characteristics and state fixed effects, find that districts with more frontloaded salary schedules have higher student achievement as measured by proficiency rates on state tests. This is consistent with frontloaded salary schedules resulting in better staffing outcomes. However, such an interpretation finds only mixed support in later work in California, where Goldhaber et al. (2018) find that districts with more heavily frontloaded salary schedules posted fewer teacher position vacancies per student, suggestive of better teacher retention, but not fewer postings after the start of the school year, nor were their vacancies posted for shorter durations. Because their data are cross-sectional, authors of both studies are careful to point out that their ability to make causal claims is limited. Imperfect information about teachers. Given the theory and evidence discussed above in favor of frontloading, the considerable variation in teacher salary schedule frontloading presents a puzzle. Why, if backloading is less efficient or effective, do more districts not frontload salaries, 13 or frontload more heavily? In fact, it is not uncommon for workers generally to be compensated in a backloaded fashion (Hek & Vuuren, 2011; Prendergast, 1999). Why might this be the case? Over and above potential cost constraints discussed above, two theories justify backloaded compensation as a rational response by employers to imperfect information about workers. In both cases, difficulties in discerning worker quality give employers a reason to defer compensation even if frontloaded compensation would make the job more attractive to workers in general. I consider each of these two theories, and whether they are likely to be salient in the case of teachers, in turn. Wo rker self -sel ection. In many cases it is difficult to know ex ante which workers are most desirable. If workers have better information about their potential productivity or commitment to the job than is available to employers, then deferring compensation until later in workers' careers may tend to select for workers who have reason to believe that they will continue in the job until that compensation can be obtained (Salop & Salop, 1976). Alternatively, even if workers do not self -select into jobs with deferred compensation as a result of their knowledge of their own commitment or quality, such jobs may be attractive to those who are predisposed to save (rather than consume) their income. To the extent that they are also more effective ( e.g., because they are more conscientious), attracting workers with a higher propensity to save will tend to select for better employees (Ippolito, 2002). Whether this logic applies when hiring teachers is not obvious. On the one hand, teacher quality is difficult to predict using easily observed teacher characteristics ( e.g., credentials; Chingos & Peterson, 2011; Goldhaber, 2007), and school districts often lack the capacity to screen teachers intensively prior to hire (Liu & Johnson, 2006). This should make potential worker self selection attractive. On the other hand, given relatively high rates of turnover among novice teachers (Boe, 14 Cook, & Sunderland, 200 8; Keigher, 2010; Strunk & Robinson, 2006), even among those who have made investments in relatively costly traditional preparation programs (Redding & Smith, 2016), it is not clear that prospective teachers are substantially better informed about their likelihood of persistence than are their potential employers. Additionally, a growing body of research suggests that schools and districts can, in fact, discern useful information about teacher quality during the initial screening and hiring process (Bruno & Strunk, 2019; Goldhaber, Grout, & Huntington-Klein, 2017; Jacob, Rockoff, Taylor, Lindy, & Rosen, 2018), obviating some of the need to have workers self-select. Moreover, even if worker self - selection would be useful, it is not clear that a backloaded salary schedule would be an effective incentive in this regard. For example, Fitzpatrick (2015) finds that public school teachers in Illinois are willing to pay only 20 cents on average for an additional dollar in the present value of future retirement benefits, suggesting that the cost of deferred compensation substantially outstrips its motivational power. Moreover, as discussed above, backloaded salary schedules are not consistently associated with higher student achievement (Grissom & Strunk, 2012) or lower vacancy rates (Goldhaber et al., 2018), as would be expected if deferred compensation was selecting for more capable or committed teachers. Dif ficulties of monitor ing. Compensation deferred into the future can serve as an incentive to workers who risk losing deferred compensation if caught shirking (Lazear, 1981 ; Prendergast, 19 99). This may help to explain why frontloading is more prevalent in occupations, such as sales, where performance is relatively easy to observe, and unnoticed shirking therefore less of a concern (Kotlikoff & Gokhale, 19 92; Prendergast, 19 99). Again, however, it is not clear that these considerations are relevant in the case of teachers. As noted above, teachers appear to value the expected present value of pension benefits far below the cost of providing those benefits, suggesting that they are not highly motivated by this type of 15 deferred compensation (Fitzpatrick, 2015). Teachers also enj oy considerable job protections that make even observed shirking difficult to punish, rendering deferred compensation unnecessary as an incentive (Ballou & Podgursky, 2002). Even today, as many states have repealed tenure protections for teachers or attempted to increase the rigor of, and stakes associated with, teacher evaluation (Kraft, Brunner, Dougherty, & Schwegman, 2018), teachers do not appear to be substantially more likely to receive unsatisfactory evaluation ratings (Kraft & Gilmour, 2017). On the other hand, a substantial - and perhaps growing - share of teachers report concerns about their performance-related job security (Warner-Griffin, Cunningham, & Noel, 2018), and this perception of accountability may make deferred compensation a meaningful incentive even if the true risk of dismissal, accurately perceived, would not. Heutel (2009) looks specifically for evidence that districts defer compensation as a substitute for monitoring. However, in three waves of the SASS, the administrator-to-teacher ratio - a proxy for a district's ability to catch teacher shirking - is unrelated to the extent to which salary is deferred. This suggests that districts do not use deferred compensation to disincentivize shirking, perhaps because shirking is unlikely to result in termination even if caught. 4 Union Influence An alternative theory of deferred compensation, and perhaps the theory most frequently emphasized in the literature on teacher compensation, is that backloading of compensation is not in fact useful for schools but rather a mechanism by which teachers' unions are able to extract rents from districts for their more experienced members. On this account, when salary schedules are 4 The ratios of tenth- or twentieth -year salary to starting salary proxy for compensa tion deferral; the se measure s capture only the average slope of the wave profile over ten or twenty years, resp ecti vely. Note that the se resul ts do not imply that districts do not attempt to incentivize effort at all. For example, Heutel (2009) argues that the negative relationship he observes between the administrator-to-teacher ratio and the ratio of admini strator salaries -to-teacher salaries is consis tent with districts usi ng promotion as an incentive and making a tra de-off between the probability of promotion and the returns to promoti on. 16 collectively bargained by teachers' unions and district officials the outcome will tend to reflect the interests of veteran teachers (who are often more common or influential in unions) since administrators may be averse to conflict, be only weakly accountable to taxpayers, or have their own compensation linked to maximum teacher salaries (Hek & Vuuren, 2011; Lankford & Wyckoff, 1997; Monk & Jacobson, 1985) . Elected school board members may also be amenable to this kind of rent extraction because teachers' unions are typically among the most influential advocacy groups in local education-related elections (Moe, 2006). 5 Importantly, this is by no means the only theory about how unions may influence the shape of the salary schedule. Another possibility is that unions will advocate for more heavily frontloaded schedules because this will allow members to earn the highest possible salaries more quickly and for a longer period (Ballou & Podgursky, 2002). Such behavior might or might not constitute rent seeking; as discussed above, there are reasons to believe frontloaded compensation profiles might improve school district operations. Both theories find some support in the literature. In their study of New Yo rk, Monk and Jacobson (1 985) observe relatively more backloading in larger districts and suggest that this is consistent with lower rates of turnover in larger districts leading to the greater influence of veteran teachers in those districts' unions. Grissom and Strunk (2012), however, do not find a significant relationship between backloading and district enrollment in a cross-section of districts represented 5 It is common in the poli tical science and public economy literatures to use union rent see king as an explanation for generous pension or other retiree benefi ts - ty pes of deferred compensa tion - in the public sec tor. These ty pes of compensa tion are thought to be particularly amenable to union rent seeki ng because it is difficult for voters to assess their true costs, and thus to hold public officials accountable for them (Anzia & Moe, 2015; Bawn et al., 2012; Freeman , 1986; Glaeser & Ponzetto, 2014 ). This logic may be less sali ent in the case of salary sched ules because indi vidual teacher s' salaries are paid in the short term and the costs of those salar ies are explici t in the schedule it self . This contrasts with the case of retiree benefits, the costs of which are often dif fic ult to determine and paid at some distant point in the futu re. Inde ed, the high visi bili ty of the salary sched ule is someti mes cited as an impor tant determinant of bargaining dynamics (Gustman & Segal, 1977; Lankford & Wyckoff , 1997). 17 in the SASS. They test the union influence hypothesis more directly, comparing salary schedules in districts that collectively bargain contracts to those that do not. Again, consistent with the union influence hypothesis, they find significantly more backloading in jurisdictions with greater union involvement in contract negotiations. Winters (2011 ), also using SASS data but adj usting for salary spillovers between nearby districts, finds that collective bargaining activity is associated with higher teacher salaries, but more so for veterans (i.e., those with 20 years of experience and a master's degree) than for starting teachers with only a bachelor 's degree. Though this speaks only indirectly to the shape of teachers' salary trajectories, it is consistent with unions prioritizing salary increases for more experienced teachers over those of newer teachers. On the other hand, Gustman and Segal (1977) compare a cross-section of unionized and non-unionized districts and find that not only are maximum salaries higher in unionized districts' salary schedules, but that they are obtained after fewer steps. These steeper initial wage-experience profiles are consistent with unions advocating frontloaded compensation because this involves few trade-offs with later-career salary levels in practice. While the results from Gustman and Segal are now very dated, West and Mykerezi (2011) find more recently in two separate national samples of districts that collective bargaining is associated with teachers receiving larger annual raises early in their careers and reaching maximum salary levels more rapidly. This is again consistent with the frontloading theory of union behavior, though they find only mixed evidence of a relationship between collective bargaining and starting salaries. One way to reconcile these competing theories - and mixed results - is to suppose that teachers' union priorities are moderated by the seniority of the union's members. Even if veteran teachers' interests are disproportionately advocated for by the union, union leadership may nevertheless face considerable political pressure to advocate for the interests of less experienced 18 members. Median voter models of union behavior predict that union leaders facing these kinds of competing pressures will advocate for the interests of a representative member (Farber, 19 86). Thus, when less experienced teachers represent a larger share of union membership, union leaders will attend more heavily to the interests of relatively novice teachers during the bargaining process (Babcock & Engberg, 19 99). In other words, unions will tend to advocate for more frontloaded salary schedules when their membership is less experienced because higher salaries at lower steps of the salary schedule are more valuable to novices than to veterans. On the other hand, when union membership is more experienced on average the union will instead tend to advocate more aggressively for salary increases at higher steps of the schedule, which are occupied by veterans. This view finds only mixed support in the literature. Babcock and Engberg (1999) use teacher-level data to estimate salary schedule structure in Pennsylvania schools in the 1980s. They find that the difference in salaries between more and less experienced teachers is larger in districts where the median teacher is more experienced, but only among districts with high union support in the local community. This is consistent with unions adjusting their bargaining behavior based on the specific interests implied by the seniority composition of their membership. Moreover, the fact that this pattern obtains only in districts where unions are likely to be more influential suggests that it is driven by union behavior rather than by backloaded salary schedules attracting a more veteran workforce. However, while Ballou and Podgursky (2002) find that teacher seniority is associated with larger salary increases for veterans than for novices in their study looking at salary changes over time discussed above, they do not find consistently significant interactions between seniority and whether the district engages in collective bargaining over salaries. This raises questions about whether a causal mechanism - if any - between teacher seniority and salary schedule backloading operates through union activity. 19 The literature on unions' influence on salary schedule frontloading is thus mixed. This may be because existing work typically employs crude proxies for union influence and lacks the ability to account for major sources of endogeneity. Summary In sum, there are strong theoretical reasons to believe - and some empirical evidence to suggest - that frontloaded salary schedules will better attract and retain teachers. Nevertheless, there is considerable variation in the extent to which salary schedules are frontloaded, and it is not uncommon for states and districts to adopt salary schedules that are substantially backloaded. This variation may reflect alternative teacher selection and incentive strategies, budget pressures, or teachers' union advocacy. However, this literature suffers from three limitations. First, while I discuss many studies above, the number of empirical studies tackling any specific question about the prevalence, causes, or consequences of salary schedule frontloading is small. Second, these studies are often very dated. For example, of the studies discussed above, most consider salary schedules operative before the tum of the century and only three (Goldhaber et al., 2018; Hendricks, 2014, 2015) use schedules operative in the last decade. Third, most of the studies discussed above do not allow for credible causal inferences, for example because they use cross-sectional datasets and so cannot control for unobserved differences between districts as is possible, to varying degrees, with longitudinal data. Their results may therefore be biased by such unobserved factors, and this may help to explain why collectively their results are somewhat mixed. As a result of these limitations, the literature leaves unanswered several questions about teacher salary frontloading, which I roughly organize into three broad categories. First, there is much we do not know about the prevalence of teacher salary schedule frontloading. For example, 20 while the evidence discussed above suggests that there is considerable variation in the extent to which teacher salary schedules are frontloaded, it is not clear whether the prevalence of frontloading tends to change in systematic ways over time. Second, despite numerous well-developed theoretical arguments about why districts frontload or backload their teacher salary schedules to different degrees, none of these theories can claim clear support from the empirical literature. Studies to date thus leave important questions unanswered about why if frontloaded salary schedules are more efficient or effective, backloaded schedules remain common. Third, and relatedly, the evidence indicating benefits from frontloaded salary schedules is suggestive, but inconclusive. Theory may overstate the benefits of frontloading or there may be disadvantages to frontloading that extant work overlooks. These possibilities remain not only because of the limitations in the literature discussed above, but because no studies to date empirically examine potential trade-offs faced by districts that frontload salary schedules more aggressively, instead considering relationships between only one feature of salary schedules ( e.g., base pay levels or relative frontloading) and one district outcome (e.g., hiring or achievement) at a time. It is therefore not clear, for example, whether districts that offer larger wage returns to early career experience achieve them by reducing other expenditures ( e.g., on administration). Even if such trade-offs are worthwhile, their existence may help to explain the persistence of seemingly inferior salary schedule structures. Research Questions I consider three sets of research questions related to ( 1) the prevalence of salary schedule frontloading; (2) the causes of salary schedule frontloading; and (3) the consequences of salary schedule frontloading. These research questions and the methods I use to answer them are 21 summarized in Table 1, along with whether I find support for my hypotheses (when applicable). In all cases, I consider the sensitivity of answers to the way frontloading is operationalized because, as discussed below, in some cases different theories of frontloading imply that that different measures of frontloading are most relevant for teachers, unions, or administrators. RQ l: Th e Prevalence of Frontloading My first set of research questions are descriptive and are about the prevalence of frontloaded salary schedules in California districts. These questions correspond to the center portion of Figure 2 and the topmost row of Table 1. These questions are primarily descriptive in nature and will provide helpful context for interpreting results from my subsequent research questions. Specifically, I ask: 1.a: How frontloaded are teacher salary schedules in California? 1.b: How has the prevalence of frontloaded teacher salary schedules changed over time? 1.c: How much of the variation in salary schedule frontloadedness is within salary schedules (i.e. , between lanes), how much is between districts, and how much is within districts over time? RQ2 : Th e Causes of Frontloading My second set of research questions are about why districts frontload their salary schedules to different degrees. Specifically, I use a variety of approaches ( discussed below) to evaluate the extent to which various labor market and union-related factors ( discussed above and depicted in the leftmost portion of Figure 2) appear to influence salary schedule structure. These questions and their associated hypotheses, methods, and results are previewed in the center rows of Table 1. 2.a: Is the shape of the salary schedule the result of teachers ' union influence? If 22 backloaded salaries indicate rents being captured by unions, union strength should be associated with less frontloading. Moreover, if unions advocate in the interests of their members, the relationship between union strength and frontloading should be moderated by the experience level of teachers in the district. Specifically, union strength should be associated with more backloading when union members (i.e., teachers) are more experienced. Additionally, local teachers' unions served by the same supra-local union organizations should have similarly frontloaded salary schedules. 2.b: Is the shape of the salary schedule the result of district responses to labor market factors ? If districts substitute backloaded compensation for monitoring, frontloaded compensation should be more prevalent when district administrators can more easily monitor teacher performance. Alternatively, if frontloading is a means of attracting new teachers, then frontloading should be more prevalent when districts have a smaller pool of potential teachers from which to hire, or if neighboring districts frontload compensation more heavily. RQ3 : Th e Consequences of Frontloading My third and final set of research questions ask whether the frontloadedness of salary schedules matters for districts' operations and outcomes. These questions correspond to the relationships depicted in the rightmost portion of Figure 2, and their associated methods and results are previewed in the bottom rows of Table 1. 3.a: What is the relationship between salary schedule frontloading and the credentials and experience of districts ' newly hired teachers ? Because they are more attractive to newer teachers, more frontloaded salary schedules should be associated with better-credentialed, but perhaps also less-experienced, teachers being hired into districts, particularly in the hardest-to staff positions (i.e., math, science, and special education). However, these relationships should be 23 moderated by differences in the amount of salary schedule credit teachers can receive for working in other districts, as being able to enter the salary schedule at a higher step should tend to make the frontloadedness of the salary schedule less salient to more experienced teachers. 3.b: What is the relationship between salary schedule frontloading and student achievement? If they improve hiring outcomes, more frontloaded salary schedules should be associated with higher student achievement. This should be particularly true in lower-achieving districts, where staffing difficulties - and student need - are often most acute. 3.c: What is the relationship between salary schedule frontloading and districts ' spending on (1) all operations ; (2) teacher salaries ; (3) contributions to the state teacher pension system ; (4) certificated staff health and welfare benefits ; and (5) general administration? By increasing expected salary compensation for teachers, frontloaded salary schedules will be associated with relatively higher teacher salary and, consequently, pension spending by districts. However, this may be offset to some extent by savings on health benefits for teachers ( e.g., due to trade-offs between types of compensation or having a younger teaching force, which could also reduce salary spending) or general administration ( due to reductions in turnover costs). Data I use data on 943 unique school districts in California covering the school years 2003-2004 through 2016-2017. Salary Schedules Data on California district salary schedules come from annual "Salary and Benefits Schedule for the Certificated Bargaining Unit" surveys - commonly known as "J-90" surveys - submitted by districts to the California Department of Education (CDE). These surveys ask 24 districts about the composition of their teacher salary schedules, including the salary offered at each step of each lane, as well as the number of full-time equivalent staff placed in each step-and lane cell and the number of teaching and service days in the school year. This is considerably more detail about each salary schedule than is available in similar data sets ( e. g., the SASS), though the fact that the J-90 includes only one state introduces concerns about generalizability. I consider those concerns below. Though completion of these surveys is voluntary, the CDE actively encourages completion, particularly among larger districts. Typically, more than 80 % of districts in California representing more than 97% of the state's average daily attendance submit J-90s each year. 6 Operationalizing salary schedule frontloading. Like Grissom and Strunk (2012), I focus primarily on the structure of each salary schedule in each year, rather than characterizing changes to schedules over time as frontloaded or backloaded, as the former likely better reflects the considerations faced by teachers in the labor market. 7 However, how best to characterize any 6 I exclude 10 all- charter school districts from my analysis samples because, while they someti mes report staff compensa tion data via the J-90, their salary schedules tend to be developed through very different pr ocesses than those in a typical California school district ( e.g., because charter school districts do not collectively bargain the sched ules with a teache rs' union) . Because the se districts represent a small fraction of all districts and report on the J- 90 only inc onsi stently, including them makes little difference to my resul ts. While the J- 90 data cover the large majority of the state 's districts and an even larger maj ority ofits students, districts that do not submit responses to the J-90 are observably very different on average from districts that submit respon ses. The most striking differe nces are diff erenc es of enrollment and urbanicity. For example, in 20 1 6-20 17 30 % of districts responding to the J-90 were rural districts and the medi an enrollment of resp onding districts was approximately 2,500. Among non-responders, 70% were rural and the media n enrollment was 169. These diff erenc es point to likely limits to the generalizab ili ty of my results, since th e smalles t and most rural districts may be very distinctive collective bargaining and labor market contexts in which to es tablish salary sched ules. Diff erenc es in other observable charact erist ics are more modest; for example, students in non-resp onding districts were somewhat more likely to be white than those in resp onding districts (49% vs. 36%), and they had simi lar rates of free or reduc ed-p rice lunch eligibi lity . 7 As implied by my resea rch questions above, in my descriptive analyses I also consi der the extent to which salary sched ules have become more or less frontloaded over ti me, and thus provide some descriptive evidence of the extent to which districts have incre ased salaries relatively more at the lower or higher steps of their salary schedules 25 given salary schedule is not obvious and results may be sensitive to precisely how "frontloading" is defined. I thus consider three distinct measures of frontloading, each with a different rationale. 8 Rel ative experience premium. My first measure of frontloading is chosen with an eye toward comparability with prior work. Specifically, I use a measure that Grissom and Strunk (2012) call the relative experience premium (REP , ;t REP ) , where: ;t REP = salaryz 1 -sala ry 11 salary 11 -sala ry 1 --� 1 = 0 s - a -,- la - r - y 1 _ 1 _ - - sa --, l - ar _ y _ 1 = 10 �-- X 1 00 10 (1) Here salarys is salary received by teachers at step s of the salary schedule. 9 That is, a salary schedule's REP is the additional average annual experience raises teachers are given in their first decade (with O to 10 years of experience) compared to teachers in their second decade, expressed as a percentage of the average raises given in the first decade. If veterans receive larger raises at each step than novices (i.e., if the salary schedule is backloaded), the numerator, and thus the REP, will be negative, whereas a frontloaded schedule will be indicated by REP > 0. A salary schedule that is perfectly linear - offering identical raises at each step - will be neither frontloaded nor backloaded, with REP = 0. 8 Impor tantly, by focus ing on the shape of the salary schedule, all three of my frontloading measure s necessa rily exclude other components of teacher compensa tion, including non-wage benefi ts. This will tend to overstate the frontloaded ness of teache rs' overall compensa tion because many of these non-wage benefi ts have a heavily backloaded structu re. For example, teachers will generally not realize any pension or retiree health benefi ts until they have worked in a district for a decade or more. This likely has few imp lica tions for my results below because the se benefi ts tend to be simila rly backloaded across districts and over ti me. However, it is useful to remember that frontloading defined and measured in term s of the shape of the salary sched ule will tend to overstate the frontl oadedness of teacher compensa tion taken as a whole. 9 As is conventional in California, I refer to the first step on the salary schedule as "step one". In general, teachers on step s of the salary schedule will have s - 1 years of prior teaching experience, and I therefore refer to teachers on the first step of the salary sched ule as "first year teache rs". However, districts award diff erent amounts of prev ious experience credit to teachers when they enter the district ( e.g., placing a new hire no higher than step six on the sched ule), differ in the kind of prev ious experience they will award credit for at all ( e.g., mili tary experience or teaching in a private school), and may choose not to allow teachers to advance on the schedule under some circumsta nces (e.g., if they recei ve a poor evaluation ratin g). St eps on the salary schedule therefore do not map perfectly on to teacher experience levels. 26 Due to data limitations in the SASS, Grissom and Strunk (2012) can consider salaries at only three steps in the experience distribution (zero, 10, and 20 years). This is potentially limiting for two reasons. First, they are unable to observe the salary increments available to teachers in their very first years. This is potentially of practical importance because novice teachers may be much more sensitive to the slopes of their wage profiles in their earliest years in the classroom, and the slopes of those profiles might vary a great deal within a 10-year experience window. 10 Second, because they can use salary information only for teachers with up to 20 years of previous experience, they are unable to observe the extent to which salary increments continue to change for the most veteran teachers. These late-career salary profiles may be important in determining the overall structure of the salary schedule, for example because California's state teacher pension rules determine benefit levels in part based on teachers' highest salary levels. Most local education agencies in California have at least one salary schedule lane with more than 20 steps, and approximately 14% of teachers occupy those steps, suggesting that these higher steps are of some importance for both districts and their teachers. For my remaining two measures of frontloading, I use additional data available in the J-90 files to take into account the facts that salary schedules often include many more than 20 steps and that salary increments can vary from step to step. Five-year lo ading. As discussed above, teachers' salaries during their earliest years in the classroom may be especially important because teacher turnover and skill development are particularly high during their first five years of teaching, and novices may be more sensitive than veterans to changes in salary (e.g., Ingersoll, Merrill, & Stuckey, 2014; Lankford & Wyckoff, 1997; 1 ° For example, Vig dor's (2008) presen tation of North Carolina 's salary schedule sugge sts that it would be neither strongly frontloaded nor strongly backloaded as measured by its REP, yet teache rs' first two salary increments are approximately nil. 27 Rockoff, 2004). To focus more directly on earlier-career salary increments I construct a measure that focuses on the first five years of teachers' careers. To account for salary levels at higher levels of experience, I also include all salary schedule steps up to 30, since teachers in the state's teacher pension system become eligible for full benefits with 30 years of service credit, substantially changing their retirement incentives. 11 I define a five-year loading measure, A 5 , as ,1 5 = salary 6 -salary 1 X l OO salary 30 -salary 1 (2) Here salary 5 is defined as above and, .-1 5 represents the percentage share of all raises (up to step 30) received by teachers in their first five years. Treating step 30 as the final step in the schedule, reached after receiving 29 annual raises, by this measure a salary schedule would be considered frontloaded if .-1 5 > 17.2, that is, if more than five twenty-ninths (17.2%) of teachers' raises occur in the first five years of their (hypothetical) 30-year career. 12 11 Less than 15 % of districts have salary schedules that extend beyond 30 step s, and the se st eps include less than 1 % of full-time equivalent teachers statewi de. My fron tloa ding measure s can be defined for a lane only when that lane has a salary defined at specific step s: namely, the first step and, depending on the measure, the sixth, eleventh, twenty -fi rst, and thirtieth step s. However, districts do not always report on the J-90 a salary at every step for every lane. Based on compari sons with salary sched ules publis hed in actual district collective bargaining agreements, this is most commonly because districts in some cases choose not to report salaries for st eps at which teachers recei ve no rais es. In cases where there is a gap in a lane - or the lane terminates completely - at a given step on the J- 90, I assume that teachers continue to earn the salary available at that step until a later salary (if any) is reporte d. Additionally, approximately 4% of salary schedule lanes in th e J-90 are not available to first year teachers (i.e., they begin at a step higher than one) . For the se lanes where salaries at the lowest st ep(s) are not reported, I assume that teachers at those st eps would earn the salary available at the same step in the next lowe st lane on the sched ule. For example, some salary sched ules require all new teachers to begin in the lowe st lane, allowing them to advance to the lane appropriate for their education only in th eir second year. In that case, if districts do not report a step one salary at those higher lanes in the J-90, I define the step one salary in each of those lanes as the step one salary in the lowe st lane. This is likely to accurately characterize the salary teachers would earn if they have enough education - but insuf fic ient experience - to occupy the later-starting lane. In this way I ensure that every lane in every salary sched ule in the J-90 has a salary defined at every step . 12 While the decis ion to focus on th e first five step s of the salary schedule can be motivated by the theoretical consi derations discussed above, an alternative approach would use the actual distribution of rai ses across 28 Gini loading. While A. 5 captures more information than ;i_ REP about the nature of salary schedules as they are experienced by very early career teachers, it may be that both measures obscure the importance of absolute early-career salary levels by focusing on the distribution of raises after the initial salary level has been achieved. As discussed above, some researchers have argued that considerations about aggregate absolute salaries are why teachers' unions should be expected to advocate for frontloaded salary profiles ( e.g., Ballou & Podgursky, 2002). Below I consider starting and ending salary levels in addition to my other frontloading measures, but I also define a measure of frontloading that directly incorporates information about the initial salary level. Specifically, I adapt the Gini coefficient from the income inequality literature to define my third measure, Gini loading (A G ): (3) That is, ;i_ G is the percentage of total salary across all 30 steps of the salary schedule that is earned across the first 5 steps. 13 Since these first 5 steps correspond to one-sixth of a hypothetical 30-year steps in distric ts ' salary sched ules to infer which st eps are most important in prac tice . As shown in Appendix Fig ure Al, there do appear to be patterns in common to districts for when rai ses are awarded. For example, districts are much less likely to offer teachers rai ses after the 20 th step than they are at earlier step s. However, there is a great deal of variation between districts in the sizes of the rai ses offered at earlier st eps, and there are also noticeable differ ences between lanes. This makes it difficult to identi fy a specific step below which frontloading is most impor tant in prac tice . The distribution of rai ses depicted in Fig ure Al also previews results below indicating that salary schedules in California are heavily fron tloaded on avera ge. A measure defined in terms of California 's actual salary schedules may th erefore be difficult to generalize to other contex ts. I thus prefer th e measures of frontloading I discuss in this sec tion to a measure somehow defined in terms of the average shape of actual salary schedules in Califor nia. 13 The Gini coefficie nt of inequality is defined by comparing the Lorenz curve of the cumulative proportion of total income earned by th e bottom X% of the population to the 45-degree line of perfect equality that would obtain if every unit (e.g., person) in the population had identical income. The Gini coefficie nt is defined as the area between the line of perfect equality and th e Lorenz curve as a proportion of the total area under the line of perfect equality. If we imagine an analogous "Lorenz cur ve" for a salary schedule that is the cumulative percentage of lifetime salary earned across the bottom S step s of the salary schedule, A c corre sponds by analogy to the value of this "Lorenz curve" at S = 5. 29 career, by this measure a salary schedule can be thought of as frontloaded if;\, G > 16.67. However, note that unlike my other two measures of frontloading, which focus on the distribution of raises across steps, the Gini measure focuses on the distribution of salary across steps. In practice salaries never decrease at higher steps, so while salary schedules can be backloaded to different degrees by the Gini measure, in practice they are never frontloaded in absolute terms because salaries are never higher on average in the first 5 steps than they are in subsequent steps. 14 My frontloading measures are summarized in Table 2. Because districts can establish different numbers of lanes on their salary schedules for different levels of education, comparisons between salary schedules are more straightforward if I focus on a specific lane. I therefore focus my analyses on the lane for credentialed teachers with a bachelor 's degree and 60 additional semester units of education (BA+60), as districts were required to explicitly identify that lane on the J-90 in all years. 15 I also describe the extent of the variation between lanes on a given schedule I also construct an alternate version of it. G that is the total salary teachers would receive on over a 30- year career (i.e., across all 30 step s) expre ssed as a percentage of the total salary they would re cei ve if raises between the first and last step were distributed equally across step s. This alternate measure reflects the possi bili ty that what is of primary interest to teachers about their early-c areer wage pr ofiles is that more rapid early-career rai ses eventually translate into higher aggregate compensa tion over a care er. Unsurprisingly given its focus on aggregate salary levels, greater salary frontloading by this measure appears to be more costly for di stricts, but results are otherw ise simila r between th e two measure s. This is also true ifl apply various disco unt rates to salaries earn ed at st eps greater than one to reflect the fact that they are earn ed in the future from the point of view of a pro spec tive first year teacher. 14 For my primary analyses I calculate each measure usi ng raw salary levels, but results are very simi lar if I use natural logarithms of salary . This sugge sts that it makes little diff erence whether rai ses are more usefull y thought of in proportional, rath er than absolute dollar, term s, and that results are not driven by changes in measured frontloading reflecting only proportional across-the-board rai ses from year to year. 15 Manually identi fy ing other lanes (e.g., BA- only) is not eas y to do with the J-90 files because districts can es ta blish lanes for any combination of certification and education that they wish. This means that in addition to lane classifica tions bei ng very diverse between sched ules, it is often ambi guous which lane a teacher with a given level of education would occupy. For example, it is often unclear whether a maste r's degree would make a teacher eligible for a lane labeled as requiring a mi nimum number of additional semester units . 30 below. 16 Because my frontloading measures differ in their treatment of frontloading - and may even classify salary schedules as "frontloaded" or "backloaded" differently - in most of the analyses below I standardize the measures to make them more comparable. Co rrelations between me asures. Correlations between my measures of frontloading provide some reason to believe that the choice of measure matters. As shown in Table 3, among 2016-2017 salary schedules, correlations between different measures using the same lane information (i.e., BA+60) are as low as r =.3 4. The Gini measure is particularly weakly correlated with other measures, while the REP and the 5-year measure correlate highly (r = .80). This reflects The BA+60 lane is likely of growing importance for districts since the share of teachers with at least a maste r's degree incre ased from 32% to 42% between 2003 -2004 and 20 1 6-20 17, and from 15 % to 23 % for first-year teache rs. This further motivates my use of the BA+60 lane to characterize th e shape of salary sched ules. However, changes in the education level of teach ers over time also make it more dif fic ult to identi fy a si ngle lane that is appropriate for compari sons over ti me. 16 Focusi ng on a si ngle lane will give a misl eading impre ssi on of the salary pr ofiles faced by many teachers upon entering a district if there are substantial diff er ences between lanes. As a check for this, for all results below I construct "lane average" measures of frontloading in which I construct each of my three frontloading measure s for each lane of each salary schedule and then average each measure across all lanes within a sched ule. Results usi ng the se "lane average" measures are very si milar except where otherwise not ed. An additional conside ration is that teache rs' true salary pr ofiles may reflect movement not only within lanes (as teachers accumulate experienc e), but across lanes (as they accumulate educati on). Some prior work has attempted to address simila r iss ues by usi ng the observed distribution of teachers to estimate an "averag e" salary profile ( e.g., Lankford & Wyckoff , 1997). I attempt something si milar, creating a single salary profile for each schedule that is the FTE-weig hted average salary earned by teachers at each step in any lane. However, bei ng able to observ e the se FTE-weig hted avera ges in conse cutive years makes it clear that this kind of weighting works poorly in practice because loading measures constructed in this way vary substantially within districts from year to year due to small changes in the di stribution of teachers, even in larger districts and when the underlying salary sched ule doesn't change. Inde ed, even in large districts this kind of FTE weighting someti mes produc es measures that are nonsensical, such as negative salary returns to experience for teachers early in their care ers . These FTE-we ighted measure s also conflate returns to experience with returns to education and with diff erenc es between the attri tion, retention, and recruitment of staff with different education levels, making their interpretation somewhat more compli cate d. For example, if teachers with higher education levels are more likel y to stay in thei r jobs, the FTE-weig hted average salary at each step will increasingly reflect higher lanes on the salary schedule at higher st eps even if teachers never move between lanes. I therefore do not use FTE-we ighted salary pr ofiles in my analyses. 31 the fact that the Gini measure is sensitive salary levels at specific steps, including the first and thirtieth steps. In contrast, the REP and, especially, the 5-year measure average raises across many steps and are unaffected by the shape of the salary schedule above steps 21 and 6, respectively. Thus, for example, a salary schedule that was modified to increase salaries between steps 6 and 11 while decreasing salaries between steps 12 and 21 would become more frontloaded by the REP the 5-year measure. However, whether it became more frontloaded by the Gini measure is ambiguous, and would depend on exactly how much salaries were increased or decreased at each step, as these details have implications for the aggregate present value of salaries a teacher would expect over 30 years. 17 Staff Data The CDE releases staff data files each year that link teachers and administrators to schools. While they do not allow individual employees to be followed over time, these files contain information on each teacher's years of experience and credential ( e. g., their subject authorizations and whether they are fully credentialed, working on an intern permit or credential waiver, etc.). In addition to their total years of teaching experience, these staff files also indicate the number of 17 Applying a disc ount rate to salaries at higher st eps when calculating the Gini measure results in weaker correlations with the other measures, with higher disc ount rates resulting in weaker corre latio ns. However, correlations between the Gini measures with and without disc ount rates are extremely high (r > .98 for plausible disc ount rate s). The choice of whether to consider the BA+60 lane in iso lation or to average lanes together appears to be somewhat less conseq uential than the choice of which measure - th e REP, 5- year, or Gini - to use. Correlations between each measure in the BA+60 lane and its analogous measure averaged across lanes are at least r = .53, and as high as r = .72 for th e REP. Still, diff ere nces between what is observed in the BA+60 lane and what is observed in other lanes on the same schedule appear non-tri vial, and this previews resul ts below indicating that there is substantial variation in th e frontl oadedness of lanes even within the same salary sched ule. This is particularly true for th e 5- year measure, which may reflect the fact that this measure is very sensi tive to the step at which each lane plateau s in salary. For example, lanes with simila r rai ses on early st eps may have very different frontloading as measured by the 5- year measure if the maximum salary is reached at step 20 as opposed to step 25 or step 30. This is much less true for the REP, which does not incorpor ate information about step s above 21. 32 years that a teacher has worked in their current district, allowing new hires to be characterized based on their total experience and certification. Student Achievement Data The CDE releases average student scores at the district level from annual statewide standardized tests in math and English/language arts, which I standardize across all districts in the state in a given year. Prior to 2013-2014 this is done simply, as the Standardized Testing and Reporting (STAR) system in place during that time used the same score scale in each grade level, such that student scores in any grade level can simply be averaged up to the district level. However, in 2013-2014 the state transitioned to a new set of tests - the California Assessment of Student Performance and Progress (CAASPP) - that is vertically scaled, meaning that younger students tend to have lower scores than older students. 18 As a result, districts' average scores are not directly comparable if they have different grade level enrollments, and indeed the state no longer reports school- or district-level average scores. I address this by first standardizing average CAASPP scores at the district level for each grade level such that, for example, a district with a standardized sixth grade ELA score of one can be understood as having an average sixth grade ELA scale score that is one district-level standard deviation above a district at the mean. Each district's overall score is the enrollment-weighted average of its standardized grade level scores. For both CAASPP and STAR, district average scores are standardized to have a mean of zero and a standard deviation of one across all districts in the state in each year. Financial Data 18 Because it was considered a pi lot year for the new exams, scores were not re leased in the 2013- 2014 school year. 33 Data on district expenditures come from annual financial reports submitted by districts to the CDE using a standardized account code structure, or SACS. The SACS requires that districts identify expenditures on specific goods and services - known in the SACS as "objects" - including certificated teacher salaries, specific types of benefit for certificated and non-certificated staff, and general activities - sometimes called "functions" - such as general administration. This detail allows for analyses of how district per-pupil spending is associated with salary schedule structure. The specific SACS codes used to capture my expenditure variables of interest - spending on all operations, teacher salaries, teacher pensions, health and welfare benefits for certificated staff, and general administration - are described in Table 4. 19 I adj ust both the J-90 and SACS data for inflation using the Consumer Price Index as well as local differences in the costs of labor using the Comparable Wage Index (Taylor & Fowler, 2006). 20 Even on a per-pupil basis these spending figures are sometimes substantially skewed. I therefore subject them to an inverse hyperbolic sine (IHS) transformation. This serves a similar purpose as a natural log transformation but allows me to retain a small number of observations that report no spending on some categories of expenditure (Burbidge, Magee, & Robb, 198 8). 19 I generally exclude charter schools affiliated with districts from my various data sour ces, and thus from my analyses, because they are unlikely to be directly bound by the district 's salary sched ule. However, an impor tant limitation of the SACS data is that a small minority of charter schools report their financial data through the general fund of their affil iated district, and thus cannot be di sting uished from other schools in the district. This means that a small percentage (roughly 1 % ) of schools used to construct my distric t- level data are in fact charter schools. In other work I find that the presence of these charter schools appears to matter little in analyses of district financ es (Bruno, 2019), and the fact that they report financial data in this way likely indicates that they have relatively tight operational lin ks with their districts compared to other charter schools. Their presence should thus make little difference to my resul ts. 20 Di strict- level CWI data are available consi stently only through the 20 12-20 13 school year. I use figure s from that year in all later years . The CWI is defined at the labor market-year level and, as discussed below, in many analyses I also estimate models with labor market-by-year fixed eff ects . 34 Collective Bargaining Agreement Data As a proxy for union strength I use a measure of the extent to which collective bargaining agreements (CBAs) restrict school district administrators. This measure comes from a close content analysis of actual CBAs collected from approximately 50 0 of the largest districts in California every three years from 2005-2006 through 2014-2015. 2 1 To produce the measure contracts were dichotomously for the presence or absence of 253 items that appear to impose constraints on district administrators ( e.g., the imposition of a maximum class size of 25) on the assumption that the presence of more such items reflects a latent property of "restrictiveness. " After coding, these 253 items were reduced via alpha item analysis to 34 items, presented in Table 5, which were then entered into a partial independence item response model to estimate latent contract restrictiveness, similar to the manner in which standardized test responses are sometimes used to estimate students' latent subject knowledge. For additional details about how this measure of CBA restrictiveness is constructed, see Marianno and Strunk (2018) and Strunk and Reardon (2010). This restrictiveness measure has been shown to correlate with school board members' perceptions of union power and with union involvement in school board elections (Strunk & Grissom, 2010), suggesting that it is a reasonable proxy for union strength. Importantly, of the 34 CBA provisions incorporated into this measure of contract restrictiveness, only one is directly related to compensation: an indicator of whether teachers receive a salary increase for possessing a doctorate. There should therefore be little mechanical relationship between the restrictiveness measure and the features of the salary schedule. The CBA data from which overall contract restrictiveness measures are generated are of one additional use. One of my research questions considers the possibility that backloaded 2 1 CBAs in California are required to be renegotiated at least once every three years. 35 compensation serves as a substitute for employee monitoring. As a proxy for monitoring intensity in a district, I use a measure of the extent to which the CBA restricts administrators specifically in the evaluation of teachers. This measure is like the overall CBA restrictiveness measure described above, with two major differences. First, while the overall restrictiveness measure uses provisions from many different areas of the CBA, the evaluation restrictiveness measure uses only provisions that place limits on the ability of districts to evaluate teachers ( e.g., specifying the length of classroom observations or the minimum advanced notice for teachers prior to those observations). Second, while the overall restrictiveness measure includes only those items with a sufficiently high scale reliability, due to a smaller number of available items the evaluation restrictiveness measure includes all 21 evaluation-related CBA provisions collected in all years. These items are presented in Table 6. Other Data The CDE releases enrollment and student demographic data at the district level, such as student race, free- or reduced-price lunch (FRL) eligibility, and English learner status. I additionally use data from the National Center for Education Statistics to obtain the share of students in each district who are eligible for special education services and to associate districts with labor markets (Taylor & Fowler, 2006). I take shapefiles describing district boundaries from the National Historical Geographic Information System (Manson, Schroeder, Van Riper, & Ruggles, 2018). Summary statistics are presented in Table 7. Methods RQ l: Th e Prevalence of Frontloading I use basic descriptive techniques to answer my first set of research questions, providing both visual and summary statistical evidence about the frontloadedness of teacher salary schedules 36 in California over time. I estimate simple ANOVAs to assess the extent to which variance in frontloading is between districts, between lanes within a salary schedule, or within districts over time. RQ2 : Th e Causes of Frontloading As discussed above, and as illustrated in Figure 2, I test three theories about the causes of teacher salary schedule frontloading: teachers' union influence, imperfect information about teacher quality, and competition for teachers. Testing these different theories requires a range of methods and proxy measures, which are summarized in Table 1. I discuss my approaches to testing each theory in more detail here. 2.a: Is the shape of the salary schedule the result of teachers ' union influence? First, to explore the relationship between salary schedule structure and union strength, I predict each of my frontloading measures (A *) in turn for district din year t: 22 Act t = 0 1 [restrict iveness dt x media n_exp dt -i] + 0 2 rest rictiv eness dt (4) Here restrictiveness is the standardized contract restrictiveness measure described above which I interact with the median within-district experience level of district teachers (median_exp). If, as theorized (Grissom & Strunk, 2012; Lankford & Wyckoff, 199 7), unions exert substantial influence over salary schedule structure and bargain in the interests of their members, then CBA restrictiveness (my proxy for union strength) should be associated with relatively greater frontloading when district teachers are less experienced. I use teacher experience in the prior year since it is more likely that the salary schedule was negotiated prior to its effective date. 22 Though not explic itly disc ussed her e in the interest of brevity, in addition to predicting �_* I also predict the salary off ered at the first and thirtieth st eps in the salary schedule to determine whether districts are "frontloading" schedules by incre asing the absolute level of starting salar ies relative to maximum salar ies. 37 Grissom and Strunk (2012) find that districts that frontload their salary schedules differ somewhat along observable characteristics from districts that backload. I therefore include in D the shares of students who are black, who are Hispanic, or who are eligible for free or reduced price lunch. 23 Additionally, Winters (2011) identifies several district characteristics that are likely to be determinative of salaries and which I therefore also include in D: the natural log of enrollment, an indicator of whether a district has declining enrollment, and the number of teaching days in the year. As with teacher experience, all variables in D are measured in t-1 except for number of teaching days, which is likely to be determined concurrently with salaries. 24 i5 and y are district and year fixed effects, respectively, and e is an error term. I cluster standard errors at the district level. 25 2.b: Is the shape of the salary schedule a result of district responses to labor market factors ? Imperfect information about teacher quality. As discussed above, one theoretical rationale for backloaded compensation holds that when monitoring worker performance is difficult, deferred compensation can deter shirking by making it more likely shirking will be caught and punished 23 Gri ss om and Strunk (20 12) also find modest diff er ences in per-pupil spending between districts that frontload and districts that backload. However, they argue that frontloaded salary schedules should result in cost savings for districts, which might in turn be a cause of reduc ed per-pupil spending . Moreover, there is evidence that unions increase spending in districts (Cowen & Strunk, 20 1 5), and this may be due to their impacts on salary sched ules. I thus do not include per-pup il spending as a right-hand side variable in model 4 as it may capture the eff ects of my predictors of interest on my outcomes of intere st. 24 Alternatively, rather than controlling for teaching days I control for the number of ser vice days for returning teacher s, also available in the J-90, but this makes little difference to results . The fact that the length of the school year is often determ ined simultaneously with salaries may suggest some concerns about including it as a pred ictor of salar ies. In practice within-district variation in the length of the school year in California during this time is driven almost entirely by the relaxation of statutory restrictions on the minimum length of the school year during the Great Recession. Controlling for the number of teaching d ay s thus accounts for districts reducing salaries in proportion to the number of furlough days for teache rs. 25 Standard errors change only sli ghtly if clustered instead on ser vice center or ser vice center-by-year. 38 before compensation is earned. This implies that backloaded compensation serves as a substitute for monitoring. I test this by estimating: (5) Model 5 is like model 4 but replaces the CBA restrictiveness and teacher experience predictors with monitoring, a proxy for employee monitoring intensity. I consider two proxies for monitoring intensity. First, like Heutel (2009), I use the ratio of administrators to teachers. Second, I use a measure of the restrictiveness of the evaluation provisions of the district's CBA, described in the Data section above. Both higher administrator-to-teacher ratios and CBAs that impose fewer restrictions on districts' abilities to evaluate teachers will tend to make employee supervision easier and will be associated with relatively more salary schedule frontloading if backloading is a substitute for employee monitoring. 26 Co mpetition fo r teachers. Also as 1s discussed above, districts might frontload compensation for teachers at least in part to compete for teachers, because the ability to attain higher salaries relatively quickly will tend to be attractive to potential hires. If so, districts hiring for more difficult-to-staff positions should have more frontloaded salary schedules ceteris paribus, because this will tend to make it easier to hire for open positions that might otherwise go unfilled. Moreover, even if, as discussed above, backloading compensation is a useful way to select for applicant teachers who are more likely to persist in the job (and thus receive deferred compensation), this will be a less salient consideration when the supply of teachers from which to select is small to begin with. 26 It might be that admini strato rs' abili t ies to monitor teachers is not all that matt ers, and that it is also releva nt whether there are conseq uences for teachers if they are caught shir king . I cannot directly measure the stakes for teachers of monitoring, but below I consider the pos sibili ty that the relevance of monitoring intensity is higher in districts where admini strators are plausibl y more willing and able to terminate teache rs. 39 To test this possibility, I take advantage of the fact that most school districts in California are either elementary or high school districts serving primarily grades K-8 or 9-12, respectively, and typically one or more elementary districts lie, geographically, within a high school district, forming what I refer to as a "stack" of districts. As in many contexts (Cowan, Goldhaber, Hayes, & Theobald, 2016), in California the effective supply of secondary teachers - that is, the number of certified secondary teachers available to hire compared to the number of vacant teaching positions - is much smaller than the effective supply of elementary teachers (Carver-Thomas & Darling-Hammond, 2017; Darling-Hammond, Furger, Shields, & Sutcher, 2016; Goldhaber et al., 2018). Thus, elementary and high school districts in the same stack (i.e., occupying the same geographic area) will tend to face very different labor supplies despite operating in the same boundaries and serving similar households. If districts' salary schedules are sensitive to the supply of teachers in their labor market, and if districts frontload their salary schedules to better recruit and retain teachers, high school districts should adopt salary schedules that offer both higher overall salary levels and more frontloaded salaries. Because elementary and high school districts within each stack are geographically coterminous, differences between their salary schedules plausibly reflect responses to their respective labor markets rather than other unobserved differences between districts. 27 More formally, I estimate these differences using model 6, using only elementary and high school districts in these stacks: 27 While districts may offer off -sc hedule bonuses to teachers of specific subject are as, they typically do not diff erentiate the salary schedule its elf by subject area, perhaps due to poli tical dif fic ulties assoc iated with diff erentiating compensa tion between different kinds of teacher. Additionally, districts are prohibited by law from differentiating salary solely based on grade levels taught (Cal Ed. Code §45028). Thus, stacked elementary and high school districts can diff erentiate th eir salary schedules from one another even though diff erentiating the salary schedule between teachers within districts ( e.g., in a unified school district) is very rare . 40 (6) In model 6, ,1, *represents frontloading in district din elementary-high school district stack s in year t. HS is a dummy variable indicating high school districts, so !Jo estimates differences between high school and elementary (i.e., K- 8) districts. 0 is a set of stack-by-year fixed effects to control for unobserved heterogeneity between elementary-high school stacks or within stacks over time. As discussed above, districts within a stack should have very similar considerations when developing their salary schedules except for differences in the supply of teachers, but I additionally control for a set of time-varying district characteristics (D, defined as in model 4) that may be related to salary schedule structure. I cluster standard errors at the district level. 28 Elementary districts within a stack vary in size, and thus in the extent to which they are representative of the area and students served by their associated high school district. I therefore weight each elementary district based on the share of its stack's collective elementary district enrollment it represents. 29 28 Standard errors on my coeffic ients of interest incre ase by 18-3 7% if clustered on sta cks, though only one of those coef fic ients loses its (already marginal) sta tistical significance. 29 By definition, a stack inclu des one high school district and at least one elementary district, but the mean and median stack obser ved in my estimation sample includes five districts (i.e., 4 elemen tary distric ts), and one stack include s as many as 23 districts (i.e., 22 elemen tary districts ). An impor tant limitation of this approach is that it does not directly compare di stricts on the basis of other charact eristics often assoc iated with teacher supply constrain ts . For example, admini strators and policymakers are often concerned with the recruitment and retention of teachers in very rural districts or in districts with high levels of student dis advanta ge. Comparing districts on the basis of grade level ser ved will shed little direct light on the needs and behaviors of those distric ts. However, comparing the salary schedules of districts with different student characteri stic s, or districts of different urbanici tie s, poses its own challenges because those districts may differ in other ways that make it difficult to attr ibute differ ences in thei r salary schedules to thei r available supp lies of teache rs . For example, districts with many dis advantaged students may have unusually high student ser vice costs ( e.g., for counselors) or have many diff er ences in their local economic conditions compared to more affluent districts in other regio ns. These costs and contextual factors might aff ect their salary schedule designs in ways unrelated to competition for teachers . While my approach focuses only on one type of teacher supply constraint, comparing geographically coterm inous districts mitigates many of the se concerns about estimates being biased by unobse rved differe nces between distric ts. 41 Approaches assessing both union influence and competition for teachers. The methods above test one theory of the causes of frontloading at a time. I now turn to two approaches that each shed some light on both union influence and competition for teachers: spatial autoregressive models and regression discontinuity analyses. Spatial mo dels of union infl uence and competition fo r teachers. While several studies, discussed above, consider spatial correlations in district salaries, they are largely limited to cross sectional analyses and do not consider frontloading specifically. Moreover, similarities between policies (e.g., CBAs) in nearby districts might not be due to competition for teachers between districts because districts that are geographically proximal are likely to be compositionally similar, to learn from one another, and so on (Goldhaber et al., 2014). I therefore consider an approach to look for spatial relationships between districts that attempts to disentangle two causes of salary schedule spillovers. Like Goldhaber et al. (2014 ), though extended to the panel data context, I estimate the following spatial lag model: Model 7 includes two separate spatial lag terms to distinguish the unique contributions of The value of making within-stack compari sons between districts is highlighted by within-stack relat ionships in CBAs generally . For example, in 20 14-20 15 I observe overall CBA restricti veness for 175 districts where I also observe CBA restricti veness for at least one other district in the same sta ck. The stack in which the district is located explains 48% of overall variation in CBA restrictiv eness, with very si milar results in other years. Relati onship s are not only between elementary districts in the same stack. In si mple regr essions of elementary distric ts ' CBA restricti veness on the restricti veness of their respec tive high school district 's CBA, a standard deviation incre ase in the restricti veness of the high school district 's CBA is assoc iated with an incre ase in restrictive ness in elemen tary di stric ts' CBAs of0.33-0.47 standard deviations depending on the year. Those rela tionshi ps remain substantial (0. 15-0.3 8) even after controlling for the other district- level factors contained in D in model 6. This sugge sts that compari sons of salary schedules between districts in different regions will be confounded by unobserved diff erenc es between distric ts . For example, below I consider ways in which distric ts ' salary schedules might be aff ected by diff ere nces in reg ional admini strative arms of the state -l evel teach ers ' union . 42 two distinct types of spillover that I, like previous researchers, argue plausibly reflect either union influence or competition for teachers in the labor market. Each Wis an element from a weighting matrix W where element WdJ represents the proximity (however defined) between districts d and · 30 J . Like Goldhaber et al. (2014), I look for institutional spillovers between districts served by the same union service center of the California Teachers Association (CTA). These service centers serve as a kind of intermediary between the CTA and local district affiliates, providing support with, among other things, bargaining activities. Bargaining objectives, tactics, and so on may therefore disseminate more easily between districts within a service center than across service centers. 31 I operationalize this with weighting matrix w e , where WJJ = 1 if districts d andj are in the same CTA service center, and WJJ = 0 otherwise. 32 Thus, w e assumes that districts will influence one another as factors (e.g., knowledge of what can be bargained for effectively) diff use through social networks operating within these service centers, regardless of physical distance between districts. w e is row normalized such that the weights of all other districts for district d sum to one. 33 I also look for spillovers related to physical proximity, over and above spillovers associated 30 By convention Wdd = 0 since a district cannot typically have a spi llover effect on itself . 31 A map of CTA ser vice center boundari es is pre sented in Fig ure 3. 32 Roughly 2.5% of California districts are represented by the California Federation of Teachers rather than the CT A, and I treat the se as bei ng in their own ser vice cent er. 33 In addition to facili tating model estimation in some cases (Kele jian & Prucha, 20 1 0), row nor malization has two substantive advantag es. Fi rst, it equalizes the effect of ser vice centers on each district (i.e., districts are not assumed to be more heavily influe nced by ser vice center effects when their service center has more member districts ). Second, it has the intuitive and interpretable conseq uence that L J ;cd WJJ A] t for each district is si mply th e average ,f of other districts in the same ser vice center in each year. 43 with service center membership. How to operationalize physical proximity is not obvious. In my primary specification, Wdi st is a row-normalized first-order contiguity matrix. That is, each element wf j5t is equal to one if districts d and j are contiguous and is otherwise equal to zero, and then divided by the sum of its respective row. Given evidence that both teachers and administrators value proximity in the teacher labor market (Boyd, Lankford, Loeb, & Wyckoff, 2005; Killeen, Loeb, & Williams, 2015), this a plausible model of the underlying competitive spatial dynamics. 34 Wdi st thus assumes districts have more influence over one another when they are physically proximal, as would be the case if ( for example) they are competing with one another for teachers. In this case neighboring districts' salary schedules (,f) are lagged by one year since in general a district's salary schedule in year t could have been negotiated no later than year t-1. 35 Wdis t is also 34 Moreover, while more complex matri ces might also be plausible, simulation stud ies suggest that first order contiguity mat rices outperform other weight mat rices ( e.g., in terms of mean squared error) in spatial lag models usi ng geographic units with irregular boundaries and row-nor malized weight mat ri ces (Stakhovych & Bi jmolt, 2009). Of cours e, it is preferable to use a weigh t matrix that matches with real world proce sses bei ng modeled. In an alternative specification simila r to prev ious work (Goldhaber et al., 2014; Winters, 2011 ) I speci fy W; st as an inverse distance matrix, where wf j5tis the inverse of the distance between the centroids of districts d and) for districts within 50 miles of one another, or else zero. However, Stakhovych and Bijmol t (2009) find that when the true pr ocess by which the data were generated reflects inverse distance or N-nea re st neig hbor weig hts, first-order contiguity matrices outperform the other "i ncorrect" weight matrix. They argue this is consis tent with other work finding that mat ri ces with greater connectivity between units can be underpowered and can re sult in es timates that are biased downward (Anseli n & Rey, 1991; Beer & Riedl, 2012; Farber, Paez, & Volz, 2009; Smith , 2009) . The first-order contiguity matrix is thus my preferred speci fica tion . When usi ng the inverse distance weighted matrix, rather than row normalization I divide each element of the matrix by the maximum absolute value of the eigenval ues of the matrix. This alternative has simila r benefi ts in term s ensuring the es tima bili ty of th e model but is motivated by the fact that row normalization divide s each row of the matrix by a different number, and thus makes weights incomparable across rows. While common in the literature, row normalization is th us arguably inappropriate when usi ng inverse distance weights because after row normalization larger weights do not necessa rily indicate greater proximity except within-row (Elhorst, 2014; Kele jian & Prucha, 2010 ). 35 Some districts es tablish CBAs with their teache rs' unions that contain pro visions that explic itly require the salary schedule be es ta blis hed usi ng neig hbor distric ts ' salary schedules as a reference poi nt . Geographic spil lovers might be expected to be larger in such districts, but this is difficult to determine because I observe CBAs for only a portion of the districts I use in my spatial models and only a few of those have such pro visi ons. 44 row normalized. Other components of model 7 are as defined in model 4. 36 Regression dis continuity estimates of the eff ect of regulatory fle xib ility under the Local Co ntrol Funding Fo rm ula. I also conduct a more indirect test of the labor market and union influence hypotheses by considering a case in which districts were given additional regulatory 36 Spatial lag models of this form place the dependent variable on the right-hand side of the model, and thus potentially introduce simultaneity bias in estimates of p1 and p 2. This will tend to bias estimates toward finding spatial interdependence because coef fic ients on the spatial lag will capture both the effect of don} and th e effect of} on d. This can be dealt with by estimating model 7 via (quasi) maximum likelihood (ML; Franzese & Hays, 2007; Lee & Yu, 2010 ). ML estimation will not solve omitted variable bias, which is someti mes dealt with in spatial lag models usi ng two-stage least squares (2SLS) estimati on. Most commonly this is done by usi ng spatial lags of the other independent variab les (D in model 7) as instruments for th e spatial lags of the dependent varia ble. However, 2SLS does not appear to outperform ML in spatial panel data models (Fran zese & Hays, 2007). Gibbons and Overman (20 12) argue that the 2SLS approach is unlikely to produce superior es timates of spatial lag effects for two reasons . Fi rst, it is by no means obvious that commonly used instruments (viz., spatial lags of other independent varia bles) are valid. Inde ed, it is not uncommon in the spatial econometrics literature to es tima te so- called spatial Durbin models in which spatial lags of other independent varia bles are added to the spatial lag model prec isel y because they are thought to have spi llover effects over and above those of the dependent variable (Elhorst, 2014 ). In the pre sent case, a spatial Durbin model might be justified if, for example, districts respo nd to the fact that neighboring distric ts ' values of D make its own schools relatively more or less att ractive to teach ers, conditional on the district 's own values of D and the spillo ver effects of the neig hbors' salary sched ules. In a specification check I estimate such a spatial Durbin model to attempt to dis ting uish the spatially lagged eff ects of neig hbor distric ts ' salary schedules from the spatially lagged effects of neig hbors' districts other characteri stic s. Higher-order spatial lags of other independent varia bles ( e.g., for the neighbo rs' neighbors) might still be pos sible instruments in a spatial Durbin model, but this exacerbates a second challenge for the 2SLS appro ach. Namely, spatial lags of other independent variab les will in many cases be weak instruments, leading to impr ecise and biased es timates in the seco nd sta ge. This is of particular concern in the pre sent context where, as discussed below, within-district variation in salary schedules is already modest. Inde ed, modest within-district salary schedule variation pre sents a challenge even for ML estimation because it means that most districts are unlikely to experience large changes in the spatial lags used in model 7. Small changes to distric ts ' salary sched ules may induce too little spil lover in neighboring districts to reliably detect (if they induce any spil lover at all). I consider addressi ng this limitation by usi ng a sudden and substantial recent increase in salar ies in the Los Angeles Unified School Di strict (LA USD; Blume, 2015 ) as a plausible natural experiment and look for sp illover effects in nearby distric ts . However, I find no evidence of such spillovers, perhaps because even after the salary incr ease LAUSD's salaries remain among the lowest in the region. In princ iple, it is also possi ble to estimate models that look for spatial correlation in the error term . However, it can be dif fic ult to simulta neousl y identi fy parameters for the spatial lag of the dependent variable and the spatial correlations in error term (Elhorst, 2014; Gibbons & Overman, 2012). 45 flexibility in the design of their salary schedules. A common challenge for identifying the effects of regulatory flexibility on district spending patterns is that in most cases regulations either apply uniformly to districts or apply differentially, but in ways likely to be correlated with unobserved differences between districts. However, under state regulations, districts in California are subject to discontinuously different spending requirements depending on their students' demographic characteristics. Under the Local Control Funding Formula (LCFF) adopted by California as of the 2013- 2014 school year, the state provides additional funding to districts per unit of average daily attendance for "unduplicated pupils" (UPs), defined as students who are any combination of eligible for free- or reduced-price lunch, English learners, or in the foster system. This additional funding can be substantial, including "supplemental" grants worth 20% of the typical per-pupil grant per unduplicated pupil, and "concentration" grants worth an additional 50 % - i.e. , an additional 70% total - for each UP in excess of 55% of enrollment. These additional funds are intended to support the educations of the UPs in the district, and districts are therefore required to justify to their county office of education how that money will be spent. Districts can spend these additional grants on a districtwide basis - rather than targeting spending on UPs in particular - but regulations impose different justificatory burdens on districts that wish to do so. Specifically, districts with less than 55% UPs must "[ d]escribe how these [ districtwide] services are the most effective use of the fu nds to meet the district's goals for its unduplicated pupils." This requirement does not apply to districts with 55% (or more) unduplicated pupils, who must only explain to their county offices that their spending is "effective in ... meeting the district's goals for its unduplicated pupils." 37 37 California Code of Regulati ons, Title 5, §1 5496. 46 These regulations have not prevented districtwide spending of targeted LCFF dollars from becoming a source of controversy. Particularly controversial has been the question of whether across-the-board salary increases for staff could ever be justified under the aforementioned regulations, a teachers' union objective (Clough, 2015). Consequently, in June of 2015 the State Board of Education addressed this matter directly, confirming that such general salary increases would be permissible, provided that the justificatory requirements described above were met (Torlakson, 2015). Given the controversy surrounding the spending of targeted LCFF dollars on general salaries, the effects of these regulations are interesting in their own right. And because districts with shares of UPs just above or below 55% are likely to be very similar to one another, the imposition of different regulatory standards for districts on different sides of the 55% threshold present the opportunity for a regression discontinuity (RD) analysis. To the extent that teachers' unions and district administrators prefer to allocate grants for UPs toward the salary schedule, they may be better able to do so when their district enjoys the additional regulatory flexibility granted to districts where UPs are at least 55% of enrollment. Parametrically, the effects of this LCFF regulatory shift on salary schedules are estimated as: (8) where ,1 * represents the salary parameters of interest in district d. D is a dummy indicator equal to one if a district has at least 55% UPs, andf() is a polynomial fu nction of threshold-centered UP percentage (UP P) interacted with D. In this case I use data from 2016-2017, at which point virtually all districts would have had the opportunity to renegotiate CB As ( and thus salary schedules) after the adoption of the LCFF . 38 38 I also provide local linear and local quadratic es tim ates as a specification check, as the se can often outperform higher-order global polynomial contro ls (Gelman & Imbens, 2019). However, whether the additional regulatory burden for districts with less than 55% UPs is bi nding for districts in practice is not 47 If districts above the 55% UP threshold have salary schedules that are more frontloaded or more backloaded than districts below the threshold, this could be suggestive evidence that such schedules are preferred by the stakeholders who lobbied most prominently for the salary spending flexibility eventually granted by the CDE: teachers' unions. However, differences between salary schedules could also reflect the priorities of the district administrators with whom the teachers' unions are bargaining. Unambiguously distinguishing the influence of teachers' unions from that of administrators is not possible with my data but applying this RD approach not only to my frontloading measures but to starting and ending salary levels is helpful in this regard. For example, if unions tend to prefer higher absolute salary levels ceteris paribus and if districts with at least 55% UPs backload their salary schedules more heavily but do not increase step 1 or step 30 salaries, this would be suggestive (though only suggestive) of administrator influence rather than union influence. RQ3 : Th e Consequences of Frontloading 3.a: District hiring outcomes. As I discuss above, frontloaded salary schedules are thought to be justified at least in part because they are attractive to new teachers. This introduces a challenge when attempting to estimate the effects of frontloading on districts' staffing success because salary schedule structure may be caused by the same competitive pressures that affect observable hiring outcomes. Indeed, to preview the results for other research questions, I find some evidence that districts adapt their salary schedules to competition for teachers in the labor market. This could be a problem even analyzing longitudinal data using district fixed effects (FEs). To assess the impacts of salary schedule structure on districts' hiring outcomes I therefore prefer a obvious, and so effects around the thre shold may be small if they exist at all. Nonparametric es timates are thus likel y to be underpowere d. 48 lagged dependent variable model, which may better control for time-varying labor market factors facing individual districts. Specifically, I estimate: (9) Here Y is the percentage of newly hired teachers who lack a full credential in district d in labor market l in year t, which I consider separately for teachers authorized to teach hard-to-staff subjects (viz., math, science, or special education) and other teachers. ;\, *is a frontloading measure, and like Grissom and Strunk (2012) I control for the salary offered at step one of the salary schedule (starting sal) to distinguish effects of frontloading from effects of overall salary levels. The control variables included in D are defined as above with two exceptions. First, because district outcomes are likely to be influenced by aspects of specific student need, I additionally include in D the shares of students who are eligible for special education services or who are designated as English learners. Such students are likely to require additional costly services or specially certified teachers, and to have academic challenges reflected in district test scores. Second, I measure all variables in D in time t, rather than using some measures in t-1 as is done in some cases above, because district outcomes of interest may be more directly determined by contemporaneous (e.g., student) factors represented by the right-hand side variables. Rather than rely on district FEs, I use two alternative strategies to control for time-varying labor market factors that might affect districts' hiring outcomes. First, I included the lagged DV (Y d1t-1) on the right hand side of the model to capture recent hiring conditions faced by the district. Second, I include labor market-by-year fixed effects ( T zc ) to account for regional year-to-year variation in labor 49 market factors ( e.g., changes m the regional teacher supply or wages m non-teaching occupations) . 39 3.b and 3.c: Student achievement and district spending patterns. The simultaneity concerns that motivate the lagged DV approach of model 9 are likely to be less serious when considering the relationship between salary schedule structure and student achievement or district spending patterns. This is because the connection between the frontloadedness of the salary schedule and these other outcomes is less direct than the connection between salary schedule frontloadedness and teacher hiring, making it more difficult to deliberately adapt to specific student outcome needs or aspects of the budget. Rather, these district outcomes are generally well explained by fixed district characteristics or by my time-varying controls. To predict these outcomes, I therefore prefer a district FE specification: (10) In this case Y is an outcome of interest related to achievement (i.e., average achievement or student proficiency rates in math and ELA) or district spending (i.e., per-pupil spending on all operations, teacher salaries, teacher pensions, certificated staff health benefits, or general administration). In models 9 and 10, I cluster standard errors at the district level. 40 39 Labor market-by-year fixed effects are more conser vative than year fixed eff ects, particularly in a state as large as California where year-to-year changes in economic or other factors may differ substantially across regio ns. However, the se more conser vative fixed eff ects can also substantially reduce the variation available for coef fic ient identification and can eli minate it altogether in some labor marke ts. This is not a major concern for the analyses assoc iated with my third resea rch question, which rely on data available for nearly all districts in the state, but can be more of a problem in some of the analyses above relying on smaller numbers of unique districts ( e.g., districts for which I have CBA data) . Those analyses instead focus on specifications usi ng year fixed eff ects, though I also use labor market-by-year fixed effects as robustne ss checks in some cases. 40 While I prefer and focus on different models when predicting different district outcomes, this can make results dif fic ult to compare across models. Below I briefly highlight simi larities and diff ere nces between lagged DV and district FE models, though they produce qualitatively different results only when considering distric ts' staffing out comes. 50 Results RQ l: Th e Prevalence of Frontloading 1.a: How frontloaded are teacher salary schedules in California? Consistent with the previous work discussed above, I find that teacher salary schedules in California are heavily frontloaded. One way to see this is simply to consider the average salary earned by teachers in the state at each step. As shown in Figure 4, in 2016-2017 average teacher salaries increase relatively steeply across the earlier steps, from $5 1,957 to $83,25 5 between the first and twelfth steps. Salaries increase much more slowly afterward, up to an average of $94,208 for teachers at step 30. This salary profile is substantially frontloaded, at least in terms of the distribution of raises. Roughly one-third of the total increase in salary occurs between the first and sixth steps, the first 10 raises are more than twice as large on average as the second 10 raises. 41 Unsurprisingly given that the overall salary profile is rapidly increasing in earlier steps reflects the fact that most districts' salary schedules are themselves heavily frontloaded in how they distribute raises. Figure 5 shows the distribution of frontloading in 2016-2017 salary schedules by the REP (in blue), the 5-year measure (in red), and the Gini measure (in orange). Neither of the lagged DV nor the district FE approaches guarantee unbiased estimates of the effects of frontloading if there are factors correlated with both salary sched ule structure and district operational outcomes that vary within districts over ti me. Nevert heless, both longitudinal approaches allow me to addre ss some typ es of bias, and so offer some improvement over the pr evio us, primarily cross- sectional work discussed above. In robust ness checks, I further exploi t the longitudinal nature of my data to control for district specific- time tre nds. If relevant omitted variab les vary within districts over time parametrically, this will address assoc iated bias, estimating my coeffic ients of interest usi ng only deviations from each district 's time trend. This has the advantage of substantially relaxing assumptions of paral lel trends in districts in the absence of changes to my predictors of interest, but at the potential cost of pr ecision. 41 The fact that aggregate salary across all 30 st eps substantially exceeds what it would be if raises were identical across steps might be interpreted as sugge stive evidence that early-career rai ses are costly for districts because they are not substantially offset by deferral of later-career raises. However, as discussed below (RQ3), this is not necessa rily the case; conditional on starting salaries, more frontloaded salary schedules are assoc iated with lower maximum salaries and thus no net incr ease in teacher salary spendi ng. 51 Each measure has a corresponding vertical line indicating the value at which a salary schedule is neither frontloaded nor backloaded. 42 For both the REP and the 5-year measure, in Figure 5 the centers of mass of the density distributions lie far to the right of their corresponding vertical lines. This indicates that districts' salary schedules are heavily frontloaded on average, and few districts have salary schedules that are backloaded at all. The BA+60 lanes on California salary schedules had a mean frontloading of 56% as measured by the REP in 2016-2017 (the blue line in the top panel of Figure 5). That is, for the mean district the first 10 raises in this lane were larger than the second 10 raises by 56% of the first 10 raises. The fact that the vast majority of the area under the blue curve is to the right of the blue vertical line indicates that few districts use backloaded salary schedules by this measure. In fact, 95% of districts frontload to some degree as measured by the REP. The patterns are similar for the 5-year measure. Districts on average offered 33% of all raises between the first and sixth steps (the 5-year measure), well above the 17.2% that would indicate a schedule that is neither frontloaded nor backloaded (the vertical red line). Backloading is even less common by the 5-year measure than by the REP; by the 5-year measure 98% of salary schedules were frontloaded to some degree. In this lane teachers earn 12.7% of all of the salary aggregated across all 30 steps within the first 5 years (the Gini measure). This reflects backloading in the sense that higher salaries are earned subsequent to the 5 th step, but is nevertheless not drastically different than what teachers would earn in the (somewhat radically-frontloaded) case where salaries were identical at every step (16.7%). 43 Without similar salary data for other 42 Recall that so long as salary incr eases monotonically in experienc e, any salary pro file will be backloaded by my Gini measure , which is focused on when salary (rather than raises) is ear ned. 43 While all three measure s are expre ssed in percentage term s, recall that only the Gini measure will only exceed 0% if rai ses are larger on average in the first 5 st eps than in subsequent step s, and would only reach 10 0% in the unrealistic case in which teachers were paid only in the first 5 step s. 52 occupations or states, I cannot say whether teacher salary schedules in California are more frontloaded than salary schedules elsewhere when measured by the Gini measure, though this seems likely given the results for the REP and the 5-year measures. For simplicity below I describe salary schedules in California as heavily frontloaded on average. To make the measures more comparable to one another, I center each such that zero represents a schedule that is neither frontloaded nor backloaded and standardize them to have a unit standard deviation across all districts and years. This allows the frontloadness of salary schedules by each measure to be interpreted in terms of the variation between salary schedules by that measure. For example, as mentioned above the mean district in 2016-2017 has a REP of 56 %. The REPs of the BA +60 lanes in my sample have a standard deviation of approximately 28 (Table 7). Thus, the mean REP of 56% corresponds to the mean district being frontloaded by 2.0 standard deviations. Plotting the densities of these standardized measures (Figure 6) illustrates that, while the Gini measure necessarily reflects some degree of backloading of salaries, the REP and the 5- year measures provide similar pictures of the degree of frontloading of raises. Salary schedules are heavily frontloaded by both measures. This is particularly true for the REP, by which the mean district's salary schedule is 2.0 standard deviations more frontloaded than would be a "straight line" salary schedule (the blue line in Figure 6). Measured in terms of the variation between salary schedules, mean frontloading is somewhat less extreme by the 5- year measure (1. 7 standard deviations, the red line in Figure 6). Figure 4 and Appendix Figure Al provide some insight into why the 5-year measure Results for all measure s are si milar if districts are weighted based on the number ofFTE staff on their salary schedules (Appendix Fig ure A2). 53 indicates slightly less frontloading than the REP: while raises often continue accumulating rapidly for California teachers across the first decade, they begin to taper off noticeably after the 11 th step. That is, while many districts defer substantial raises until after the sixth step, few districts defer substantial raises until teachers' second decade. Since the 5-year measure is more sensitive than the REP to how the first 10 raises are distributed for teachers, California districts appear to be slightly less frontloaded by this measure. However, by either measure, the difference between the mean salary schedule and a salary schedule that is neither frontloaded nor backloaded is much greater than the average difference between salary schedules and the mean itself. 1.b: How has the prevalence of frontloaded teacher salary schedules changed since the 2003-2004 school year ? As shown in Figure 4, the shape of the average teacher salary profile in California has been roughly consistent since at least 2003-2004. Even in 2012-2013, when teacher salaries were at their nadir after the Great Recession, the average salary profile retained its heavily concave shape. However, while salaries for teachers on the first 11 steps of the salary schedule had recovered to their 2003-2004 levels by 2016-2017, salaries for teachers at later steps increased further still, exceeding their previous levels. This can be seen more clearly in Figure 7, which illustrates the percentage change in inflation-adjusted salaries earned by teachers at different steps over time compared to the pre recession peak in 2006-2007. After the recession, salaries fell for teachers across the step distribution, but fell somewhat more slowly for teachers at the twentieth step. By 2012-2013, the average salary earned by teachers at the first, tenth, and thirtieth steps had fallen by 8.3%, 8.2%, and 8.6%, respectively, from 2006-2007 levels. Salaries at the twentieth step had declined by only 7. 1 %. Districts' revenues and expenditures began to increase in the 2013-2014 school year (Bruno, 2018), and salaries began to rise accordingly. Salaries at the twentieth step grew most rapidly, 54 eventually (by 2016-2017) exceeding pre-rece ss10n levels by 0.8%. Salaries at other steps remained below pre-recession levels, by as much as 2.4% at step 10. These relatively more rapid increases ( or slower decreases) in salary at higher steps are similar to what has been observed elsewhere in earlier decades (Lankford & Wyckoff, 1997; Monk & Jacobson, 1985), and are suggestive of slightly less frontloading over time, particularly by the REP. Indeed, this is what is observed in Figure 8. By all three measures, salary schedules in California were on average less frontloaded in 2016-2017 than in 2006-2007 by at least 8% of a standard deviation. However, these changes are small in practical terms. For example, that 8% of a standard deviation mean change by the 5-year measure represents districts allocating only 0.8 percentage points less of all raises between the first and sixth steps of their schedules (32. 9% vs. 33.7%, the red line in Figure 8). These small average changes obscure many larger changes within individual districts' salary schedules. Figure 9 shows the distribution of within-district changes in frontloading between 2003-2004 and 2016-2017 for districts observed in both years. By far the most common pattern, even over this span of 14 years, is for districts to leave the structure of their salary schedule largely unchanged, providing similar raises (if any) across all steps of existing lanes. However, some districts make their salary schedules substantially more or less frontloaded during this time. For example, among the districts observed in both 2003-2004 and 2016-2017, the median district allocates essentially the same share of all raises in the first five years of its schedule in both years, but 10% of districts have increased that share by at least 3. 0 percentage points (33% of a standard deviation) while another 10% decreased that share by at least 5. 8 percentage points (62% of a standard deviation). By focusing only on differences between salary schedules in 2003-2004 and those in 2016- 55 2017, those figures slightly understate the total within-district variation in frontloading during this time. Table 8 shows the distribution of absolute changes in frontloading for 916 districts observed at least twice during this period (i.e., the differences between districts' most- and least-frontloaded salary schedules). Even using this more comprehensive measure of changes, it is very common for districts to leave their schedule structures essentially unchanged. For example, half of these districts change the share of all raises granted in the first five years to teachers in the BA +60 lane by less than 2.3 percentage points, and roughly one quarter change that share essentially not at all. However, another quarter change that share by at least 6.5 percentage points (70% of a standard deviation). Thus, while modest, this within-district variation is non-trivial. This will also be the variation I rely on in many cases below to evaluate my second and third research questions, about the causes and consequences of frontloading. 44 1.c: How much of the variation in salary schedule frontloadedness is within salary schedules (i.e. , between lanes), how much is between districts, and how much is within districts over time? Unsurprisingly, given the evidence above that most districts in California make few changes to their salary schedule structures over time, simple ANOVAs indicate that little of the variation in frontloading is within districts in my sample: just 11 % for the REP and 5-year measures and 8% for the Gini measure. Thus, while, as discussed above, many districts make changes to their salary schedule structures over this period, these changes are dwarfed by between district differences in salary schedules. Also notable is that there is considerable variation in frontloading between lanes within 44 Di stricts that make larger changes to the frontload ness of their salary schedules do not appear to be observably different from those that do not. Within-district changes in frontloading are at most very weakly related to grade levels served, enrollment, student income or race, or the number of lanes on the salary sched ule. However, I cannot entirely rule out the possi bili ty that districts making diff erent changes to their salary schedules diff er in unobserved ways, or that those unobserved diff erenc es limit the generaliza bili ty of my resul ts below. 56 salary schedules. For example, among all lanes on all observed salary schedules in 2016-2017, only 33% to 35% of the variation in frontloading is between districts, depending on the measure. The remaining variation - as much as 67% by the 5-year measure - is between lanes within salary schedules. This may suggest that focusing on a single lane could be misleading. However, as noted above, frontloading measures based on the BA+60 lane correlate moderately-to-highly with measures based on an average of lanes in each schedule and results below are not very different if lane average measures are used. RQ2 : Th e Causes of Frontloading 2.a: Is the shape of the salary schedule the result of teachers ' union influence? As I show in Table 9, CBA restrictiveness- my proxy for union strength - is not significantly related to salary schedule structure. More restrictive CBAs are not associated with higher salaries at either the lowest (columns 1) or highest (column 3) steps of the salary schedule for teachers; coefficients on the CBA restrictiveness term are both statistically insignificant and small in magnitude. 45 Moreover, these relationships are not moderated by the experience level of district teachers (columns 2 and 4). 46 This is perhaps surprising given the evidence discussed above indicating that union activity is generally associated with higher compensation for teachers. However, much of that previous evidence comes from cross-sectional studies (e.g., Winters, 2011), and their results may therefore be biased by unobserved differences between districts. 47 45 Results are nearly identical if the median teacher experience term is excluded altogether (not shown). 46 To facil itate interpretation of coef fic ients in models with interaction term s, CBA restricti veness is mean centered and media n teacher experience is set to equal zero when the median teacher in the district has no prior experience in the district. 47 Results are qualitatively simila r if I use the natural log of salaries at each step , or if I control for labor market-by-year fixed effects and district- specific linear or quadratic time tre nds. A potential concern is that within-district variation in CBA restricti veness is too small to estimate relation ships in a fixed effect framework. However, as with other simi lar work (e.g., Marianno & Strunk, 2018 ; Strunk & Marianno, 57 Previous work also generally uses categorial differences in umon participation m bargaining, for example comparing districts that do and do not have collective bargaining. In a relatively union-friendly state like California, where collective bargaining between districts and their teachers is the norm, unions may exercise influence to achieve priorities other than higher salary levels. Indeed, this is consistent with closely related work by Marianno, Bruno, and Strunk (2018). While they do not consider salary levels directly, they find that more restrictive CB As are associated with higher per-pupil spending on teacher salaries. However, this relationship is modest in magnitude and explicable in terms of lower student:teacher ratios as opposed to higher per teacher salaries. Teachers' unions in California may prefer smaller class sizes over higher salary levels at the margin, for example because California public schools have relatively high student to-teacher ratios (approximately 23 vs. 16 nationwide; U.S. Department of Education, 2018). 48 Similarly, more restrictive CBAs are not associated with more heavily frontloaded salary schedules, and this does not vary significantly when district teachers are more veteran on average ( columns 5 to 10). The 5-year and Gini measures are perhaps those where the moderating effects of teacher experience would be expected to be greatest, as these measures focus most directly on earliest-career salaries. However, results are similarly null for both measures. Thus, neither theory of union behavior discussed above finds clear support here; stronger unions do not appear to bargain for more frontloaded compensation to maximize overall compensation, nor do the bargaining outcomes shown in this paper indicate that they prefer to backload salaries to benefit 20 1 9), there are substantial changes to CBAs over time in the se distr icts . For the medi an district in my sample I observe an absolute change in restrictiv eness of 74% of a standard deviation across the four bargaining cycles. 48 It may be that much of what unions negotiate during bargaining consis ts of trade -off s between typ es of compensa tion, substituting wages for other benefi ts ( e.g., health insurance) or vice versa. I therefore attempt a specification that controls for per-pu pil spending on non-pension benefi ts for certificated employees, but this does not meaningfully impact my coef fic ients of intere st. 58 their veteran members. However, distinctive features of the California context again mean that these results should be interpreted and generalized only with caution. Given that salary schedules in California are already heavily frontloaded on average, additional frontloading may not be a bargaining priority at the margin in California even if teachers' unions prefer frontloaded compensation. If teachers' unions do in fact prefer frontloaded salary schedules, and if my null results are a consequence of teachers' unions in California having already largely obtained the frontloaded salary schedules that they prefer, this implies that there would nevertheless be a positive relationship between CBA restrictiveness and salary schedule frontloadedness in contexts were schedules are less frontloaded. Because I observe few districts with very backloaded salary schedules - or even schedules that are minimally frontloaded - I cannot directly test whether the relationship between CBA restrictiveness and frontloadedness is different in such districts. As a more limited test of this possibility, for each outcome in Table 9 I divide the observations in the sample into two groups that are above or below the median of the outcome being predicted. While districts in each group may not have values of the respective outcomes that are "high" or "low" in an absolute sense, they have values of those outcomes that are high or low relative to what is typical in the state. These kinds of relative classifications may have salience for districts themselves, which often use relative comparisons to other districts to assess administrative priorities. For example, informal correspondence with CDE officials indicate that a primary purpose of the J-90 surveys is to facilitate salary schedule comparisons between districts during the bargaining process. Some CBAs explicitly require these kinds of comparisons or even require that stakeholders attempt to set salary levels that reach a certain percentile of a CBA-defined 59 comparison group. 49 Unions in districts below the median by an outcome measure may therefore be more likely than unions in districts above the median to prioritize that outcome during the bargaining process, even if their district's outcome is not low in absolute terms or relative to districts nationwide. In Table 10 I present results from models estimated separately for districts above or below the median of each outcome being bargained over. These results are qualitatively consistent with teachers' unions bargaining more aggressively for compensation provisions when existing provisions are relatively "weak." For example, among districts with step one salaries below the median, a standard deviation increase in CBA restrictiveness is associated with step one salaries that are higher by $228 ( column 1 ). At the same time, among districts with above-average step one salaries, that relationship is similar in magnitude but negative (- $295 , column 2). This pattern of more positive coefficients on CBA restrictiveness for below-average districts is consistent across salary level outcomes but is not clearly apparent across frontloading measures. However, even districts "below average" in an outcome by California standards may be quite high in that outcome by national standards. For example, even among the sample of districts with below average frontloading by the 5-year measure, salary schedules are heavily frontloaded: on average they offer 27% of all raises in the first five years. 50 49 For example, the CBA for the Petaluma City School Di stricts says: "A study and calculation of parity will be taken ... each year, with five surrounding districts .. .I f the parity study shows that the Petaluma salary is not at or above the 50 th percenti le of the existing comparison group salary sched ules at column I step 1, maximum at 10 years and maximum, an adju stment will be made to rai se the Petaluma salary to the 50t h percentile retroactive to July 1st of that school year." (Petaluma City Elementary School Di strict, Petaluma Joint Union High School Di strict, & The Petaluma Federation of Teachers, 2012 , p. 3) 50 I also attempt quantile regre ssions (not shown) that produce qualitatively simila r res ults at different deciles of the outcome distribution, but these estimates are severely underpowered. 60 2.b: Is the shape of the salary schedule the result of district responses to labor market factors ? Is backlo aded compensation a substitute fo r monitor ing ? In Table 11 I present results predicting salary schedule structure using the number of administrators per 100 teachers, or the restrictiveness of the evaluation provisions of the local CBA (standardized within year). Like Heutel (2009), I find no support for the theory that district administrators use backloading of salaries to deter shirking when employee monitoring is more difficult. Starting salaries in districts are no higher when there are more administrators on staff per teacher, nor is the salary-experience profile consistently more frontloaded across measures (panel A). It may be that the regressions in Panel A of Table 11 suffer from endogeneity problems because districts are simultaneously determining salary schedules and administration staffing while operating within a budget constraint . For example, if growing budgets allow for both higher starting salaries and higher administrative staffing levels this will tend to create a spurious positive relationship between monitoring intensity and frontloading measured in this way. Conversely, if the costs of higher starting or early-career salaries preclude the hiring of additional administrators for a given number of teachers, this will negatively bias the relationship between the administrator to-teacher ratio and frontloading. 51 51 Contro lling for the inverse hyper bolic si ne of per-pup il spending does not substantially alter the coef ficie nts in Table 11 , sugge sting th e aforementioned potential posi tive bias due to overall spending levels is not a major concern . One way to bound the possi ble magnitude of the negative bias is to relate the costs of frontloading to the costs of admini strat ors . During this time the mean princ ipal salary districts report is approximately $120,000. This include s only school princ ipal s, and the marginal admini strator ( e.g., a new assi stant principal) likel y has a much lower salary, perhaps $80,000. I assume adding in the costs of benefi ts (i.e., pension contributions and health and welfare benefits) brings the total cost of an additional admini strator to approximately $1 00,000. This is approximately the cost of an additional $1 ,000 in salary for teache rs. Ceteris paribus, then, an additional admini strator for 10 0 teachers (the ratio used in Panel A of Table 11 ) could reduce teache rs' starting salari es by $1,000 if the costs of admini strators came entirely out of the budget for teache rs' salarie s. The near-zero estimates in Panel A, if negatively biased in this way, therefore cannot definitively rule out a true posi tive relationship between the admini strato r-to-teacher ratio and starting salarie s. However, as shown below, incr eases in my frontloading measures are not assoc iated 61 The existence of these kinds of trade-off s ( and the uncertainty about how districts will navigate them) points to another advantage of using the evaluation restrictiveness measure from the CBA as an alternative proxy for monitoring intensity. Namely, the evaluation provisions in the CBA do not have the same obvious direct budgetary impacts, and thus likely do not entail as many of the same trade-offs. 52 However, CB As that impose more restrictions on administrators during the teacher evaluation process are not associated with lower starting salaries or more backloaded salary-experience profiles (panel B). 53 Grade level diff erences in monitoring. One explanation for these null results is that, as Ballou and Podgursky (2002) argue, the intensity with which teachers are monitored makes little difference to their incentives because they are unlikely to face serious consequences even if their shirking is caught. This implies that when teachers are less secure in their employment, they should be more sensitive to the incentives created by compensation and monitoring. To test for this possibility, I exploit the fact that teachers of younger students may tend to face greater accountability pressure than teachers of older students. Previous research provides with higher spending in di stricts, and my proxy for monitoring intensity deri ved from the CBA also has no relationship with frontloading (however defin ed) . Thus, bias is unlikely to be a major factor for most of the es timates in Panel A. 52 Some of the CBA pro visions incorporated into the evaluation restricti veness measure do require larger investments of admini strator time in at least some cases, and the se pro visions may have some budgetary impact . For example, this could be true of pro visions requiring a minimum number of classroom observations before teachers can receive unsatis factory evaluation ratings or requirements that teachers and their evaluators have a pr e-obs ervation meeting . In fact, prev ious work has found that more restrictive CBAs are assoc iated with districts spending a slightly larger proportion of their expenditures on admini strat ors' salar ies (St runk, 2011 ). However, the evaluation restricti veness measure used here has only a weak-to -moder ate relationship with overall CBA restricti veness (r = .30 ) and the budgetary imp lica tions of the pro visions used to construct it are much less direct than simpl y hiring additional admini strators for a given number of teache rs. 53 Results are simi lar ifl use the natural logarithms of salaries, or ifl control of labor market-by-year fixed effects and district- specific quadratic time tre nds. If stronger unions can secure both higher salar ies and more restrictive evaluation policies, this will tend to posi tively bias my es timates of the trade -off between monitoring intensity and salary, but results are also very simi lar ifl control for overall CBA restrictive ness. 62 three reasons to believe that this is the case. First, administrators' evaluation and staffing practices are likely to be affected by supply constraints (Delli & Vera, 2003; Johnson & Semmelroth, 2014; Rutledge, Harris, Thompson, & Ingle, 200 8). As discussed above, the supply of secondary teachers is typically much tighter than the supply of elementary teachers. This should tend to make administrators more willing to terminate elementary teachers ( or otherwise encourage them to leave), because existing elementary teachers are easier to replace than their secondary counterparts. Though I am not aware of studies documenting the extent to which administrators alter their employee monitoring behavior in response to the teacher supply, there is evidence that administrators perceive a need to make additional compromises during the hiring process for harder-to-staff positions (e.g., Donaldson, 2013). This is consistent with concerns about supply constraints informing administrators' personnel management decisions. Second, evaluation and staffing practices are likely to be affected by accountability pressures on administrators (Delli & Vera, 2003; Lavigne, 2020). One of the main measures by which schools - and thus school administrators - are judged is student performance on standardized tests, and these tests are administered primarily to students in lower grades. Administrators may therefore tend to scrutinize the performance of elementary teachers more aggressively than the performance of secondary teachers because elementary teachers' students are more likely to be subject to standardized tests. There is evidence that administrators respond to these kinds of accountability pressures, for example by strategically assigning the most effective elementary teachers to classrooms in tested grade levels (Grissom, Kalogrides, & Loeb, 2017). Third, effectively monitoring secondary teachers can be particularly challenging for administrators because of sub ject specialization. Administrators in secondary settings often have to evaluate the instruction of teachers teaching relatively advanced courses. These administrators 63 often report that they lack the subject area expertise to evaluate their teachers rigorously because their own academic background is in a different field (Donaldson, 2013). Collectively, these three factors provide reason to believe that administrators will be more willing and able on average to punish poor performance at the elementary level than at the secondary level. If so, trade-offs between monitoring intensity and compensation deferral will be more salient at the elementary level. To explore this possibility, I estimate models like those used above but interacting my proxies for monitoring intensity with indicators of the grade levels served by the district (i.e., indicators for unified and high school districts, with elementary districts as the omitted group). This allows relationships between monitoring intensity and salary schedule structure to vary across district type. Specifically, the coefficient on the monitoring proxy estimates the relationship between the proxy and the outcome in elementary districts, and the coefficients on the unified and high school district interaction terms estimate the extent to which those relationships differ in unified and high school districts, respectively. The results are presented in Table 12, but they provide little support for my hypothesis that districts substitute backloading for monitoring to a greater extent in districts employing more elementary teachers because monitoring will be more salient in those districts. For example, in column 1 of panel A, the coefficient on the administrator-to-teacher ratio indicates virtually no relationship with starting salaries for a teacher in the BA+60 lane in elementary districts. Similarly, in columns 3-5, the administrator-to-teacher ratio has almost no relationship with frontloading in elementary districts by any measure. If elementary teachers face the most accountability pressure from their administrators, it is precisely in these districts that those relationships should be most positive as the ability to monitor teachers more intensely removes the need to defer compensation as a motivational incentive. 64 The coefficients on the interaction terms, even when they are in the expected direction, also provide little support for the substitution theory. For example, the coefficient on the unified district interaction term indicate that the relationships between the administrator-to-teacher ratio and starting salaries is slightly (and marginally significantly) more negative in unified districts than in elementary districts (panel A, column 1 ). This relative difference between unified and elementary districts is consistent with monitoring being more salient in elementary districts, and thus more likely to be substituted for backloading. Yet because these relationships are so weakly positive in elementary districts, these estimates imply that the absolute relationship between the administrator-to-teacher ratio and starting salaries is, if anything, slightly negative in unified districts. Results in panel B, using the restrictiveness of CBA evaluation provisions as the proxy for monitoring intensity, similarly provide little evidence that administrators are substituting backloaded compensation for monitoring more heavily in elementary districts. For example, the coefficients on evaluation restrictiveness are small, insignificant, and mostly positive when predicting frontloading, the opposite of what the theory predicts. The coefficients on the interaction terms also suggest that those relationships differ little, if at all, in unified or high school districts. In sum, districts in California do not appear to frontload compensation more heavily when monitoring teachers is easier. This may be because, as discussed above, deferred compensation does not appear to effectively motivate teachers. It may also be that teachers face little accountability pressure from their administrators in practice. This is consistent with the evidence, discussed above, that very few teachers receive poor evaluation ratings, if they are evaluated at all. Moreover, in California teachers typically receive full tenure protections after competing their second year in a district, making them much more difficult to fire. Thus, regardless of the grade 65 levels their district serves, administrators in California districts may supervise relatively small numbers of teachers who could readily be fired even if their performance is poor and well monitored. Results might differ in contexts where teachers' job protections are weaker, and where evaluations by administrators may thus have higher stakes in practice. Do districts frontload compensation to compete fo r teachers ? Results in Table 13 are consistent with districts adapting their salary levels to the supply of teachers, as proxied by whether the district hires primarily high school teachers (who are in relatively low supply) or teachers in grades K- 8 (who are in relatively high supply). If high school districts frontload their salary schedules more heavily than elementary districts serving the same geographic area, this would be strongly suggestive evidence that the difference is due to high school districts needing to compete more aggressively in a tighter teacher labor market. Indeed, compared to elementary districts, high school districts both offer higher salary levels and frontload salaries more aggressively. High school districts have higher average salaries than geographically overlapping elementary districts at both the bottom and top of the salary schedule ( columns 1-2). Salaries at the first step of the schedule are higher in high school districts than in their overlapping elementary districts by at least $1,665 (for teachers with a BA+60), a premium over elementary districts of 3.3%. At step 30, the high school district salary premium is even larger: $2, 872 (3.6%). This is suggestive of, if anything, slightly greater backloading of compensation in high school districts. However, the coefficients predicting the REP and 5-year frontloading measure are substantial and positive and at least marginally statistically significant. Thus, while the salary premium in high school districts may be particularly large - both in absolute and proportional terms - at the top of the schedule, high school districts also allow their teachers to achieve those higher salaries earlier in their careers. For teachers in the BA+60 lane, salary schedules frontload 66 raises more in high school districts than in corresponding elementary districts by 20-24% of a standard deviation, depending on the measure, though only the estimate for the 5-year measure is statistically significant at the 5% level. This represents high school teachers receiving roughly three percentage points more of their raises in the first five years than elementary teachers (36% vs. 33%, the 5-year measure). Similarly, the first 10 raises offered by high school districts are larger than the second 10 raises by 66% of the first 10 raises on average (i.e., the REP), vs. 56% in elementary districts (p = .08) . Only the coefficient predicting the Gini measure of frontloading is small and entirely insignificant statistically. This difference between the measures likely reflects the fact that, as discussed above, the salary premium in high school districts is larger at step 30 than at step 1, reducing to some extent the proportion of all salary earned in the earliest steps in high school districts even as starting salary levels increase. 54 In sum, high school districts appear to offer not only higher salaries compared to elementary districts serving the same communities, but more frontloaded salary schedules, at least in terms of how they distribute raises. This is consistent with high school districts adapting their salary schedules to a comparatively tight teacher labor market by attempting to make those schedules more attractive to teachers. Approaches assessing both union influence and competition for teachers. Spatial model s of union infl uence and competition between districts. As I discuss above, spatial models of districts' relationships to one another offer another means of assessing not only the extent to which districts compete with one another for teachers on the basis of salary, but also mechanisms by which unions might influence salary schedules through institutional connections. 54 The resul ts for frontloading are more equivocal when averaging all lanes on the salary schedule together . Coef fic ients are more negative (and stati stically insignifica nt) for all three frontloading measur es. Salary prem ia at step 1 and step 30 are also sli ghtly larger in both absolute and proportional terms in high school districts when lanes are averaged together. This may indicate that high school distric ts ' salary schedules have systematically different lane structures than sched ules in elementary distric ts . 67 I present results from spatial autoregressive models predicting salary levels and salary schedule frontloading in Tables 14 and 15, respectively. For each outcome, I present models with each spatial lag term separately, as well as a model with both lag terms included simultaneously. 55 In all cases, models are estimated using only a subset of 50 2 districts observed with complete data in every year between the 2005-2006 and 2014-2015 school years. This panel, while smaller than some of my other estimation samples in both the district and time dimensions, is thus strongly balanced, eliminating concerns that the characteristics of districts' neighbors (and thus the spatial lag terms) change over time only because different neighbors are observed in different years. As shown in Table 14, I find spillovers in salary levels between neighboring (i.e., contiguous) districts at both the top and bottom of the salary schedule. A one dollar increase in the average salary of neighboring districts is associated with an increase in salary of 32 cents on a district's own schedule in the subsequent year, and this is similar at the first and last steps ( columns 1 & 4). This is qualitatively similar to previous work, though my estimates are smaller in magnitude than what has been observed before. For example, Wagner and Porter (2000) find geographic spillovers of at least 51 cents on the dollar for beginning teacher salaries in Ohio. This may reflect differences between state contexts or may indicate that omitted variable bias is substantial factor in cross-sectional work. Indeed, if I omit the district fixed effects from these models (not shown), estimates of geographic spillovers roughly double in magnitude, more in line with previous studies. Additionally, these geographic spillovers shrink fu rther when I control for service center lags, adjusting for spillovers between districts in the same regional branch of the state teachers' 55 Recall that the geographic (i.e., contiguity) spatial lag term is also lagged in ti me, and that the ser vice center lag term is defined institutionally, rather than geographically "i n spa ce." For simplici ty, I refer to both simply as "spa tial lag ter ms." 68 union (i.e., comparing column 1 to column 3 or column 4 to column 6). This echoes the findings of Goldhaber et al. (2014), who find that spatial relationships between districts' CBA provisions are driven to a large extent by institutional similarities rather than geographic proximity per se. Indeed, the coefficients on the service center lag terms are much larger than those on the geographic lag terms even when both lags are entered the model simultaneously. For example, controlling for service center effects causes the coefficient on the geographic spatial lag to fall by 38%, from 0.32 to 0.20, for salaries for first year teachers. At the same time, the estimated service center effects remain large even after controlling for spillovers from contiguous districts; in no case does controlling for districts' geographic proximity effects cause the estimated service center spillovers to fall below 62 cents on the dollar, or to lose more than 13% of its magnitude. Winters (2011) finds that geographic salary spillovers are moderately (27%) larger at the bottom of the schedule than at the top, which he argues is consistent with districts competing more aggressively with one another for newer teachers. Though my estimates are smaller in magnitude overall, they are consistently at least as large for step 1 salaries as for step 30 salaries. After controlling for service center spillovers, geographic salary spillovers are larger at the first step on the schedule, compared to the 30 th step, by 18% (0.20 vs. 0.17). This pattern is not apparent for service center spillovers. This is perhaps consistent with geographic spillovers being driven by between-district competition for teachers, and with that competition being more intense for less experienced teachers, though the geographic spillovers themselves and the differences between them are not large in absolute terms. The fact that geographic salary level spillovers are slightly larger at step 1 than step 30 might indicate spillovers in overall salary schedule shape. After all, if these spillovers arise because competitive pressure between proximal districts is greater for less experienced teachers, districts 69 might also be expected to compete with one another for those teachers by frontloading raises for teachers more heavily. However, in contrast with substantial spillovers in salary levels, as shown in Table 15 I find little evidence of spillovers in overall frontloading by any measure, and regardless of whether the spillovers are assumed to be driven by geographic contiguity or service center membership. Indeed, the spatial lag coefficients are not even consistently positive. In the case of service center spillovers this is perhaps unsurprising, since the results in Table 14 suggest that service center spillovers in salary levels are similar at different steps in the schedule. However, even for contiguous districts, salary level spillovers are relatively small in magnitude. Differences in spillovers for salaries for more and less experienced teachers may thus be too similar to measurably alter the overall shape of the salary schedule. Additionally, across-the-board raises are the norm for districts in California, and differentiating raises by step may be politically difficult. It may be easier for districts to disproportionately increase salaries at step 1 - which are uniquely salient as "starting salaries" - than to target raises at other specific steps. This would result in districts competing for new teachers primarily by increasing salaries at step one, without substantially altering overall frontloading (particularly for the REP and 5- year measures, which are defined in terms of subsequent raises). 56 56 Results are very simi lar if natural logs of salaries are used. Geographic spillo vers in salary levels roughly double in magnitude if instead of a first order contiguity matrix I use the inve rse-di stance weight matrix desc ribed above (Appendix Table A 1 ). However, these es timates are still smaller in magnitude than service center spillo vers and shrink by a simi lar proportion after controlling for those spil lovers . Geographic spil lovers in frontloading are generally more negative if the inve rse-dis tance weight matrix is used (Appendix Table A2). However, usi ng the inverse distance weight matrix also substantially incr eases the standard errors of those estimates (by roughly 50 % when predicting salary levels and by much more when predicting frontl oading) . This is not surprising given the considerations discussed above about poor performance of invers e-di stance spatial weight mat rices in contexts like this one. Estimates of geog raphic spil lovers are sensi tive to controlling for distric t-specific quadratic time trends, though other estimate s, and espec ially es timates of service center spill overs, mostly are not (Appendix Table A3). I also consider th e possi bili ty that there are spatial spil lovers in salary schedule structure between districts driven not only by salary schedule features themselves, but also by other district characteri stic s. To do this 70 Regression discontinuity estimates of the eff ect of regulatory flex ibility under the Local Co ntrol Funding Fo rm ula . If districts with unduplicated pupil (UP) shares of at least 55% face lower regulatory burdens in their spending than districts with smaller unduplicated pupil shares, it is worth first considering whether districts appear to manipulate their UP shares to place themselves above the 55% threshold. If so, districts on either side of the threshold, even if very near to the threshold, may not be comparable to one another. Figure 10 shows the distribution of districts' UP shares in 2016-2017, the year on which I focus for these analyses. There is little evidence of manipulation around the cutoff. The number of districts just over the 55% line is not markedly higher than the number just below the threshold. Indeed, if anything the reverse is true, and the kernel density function continues its smooth increase in this region of the distribution. More formally, I implement the manipulation test proposed by Cattaneo, Jansson, and Ma (2019) using local polynomial density estimators with bandwidths optimized to minimize mean squared error, estimated separately on either side of the cutoff. 57 This test fails to reject the null hypothesis of no manipulation (p = . 78). 58 Figures 11 presents visual evidence of the relationship between teacher salaries and districts UP shares for teachers with a BA +60 units. Since there is considerable variation in salary I es tima te spatial Durbin models allowing the control variab les to have spi llover effects of their own and pre sent the resul ts in Appendix Table A4 . However, few such spil lovers are apparent. 57 I implement the manipulation tests usi ng the user -written Stata command rddens i ty (Catta neo, Jansson, & Ma, 20 1 8). I focus on results usi ng the default option s, which include local quadratic dens ity estimation, a triangular kernel function, and jackknife standard errors, but my inferenc es are not sensi tive to alternative combinations of the se option s. 58 I cannot rule out the possi bili ty that districts manipulate their UP shares across the distribution of those share s, as might be likely given that the LCFF awards districts additional revenue for additional unduplicated pupils. However, this does not appear to be an is sue unique to districts in th e vic inity of the 55% thre shold. 71 levels between districts, I group districts into 20 equally spaced (i.e., 5- percentage point) buckets based on their UP shares and plot conditional means. For initial illustrative purposes, I also fit cubic polynomial functions of the running variable separately on each side of the 55% threshold, which I plot with their associated 95% confidence intervals. The figure shows little visual evidence of a discontinuity in teacher salaries across the threshold at either the top or bottom of the salary schedule. This is initial suggestive evidence that neither teachers' unions nor district administrators are not exploiting looser regulations to allocate more of LCFF's supplemental and concentration grants toward higher salaries. Figure 12 performs a similar exercise for my three frontloading measures. Again, there is little evidence of salary schedules being substantially more or less frontloaded on either side of the 55% threshold. Salary schedules appear slightly more frontloaded in districts with at least 55% UPs by all three measures, but the differences are very small. A limitation of this strongly parametric approach is that it is not clear, even visually, what the appropriate functional form of the running variable is. To check for this possibility, in Table 16 I present estimates for each outcome using linear, quadratic, and cubic polynomials, and using three different bandwidths around the 55% cutoff (viz., all districts or only those with UP shares within 35 or 15 percentage points of the cutoff). Additionally, I include my usual control variables in some specifications as an additional robustness check. 59 Consistent with the visual evidence, my estimates are mostly small in magnitude. They are also often sensitive - in both magnitude and direction- to my choice of bandwidth and fu nctional form. The most consistent estimates are those that are visually suggested in the figures above. For example, consistent with the visual evidence in Figure 11, salaries at step 30 in the BA+60 lane are consistently and substantially lower in districts above the 55% UP threshold than would 59 Results are simila r ifI use natural logarithms of salar ies or include labor market fixed eff ects . 72 otherwise be expected based on the relationship between UP shares and salary levels. These estimates are only even marginally significant in two cases, in part because they are imprecisely estimated, though they are consistently large regardless of choice of polynomial, bandwidth, or controls, never falling below $3 ,385 in absolute value (3.6% of the sample mean). As suggested by the evidence in Figure 11, differences in step 1 salaries are much smaller in magnitude and the estimates in Table 16 are not even consistently negative. The most negative estimate in Table 16 implies that being over the 55% threshold is associated with step 1 salaries that are $1, 875 lower (3 .1 % of the sample mean). Though underpowered, these results are not consistent with additional spending flexibility above the 55% threshold resulting in additional spending on the salary schedule. If anything, results are suggestive of the opposite, at least at the highest steps of the schedule. 60 These salary level results are suggestive of additional frontloading of salary schedules above the 55% threshold as the top of the schedule is lowered. However, as suggested by the visual evidence in Figure 12, I find only very limited evidence of this in Table 16 using my measures of frontloading. There are no clear effects on the REP; estimates of effects on the REP vary considerably across choices model and sample specification, ranging from -0.32 to +0.40 standard deviations. Estimates of effects on the 5- year frontloading measure are consistently positive and are generally largest in the more conservative specifications. Estimates are consistently positive for the Gini measure, ranging from 0.32 to 1.42, and are in most cases statistically significant at at 60 My primary salary estimate s are CWI-ad juste d, which may be problematic because this requires projecting the most recent CWI forward by several years . I pre sent resul ts for unadj usted salaries in Appendix Fig ure A3 and Appendix Table AS. These estimate s are generally more negative for salary levels at both the top and bottom of the schedule and across lanes. They are also typically more pr ecise, sugge sting that they might be preferable to the CWI-adjus ted estimate s, but they are also still sensi tive to model specification and in any case do not indicate that LCFF regulatory flexib ili ty for districts with at least 55% UPs results in rai ses for teachers at all, let alone across- the -boa rd raises. 73 least the 10% level. Qualitatively different results across the frontloading measures are consistent with the results for step 1 and step 30 salaries. If districts over the 55% UP threshold are more likely to divert spending away from the highest steps of the salary schedule, this will tend to increase frontloading by the 5-year and Gini measures by compressing the schedule. Nevertheless, these estimates are imprecise and so not always statistically significant even without any adjustments for multiple hypothesis testing. Given the limited power of these analyses, the results are at most suggestive of any differences in salary schedules between districts with different UPPs. 61 Overall, I find no clear evidence that relaxed regulatory standards for districts with larger shares of unduplicated pupils result in districts structuring their salary schedules in very different ways. There is some evidence that districts use this regulatory flexibility to reduce the highest salaries for teachers, but this does not appear to be true for all lanes on the schedule. Nor do reductions in step 30 salaries (if any) appear to be accompanied by higher starting salaries. The effects on the frontloading measures are similarly mixed. I thus find little support for the hypothesis - or the concerns of some student advocacy group - that teachers' unions are exploiting looser regulations across the 55% threshold around the use of LCFF grants to fu nd changes in the salary schedule. Rather, if those looser regulations are allowing changes to salary schedule spending, those changes appear if anything to reflect the allocation of resources away from the salary 61 In Appendix Table A6 I pre sent resul ts from local linear and quadratic polynomial regre ssi ons, further relaxing assumptions about functional form, with bandwidths chosen sepa rately above and below the cutoff to optimize mean square error, and implementing explici t bias correction usi ng proced ures discussed in Calonico, Catta neo, Farre ll, and Titiunik (20 17). As shown in Table 16, my estimates rapidly lose pr eci sion as my bandwidth narrows and as my polynomials become more flexib le, and this could be exacerbated by less parametric approac hes. However, the estimates in Table A6 also reflec t more conservative and data driven modeli ng choices, which may be substantively preferable to the more ad hoc methods I use above. Results are simila r, and simila rly mixed, and only the es timates offrontloading by the Gini measure achieve statistical significance even at the 10 % level. 74 schedule. 62 If so, and if teachers' unions prefer higher salaries, this would likely to reflect the priorities of district administrators rather than the influence of the unions. And to the extent that salaries above the 55% threshold are lower only for veteran teachers salary frontloading is greater by some measures, this could reflect some concerns among administrators that salary level is more important for competing for novice teachers than it is for the recruitment and retention of veterans. As a final assessment of these possibilities, I repeat the analysis above for each of the first four years of LCFF implementation. If districts - administrators or teachers' unions - aim to use LCFF dollars to alter the salary schedule in particular ways, their ability to achieve that aim should be increasing over time as CBAs get renegotiated and regulations are clarified. For illustrative purposes, I focus on the cubic polynomial model, including 51 9 districts observed on the same side of the 55% threshold in all four years. No clear time trend is apparent in the results, which I present in Figures 13 and 14. If regulatory flexibility for districts gave unions growing influence over how LCFF revenues could be spent, especially on salaries, and if unions were able to increasingly pursue their objectives as their CBAs were renegotiated, we should expect to see coefficients predicting salary levels or frontloading for districts become steadily more positive over time. Instead, estimates of the effect of regulatory flexibility above the 55% threshold on salary levels (Figure 13) hover consistently close to zero at step 1, and are perhaps even declining over time at step 30. This is again perhaps more consistent with administrator priorities driving differences in salary schedules between districts on either side of the threshold. However, the effect on frontloading (Figure 14) appears to 62 This is not to say that districts have not used LCFF revenues to inc rease overall salary levels. On the contrary, there is evidence that districts have often used LCFF revenues to incre ase teacher salaries ( e.g., Johnson & Tanner, 20 1 8). This may be because districts have seen incr eases in per-pupil revenue in the LCFF era, or because the LCFF relaxed various categorical restrictions on how all di stricts, regar dless of UPP, could spend their reven ue. But incre ased teacher salary spending does not appear to be driven by districts exploiting different regulations across th e 55% UPP thre shold specifically. 75 also be steady or trending downward toward zero for the REP and 5- year measures. The effect on frontloading is perhaps trending upward, again consistent with the downward trend for step 30 salaries. These estimates are imprecise, but do not indicate qualitatively that greater spending flexibility under LCFF has allowed teachers' unions to increasingly achieve their salary objectives. Similarly, if district administrators' have been able to exploit that flexibility, they appear to be using it to divert resources away from the salary schedule, except perhaps for the most novice teachers' salaries. Even that possibility, however, finds only suggestive support in my results. 63 One possible explanation for these largely null results is that regulatory constraints are not in practice very different on either side of the 55% UP threshold, even if the official regulations differ. This would be consistent with other studies finding that there is considerable disagreement and confusion over what constitutes appropriate use of LCFF's supplemental and concentration grants, or even about how decisions about their use should be made, regardless of districts' student demographics (e.g., Koppich & Humphrey, 2018). If there is a great deal of uncertainty among stakeholders about what kinds of uses are appropriate, it may make little difference whether regulators grant additional flexibility formally to some districts. Alternatively, even if the additional flexibility is real and would otherwise have some effect on districts, administrators in districts above the 55% threshold may also face additional countervailing pressures that prevent them from conceding to union pressure to alter the salary schedule. For example, as I discuss above, districts with more than 55% UPs are eligible for concentration grants. Since concentration grants 63 The increasingly posi tive or negative coef fici ents in Fi gure s 13 andl4 could reflec t the fact that districts renegotiating salary sched ules in different years did so in diff erent economic and policy contex ts. For example, a state law adopted in 2014 phased in incr eases in teachers ' and distric ts ' contribution rates to the state teache rs' pension system over the next several years (Koedel & Gassma nn, 20 1 8). These contribution rate incr eases may have increasingly strained distric ts ' budgets generally or disin centivized salary incre ases specifically. This may have changed both admini strat ors' and teachers ' union incentives when deciding how to use the apparent regulatory flexibility around the 55% thre shold. Again, however, the impr ecisi on of the se es timates makes their trends over time difficult to interpret. 76 are, by design, intended for districts where student need is thought to be particularly intense, their receipt may focus stakeholders' attention on how both supplemental and concentration grants are used. This may create pressure on districts to allocate the grants in a more targeted way than a change to the salary schedule. This may be particularly true in districts very near the 55% threshold, which by definition will have many students those grants are not intended to serve. Because my regression discontinuity approach is only an indirect test of administrator and union influence, I cannot rule out the possibility that my estimates are driven ( or attenuated) by factors other than those forces. However, it may also be that the shape of the salary schedule is not a high priority for either teachers' unions or administrators in California. These regression discontinuity estimates would then be consistent with the results above indicating that stronger CBAs are not associated with significant differences in salary schedule structure within districts over time, and that there are no geographic spillovers in the frontloadedness of districts' salary schedules. RQ3 : Th e Consequences of Frontloading 3.a: District hiring outcomes. Recall that my proxy for districts' abilities to hire teachers effectively is the percentage of newly hired teachers who do not have a full credential. I show results from models predicting that outcome in Table 1 7, and I distinguish math, science, and special education teachers - teachers in positions that typically are more difficult to staff - from other teachers. The evidence above indicates that districts structure their salary schedules in part to compete more effectively for teachers. This underscores the advantages, discussed above, of estimating hiring outcomes for districts using a lagged dependent variable (DV) approach rather than district fixed effects (FEs ); if districts frontload salaries for teachers more heavily precisely when they are experiencing or anticipating hiring difficulties, this will tend to attenuate, or even 77 reverse, estimates of the effect of frontloading on hiring success. For illustrative purposes, I include models in Table 17 that replace the lagged DV with a district FE. To facilitate comparisons between models, I restrict all estimation samples to observations that can be used in all models (i.e., in both the district FE and lagged DV models, and with newly hired teachers both with and without those hard-to-staff certifications. The choice of model specification is often substantively important. For example, in district FE models - columns 1, 4, and 7 - a $1,000 increase in starting salaries is (statistically insignificantly) associated with at least an additional 0.14 percentage points of new math, science, or special education teachers lacking a full credential. It is for these positions that we would expect to see the largest benefits from frontloaded compensation, as they are commonly thought of as particularly difficult to staff. The analogous estimates for other (likely easier-to-hire) teachers - columns 10, 13, and 16- are statistically significant and much larger in magnitude. These estimates are not large in absolute terms, indicating that a $1,000 increase in starting salary is associated with roughly 0.6 percentage points more new hires in these easier-to-staff positions lacking a full credential (from a mean of 18 %). However, they are the opposite of what would be expected if higher salaries make jobs more attractive to teachers. If districts are increasing salaries when staffing is most difficult, those estimates will tend to be positively biased, and may be biased even after controlling for local factors using labor market-by-year fixed effects. The lagged DV specification may then better account for districts' time-varying staffing difficulties. This is because it will adjust for districts' most recent hiring outcomes, rather than adjusting only for between-district differences in average hiring outcomes. Indeed, in the lagged DV specification higher starting salaries are associated with a higher probability that new hires are fully credentialed (i.e., smaller shares of new hires lacking a full credential), and those estimates 78 are consistently statistically significant. This is consistent with higher starting salaries helping to recruit new teachers. An increase in starting salaries of $1,000 is associated with roughly 0.35 percentage points fewer new hires in math, science, and special education lacking a full credential (columns 2, 5, and 8). That's a modest effect, representing approximately 1. 1 % of the average rate at which newly hired teachers in these subjects lack a full credential in districts during this time (see Table 7), but is nevertheless consistent with higher salaries being useful in addressing staffing difficulties. Analogous estimates for other teachers - columns 11, 14, and 17 - are at least 44% smaller in magnitude, suggesting that salary incentives are less salient for teachers with fewer alternative opportunities in the labor market. The coefficients on the various frontloading measures suggest that starting salaries are not all that matter for prospective teachers. In the lagged DV specifications, even net of starting salary, a standard deviation increase in frontloading by the REP or 5-year measure is associated with an increase in the full credential rate for newly hired math, science, and special education teachers of 1.64-1 .68 percentage points, depending on the measure. That is, higher levels of frontloading are associated with fewer of these new hires lacking a full credential. 64 Those results imply that 64 Differences in coeffic ients on the frontloading measures between the district FE and lagged DV specifications are often less striking than differe nces in coef fic ients on starting salarie s. This may indicate that districts are less likely to adapt their salary schedule shape to labor market conditions than they are to adj ust their salary levels. That is consis tent with differe nces in frontloading bei ng more mi xed than diff er ences in salary levels when comparing elementary and high school districts above, and with results from the spatial autoregre ssi ve models, which find geog raphic spillo vers in salary levels between districts - consis tent with competition for teachers - but not spil lovers in frontl oading . Usi ng the credential rates ofnewly hired teachers as a proxy for hiring success assu mes that when a posi tion cannot be filled with a fully credentialed teacher it is filled by a teacher without a full creden tial . The fact that 30 % of newly hired math, science, and special education teachers lack a full cre dential sugge sts that this is in fact a common response by admini strators to staf fing dif fic ultie s. An alternative possi bili ty is that districts may choose not to fill posi tions at all, and this would tend to improve the average credentials of new hir es. This may be a concern particularly in high schools, where the greater prevalence of elective courses gi ves administ rators more dis cretion about wh ich courses will be offered, and thus over which vacancies must be filled. Estimates in Table 17 change only slightly - and not in a consis tent direction - 79 increasing the share of all raises teachers receive in the first 5 years by 10 percentage points would reduce the share of new hires without a full credential by about 6% in these hard-to-staff positions. As with starting salaries, the coefficients on the frontloading measures are substantially smaller in magnitude for other kinds of teacher, again pointing to compensation's greater importance in more competitive teacher labor markets. 65 The relationship is smaller and insignificant for the Gini measure, but this reflects the fact that the Gini measure is partially redundant with starting salary. Results for the Gini measure are more similar to those for the other measures if starting salaries are not controlled for, or ifl control for both step 1 and step 30 salaries (not shown). Contrary to expectation, I find little evidence that these relationships are moderated by the amount of prior experience in other districts for which teachers can receive step credit on the salary schedule. Coefficients on the interaction terms are small and at typically marginally statistically significant at most for both starting salaries and frontloading measures and for both kinds of teacher. This is somewhat surprising given that the earliest steps on the salary schedule - and thus the extent to which the schedule is frontloaded - should be unimportant to new hires who can enter the schedule at later steps. However, in California during this time 89% of salary schedules allow new-to-the-district teachers to receive credit for at least five years of prior teaching experience while 81 % of newly hired teachers have no more than four years of such prior experience. The when I exclude high school di stricts, sugge sti ng that this is not a maj or concern . However, si nce I do not observe unfi lled vacancies, I cannot assess this possi bili ty directly. 65 Like Gri ssom and Strunk (20 12), I control for starting salaries to di stinguish the effects of frontloading from the effects of salary levels. Additionally, insofa r as higher starting salaries re sult in new teachers recei ving higher salar ies more quickly, they can be thought of as a form of frontloading in their own right. The coef fici ents in Table 17 on the starting salary terms are very simi lar if the frontloading term s are dropped, and vice versa. The coef fici ents are usually slig htly more negative when both sets of term s are include d. This may indicate that districts make some trade -off s in practice between starting salary levels and subsequent frontloading, offsetting some of the benefi ts of inc reasing either, though differe nces in the coef fic ients are very small. 80 amount of prior experience for which they could hypothetically receive salary schedule credit may therefore not be salient to many teachers considering district employers. Consistent with this, as I show in Table 18, while allowing teachers to claim salary schedule credit for more prior experience is significantly and positively associated with the mean prior experience of newly hired teachers in both district FE and lagged DV models, the relationship is small. A one-year increase in creditable prior experience for newly hired teachers is associated with an increase in new hires' prior experience of only 0.02 years. This implies that even the difference between the salary schedules offering the least (0 years) and most ( 44 years) credit for prior experience would be predicted to change the average prior experience of newly hired teachers by less than one year. Because salary schedules in California are so heavily frontloaded relative to what has often been observed elsewhere, a natural question is whether we should expect to observe similar relationships between frontloading and teacher credentials in other contexts. I cannot answer this question directly, but in Table 19 I present results from models that include both my standardized frontloading measures and their squares. This allows the relationship between frontloading and teacher credential rates to vary across the distribution of frontloading. Because I center my frontloading measures such that zero indicates a schedule that is neither frontloaded nor backloaded, the coefficient on the linear frontloading term can be interpreted as the relationship for districts with such a schedule. The coefficients on the linear term are for the most part larger in magnitude (i.e., more negative) than the analogous coefficients in Table 17. Accordingly, the coefficients on the squared terms, though they are almost always statistically insignificant, are mostly positive in both the district FE and lagged DV specifications. This is qualitatively consistent with marginal increases 81 in frontloading becoming less important as salary schedules become more heavily frontloaded. My estimates in Table 17 may therefore understate the hiring benefits districts with more backloaded schedules would obtain from additional frontloading, though because I observe few highly backloaded schedules this is difficult to assess with certainty. 3.b: Student achievement. The evidence above indicates that more heavily frontloaded salary schedules improve hiring outcomes for districts. If newly hired teachers are not only better credentialed but more effective, this could have benefits for student outcomes. Additionally, more frontloaded salary schedules could improve teacher retention, allowing more selective retention of the most effective teachers and reducing chum among staff that can have its own detrimental effects on student achievement (Ronfeldt et al., 2013). Here I tum to results from models using district and labor market-by-year fixed effects, presented in Table 20. They offer only limited evidence that frontloaded salary schedules improve student test scores. Higher starting salaries are associated with slightly higher student achievement. This is particularly true in math, where a $5,000 increase in starting salary is associated with an increase in mean student achievement of roughly 0.05% of a district-level standard deviation and an increase in the proficiency rate of about one percentage point. Additionally, even after controlling for starting salaries, the REP is associated with increases in both math and ELA achievement and proficiency rates, with effect sizes on proficiency rates similar to - though modestly smaller than - those found by Grissom and Strunk (2012) using the same frontloading measure. This is consistent with frontloaded compensation helping districts to recruit and retain teachers. Moreover, the fact that coefficients are consistently larger in magnitude for math achievement, compared to ELA achievement, is consistent with the hiring results above indicating 82 that staffing outcomes in harder-to-staff subject areas are particularly sensitive to compensation structure. However, for other frontloading measures coefficients are not statistically significant and are generally much smaller in magnitude. Moreover, I cannot rule out the possibility that unobserved factors correlated with salary schedule structure and student achievement explain the positive relationships I observe in some cases. For example, if districts can increase compensation for new teachers more rapidly as local economic conditions improve, those economic improvements may also contribute to student achievement and this may not be fully accounted for by my fixed effects or observable controls. Indeed, as I show in Appendix Table A7, controlling for district-specific cubic time trends shrinks even my most suggestive coefficients to insignificance. These time trends may control away the true effects of salary schedule structure, but the sensitivity of my results to their inclusion suggests that bias from time-varying district unobservables can easily explain the positive relationships in Table 20. 66 Even if frontloaded salary schedules do not measurably improve student achievement on average, it is possible that they are particularly useful in contexts where student achievement is low. Lower-achieving students may have greater educational needs, making the quality of their teachers especially important, and districts with more low-achieving students may struggle more than other districts to attract and retain teachers. In Table 21 I present results from models like those in Table 20 but dividing my sample into groups with mean student achievement above or 66 Additionally, in models that replace the district fixed effects with a lag of the dependent varia ble, coef ficie nts on the REP shrink to zero. Coeffic ients on the other term s change in different directions and do not show a clear pattern, even for the same term across te st subjects, with more posi tive es timates generally becomi ng smaller and vice versa. To the extent that district FE and lagged DV es timates bound the "true" eff ects (Angrist & Pisc hke, 2009), this is further reason to doubt a large posi tive effect of frontloading on student achievemen t. 83 below the statewide district mean. I do not find that salary schedule frontloadedness appears to be particularly important in lower-achieving districts. On the contrary, coefficients are often more positive and more significant statistically in districts with above-average student achievement. This is true for both starting salaries and my frontloading measures and in both subjects. 67 Why, if more frontloaded salary schedules allow districts to hire better-certified teachers, would they not also improve student achievement? One possibility is that my staffing outcome measure - the percentage of new hires lacking full certification - is a better measure of teacher quantity than of teacher quality. Certification is a weak indicator of teacher quality ( e.g., Angrist & Guryan, 200 8; Buddin & Zamarro, 2009), so having slightly higher credential rates per se would not be expected to indicate large differences in average quality among newly hired teachers. Also, while district administrators may be under legal or political pressure to hire better-credentialed teachers, teacher hiring decisions otherwise appear largely insensitive to teacher quality ( e.g., Liu & Johnson, 2006). This means that having a larger number of highly certified teachers willing and able to work in a district may be unlikely, by itself, to lead to large improvements in the distribution of teacher effectiveness. Even if more frontloaded salary schedules result in more effective new hires and lower levels of potentially disruptive turnover, these effects may be difficult to identify. While individual teachers vary a great deal in their impacts on student test scores, changes in average staff quality due to changes in hiring and retention will be much smaller and benefits to students will accumulate over time. Limited within-district variation in salary schedule structure will make the achievement effects of frontloaded salary schedules particularly difficult to discern. Future work 67 I also attempt quantile regre ssi ons, and the se show a qualitatively si milar pattern, with estimated relat ionships in almost every case sli ghtly more posi tive at higher deciles of student achievement. However, the se estimates are very impr ecise . 84 linking salary schedule frontloadedness to student outcomes would likely benefit from data including larger changes to salary schedules and the ability to track individual teachers and students over time. 3.c: District spending patterns. If the achievement effects of salary schedule structure are small, this will heighten the importance of their fiscal effects since costlier salary schedules will be harder to justify or will require cuts elsewhere. In Table 22 I show relationships between starting salaries, frontloading measures, maximum (i.e., step 30) salaries, and several categories of per pupil spending. Because the per-pupil spending measures are inverse hyperbolic sine transformed, associated coefficients can be interpreted roughly as percent changes, much as if they were natural log transformed. 68 Perhaps unsurprisingly, higher starting salaries are associated with higher maximum salaries (columns 1-3). This reflects the fact, discussed above, that the most common practice for districts in California is to increase salaries at all steps by the same or similar proportions. Because step 30 salaries are higher than step 1 salaries, an increase of the same proportion will tend to increase step 30 salaries by a larger absolute amount; the coefficients on step 1 salary are thus all greater than one. 69 Naturally enough, higher step 1 salaries - mostly reflecting higher overall salary levels - are also associated with higher overall per-pupil operational spending ( columns 4-6). An additional $1,000 in starting salary predicts an increase in per-pupil operational spending of 1.0- 1.4%, or roughly $120 for the mean observation in my sample. At the same time, while higher starting salaries predict higher maximum salaries, this is 68 Results are very si milar ifl control for district- specific cubic time tre nds. 69 Results are very simila r if I use the natural logs of salar ies. Estimates are qualitatively simila r but attenuated if district fixed effects are replaced with a lag of the dependent varia ble, likely reflec ting high year-to-year correlation within districts of the dependent varia bles. 85 not consistently true for my frontloading measures. Instead, a standard deviation increase in frontloading as measured by the REP or the 5-year measure is associated with a decrease in maximum salaries of $2,735 or $2,250, respectively, after controlling for starting salary. The relationship is even larger in magnitude for the Gini measure. This pattern has implications for total spending, which tends to decrease with Gini frontloading, but not with the REP or 5- year frontloading. These results are broadly consistent with districts often making trade-offs in practice between the highest salaries available to teachers and the speed at which teachers can achieve those salaries. This may help to manage the higher costs associated with higher salaries for less experienced teachers, including both direct salary costs and contributions to the state's teacher pension plan, keeping total spending down. 70 Indeed, after controlling for starting salaries, neither the REP nor the 5-year frontloading measure are associated with per-pupil spending on either teacher salaries ( columns 7 & 8) or teacher pensions ( columns 10 & 11 ). And the decreases in spending associated with the Gini measure are, unsurprisingly, driven by lower spending on both teacher salaries and teacher pensions (columns 9 and 12). 71 I find little evidence that districts frontloading their salary schedules save money elsewhere in the budget. For example, districts (or their teachers' unions) might be expected to trade non salary benefits for steeper salary profiles. However, none of my frontloading measures are 70 Notably, the resul ts above sugges t hiring benefi ts from frontloading even if districts are reducing salar ies at higher step s in the sched ule. If districts simultaneously reduce maximum salar ies, this may tend to attenuate the benefi ts of frontloading salary sched ules for teacher recruitment. Consis tent with thi s, when I control for both step 1 and step 30 salar ies, th e coeffic ients on the frontloading measure s mostly become more negative (i.e., indica ting larger improvements in credential rates) when predicting the credential rates of newly hired teachers (Appendix Table AS). 71 Because distric ts ' contributions to the pens ion plan are typically a fixed proportion of teache rs' salaries, spending on teacher salaries and teacher pensions tend to move very nearly in unison. 86 associated with lower spending on health and welfare benefits for certificated staff (columns 13- 15), and the associated coefficients are not even consistently negative. Alternatively, districts might hope that frontloaded salaries will reduce administrative costs related to turnover, hiring, and teacher development. However, greater frontloading is not associated with lower spending on general administration ( columns 16-1 8). 72 Thus, while the evidence presented above suggests that frontloading their salary schedules may allow districts to recruit teachers more effectively, especially in the hardest-to-staff positions, such frontloading could nevertheless be costly. Districts can mitigate these costs by reducing maximum salaries for teachers, but this trade-off will likely be unattractive to veteran teachers. It may also not appear worthwhile to administrators who are not greatly concerned about the supply of teachers or who cannot differentiate the salary schedule to make this trade-off only for teachers in the shortest supply. 73 This may help to explain why salary schedules remain backloaded in many contexts, particularly iffrontloaded salaries are not accompanied by large, immediate, or consistent improvements to outcomes for which administrators feel accountable, such as student achievement. 74 72 As I did when predicting new hire credentialing rates above, I estimate models pred icting student achievement and re source allocation measures that are quadratic in my frontloading measure to assess whether resul ts might vary in a context with less baseli ne frontloading of salary sched ules. The results (Appendix Table Al0 ) are more mi xed in th ese cases than when predicting teacher credential rate s, and thus do not poi nt clearly to diff erent relation ship s when salary schedules are more backloaded on avera ge. 73 When I predict step 30 salaries usi ng frontloading measure s and step 1 salaries lagged by one or two years, rather than usi ng values as observed in the same year as the step 30 salary, the coeffic ients on the frontloading measures become progre ssi vely attenuate d. This may sugge st some adjus tments by districts over ti me, and the relationships between those varia bles and operational spending, teacher salar ies, and pensions also attenuate in some cases. Lagging the se variab les does not re sult in systematically different results when predicting other typ es of spending, student achievement, or teacher credential rate s, perhaps because the within-district correlation of the frontloading measures is high . 74 In related work, Strunk and Marianno (20 19) find that between 2005 -2006 and 2011 - 2012 districts suffering the most finan ci al stre ss due to the rec ession reduced starting salari es for teachers with a BA by $1 .270 (i n 2012 dollars) more than districts insulated from the re cession. They do not find a sig nifi cant 87 Discussion There appears to be broad agreement that teacher compensation is important. Teachers' unions and district administrators often reach bargaining impasses over teacher compensation, politicians often campaign on platforms promising raises for teachers, reformers advocate changes to the way teachers are paid, and countless studies have been published on what the effects of those changes might be. For the most part, these debates and discussions tend to focus either on the level of teacher salaries or on the potential of differentiating compensation for different kinds of teacher. Both types of consideration are important. However, there is an extensive literature suggesting that the shape of the wage-experience profile is also important, and in particular that it may be advantageous to offer relatively larger or smaller annual experience raises to teachers with different experience levels. In theory, frontloading or backloading raises to different degrees might be useful for recruiting, retaining, or motivating teachers. These kinds of changes may be easier to adopt than more controversial reforms - like merit pay - that depart from the step-and-lane salary schedule paradigm, and selectively allocating raises at specific steps in the salary schedule where they will do the most good may be more efficient and af fordable for school districts than across the-board raises. Yet the existing literature on teacher salary frontloading is largely theoretical. Existing empirical studies are often dated or rely on cross-sectional samples of school districts that limit researchers' abilities to make causal inferences when testing theories about why salary schedules have different shapes or about whether those shapes matter. effect on salari es for teachers with a MA and 20 years of experienc e, which they interpret as evidence of incre ased backloading as unions disproporti onately protect compensa tion for veterans when under financial dure ss. This would be consistent with frontloading being costly for districts, and with union influence moderating how the district responds to fiscal strain. On the other hand, their point estimate for the negative effect on those veteran teacher salari es (-$3 , 11 9), while impr ecisel y estimated, is larger than the point estimate for starting salar ies both in absolute terms and as a proportion of 2005 -2006 levels. This is qualitatively consis tent with financial strain imposing similar downward pre ssure on sala ries at all steps, though impr ecision of the estimates makes this dif fic ult to establish. 88 I bring recent longitudinal data from California data to bear to shed light on the prevalence, causes, and consequences of teacher salary schedule frontloading. I find that salary schedules in California have been heavily frontloaded for many years, at least in terms of how they distribute raises across steps. This is in stark contrast to previous work in other parts of the country, and perhaps to much of the conventional wisdom about the structure of teacher compensation. At a minimum, the heavy frontloadness of California's teacher salary schedules highlights the risks of generalizing about education policies and teacher labor markets in a country as large - and with as much local control over education - as the United States. I also find considerable variation between districts in the extent to which their salary schedules are frontloaded, and in some cases considerable variation within districts over time. But I find little support for two common theoretical explanations for this variation. First, I do not find that it is driven by union influence. When teachers' unions appear to grow stronger or weaker over time - successfully negotiating contracts that impose more or fewer restrictions on district administrators - they do not simultaneously negotiate salary schedules that are frontloaded or backloaded to a greater degree. This contrasts with - conflicting - theoretical arguments that teachers' unions will either advocate frontloaded salary schedules to maximize teachers' career earnings or advocate backloaded schedules to help veteran members extract rents from districts. Similarly, while I find some evidence - in the form of spillovers between local unions in the same regional service center - that union institutions influence the salary levels for which local unions bargain, this influence does not appear to extend to the frontloadedness of the salary schedule. Nor do I find that granting some districts greater regulatory freedom to allocate revenues to salaries - a policy widely considered a win for teachers' unions - results in those districts frontloading salaries more ( or less) heavily. Competing interests in frontloaded and backloaded salary schedules 89 may effectively balance out for most unions, causing them to focus their bargaining priorities elsewhere. Alternatively, contrary to what has often been suggested in previous work (Ballou & Podgursky, 2002; Grissom & Strunk, 2012; Gustman & Segal, 1977), unions may not care very much about the shape of the salary schedule in the first place. I also find no evidence for the theory that district administrators will adopt backloaded salary schedules when assessing teacher quality is difficult. On the contrary, districts do not on average adopt more heavily backloaded salary schedules when they have more capacity to monitor teachers, whether due to larger numbers of administrators or less restrictive teacher evaluation provisions in the contract. This may reflect the relatively weak incentive power of compensation deferred until higher steps in the salary schedule, or a general lack of accountability for teachers even if administrators determine that they are ineffective. I do, however, find some support for a third theory: that districts use frontloaded salary schedules to recruit and retain teachers more effectively. High school districts offer not only higher starting salaries than elementary districts serving the same geographic area, but also subsequent raises that are more frontloaded. This is plausibly explained by high school districts needing to compete more aggressively for relatively scarce secondary teachers. Similarly, results from spatial autoregressive models are qualitatively consistent with neighboring districts competing more aggressively with one another through salaries at lower steps of the schedule, compared to higher steps. This is could suggest that at least some of the spatial spillovers are being driven by competition for teachers, though this effect appears small and does not translate into spatial spillovers in my three measures of frontloading. If districts use frontloaded salaries to compete for teachers, I also find some evidence that this may be effective. In lagged dependent variables models - though not in district fixed effect 90 models - higher starting salaries and more frontloaded raises are each uniquely associated with better certification rates for newly-hired teachers. However, this is not accompanied by higher student achievement on standardized tests, perhaps because credentialing rates are not a strong indicator of teacher quality or because teacher hiring is largely insensitive to quality even when the supply of potential teachers is larger. Additionally, I find that frontloading salaries can be costly for districts, with greater frontloading associated with either lower maximum salaries or higher spending, especially on teacher salaries. In addition to offering tests of theories of frontloading that will be of interest to academics, my results will be of interest to both district administrators and to policymakers. For administrators, my results point to benefits from frontloading salaries more aggressively, particularly when the supply of teachers is weaker. Additional frontloading of total compensation may be possible even in the California context, where substantial portions of teacher compensation - including pensions and health and welfare benefits - are heavily backloaded. And the benefits of frontloading may be particularly large in other contexts, where public school teacher salaries are often more backloaded than those of similarly educated workers in other sectors ( e. g., Vigdor, 200 8). However, these benefits may not be fully realized if districts do not simultaneously invest in initial teacher selection so that the best applicants can be selected from the larger applicant pool. That such investments - like the frontloading itself - can be costly for districts points to at least two potential implications for policymakers. First, districts, and particularly districts with the most difficulty recruiting and retaining enough high-quality teachers, may benefit from financial support targeted and new teacher selection and compensation. The fact that backloading does not appear to be driven by either union influence or strategic efforts by administrators to motivate teachers suggests that the constraints administrators face in adopting frontloaded salary schedules 91 are largely financial in nature. Many states, including California, do differentiate their funding formulae for different aspects of district need, but few differentiate based on these kinds of labor market factors (Imazeki, 2018). Second, districts might benefit from having additional flexibility to differentiate their salary schedules for different kinds of teachers. For example, California law prohibits districts from differentiating teacher salaries based on grade level taught. As I show above, high school and elementary districts - when operating independently - do appear to offer salary schedules shaped more effectively for their respective labor markets. Restrictions on their ability to differentiate their salary schedules in this way may result in other districts - e.g., unified districts serving all grade levels - adopting schedules that are more frontloaded ( and thus more costly) than is optimal for their elementary teachers, but also more backloaded (and thus less attractive to new teachers) than is optimal for their secondary teachers. While these issues have been the subject of some empirical literature in the past, my data and methods allow me to extend that prior work in several important ways. The detail of my salary schedule data allows me to operationalize salary schedule frontloadedness in several different ways. These different measures generally point to similar conclusions, but there are also sometimes modest differences that may be important . For example, I find evidence that frontloading as measured by the Gini measure (i.e. , in terms of cumulative salary) may be more cost-efficient for districts than frontloading measured in other ways ( e. g., in terms of the distribution of raises). The CBA data I use also allow for more direct measures of some factors that have often been considered important for salary schedule design, but which have been measured only crudely, such as union strength or districts' ability to monitor their employees' performance. I am also able to address potential issues of bias common in previous empirical work. For example, in several analyses I 92 exploit the longitudinal nature of my data or compare high school districts to geographically coterminous elementary districts to control for many unobserved differences between districts. Nevertheless, my work suffers from several limitations. While California is a useful context to study these issues - including many diverse districts, and detailed longitudinal data - it will often be difficult to generalize my results to other contexts. For example, teacher salary schedules in California are heavily frontloaded, and much more frontloaded than those that have often been observed elsewhere. The factors affecting frontloading, or the implications of that frontloading, may differ when salary schedules are more backloaded on average. For example, I find suggestive evidence that an increase in frontloading may have larger benefits for districts' hiring and staffing where salary schedules are not as frontloaded to begin with. 75 Additionally, while I believe that my methods represent an improvement over much of the previous literature in this regard, I also cannot rule out the possibility that my estimates are biased by unobserved factors because I do not rely on clearly exogenous variation in variables that might affect or be affected by salary schedule structure. For example, my use of district fixed effects cannot eliminate bias due to factors varying within districts over time in ways correlated with features of the salary schedule. Even my regression discontinuity estimates, though they rely on plausibly exogenous variation in formal regulations, shed only indirect light on the effects of my constructs of interest: teachers' union influence and competition for teachers. These limitations point to directions for future research. Studying similar issues in other contexts would help with issues of generalizability, and other contexts may also offer opportunities 75 It is also a cha I lenge for some of my analyses that I observe only limi ted within-district variation in salary sched ule frontloadedne ss, as this makes identi fy ing rela tionship s dif fic ult after controlling for district fixed eff ects . However, the fact that districts generally make few changes to the shapes of their salary schedules unders core s that frontloading is not highly responsi ve to for ces commonly highlighted in the literatu re. This is consis tent with prev ious literature indicating that teacher CBAs generally do not change a great deal over time (e.g., Cowen & Fowles, 2013). 93 to study natural experiments affecting the frontloadedness of salary schedules. For example, by comparing states that have recently restricted the power of unions to those that have not, or states where unions are differentially affected by a recent Supreme Court ruling prohibiting the collection of union agency fees, it may be possible to observe the effects of union power not only on teacher salary levels but on the shape of the salary-experience profile for teachers. More generally, studies of teacher salary levels should broaden their focus to include not only average salary levels, but salary levels at different points in the teacher experience distribution (i.e., the frontloadedness of the salary schedule). Given widespread interest in teacher compensation, it is surprising that previous research has not attended to teacher salary frontloading more consistently. This work, and many of the other studies discussed above, provide evidence both that changes in salary levels can differ at different steps within a salary schedule, and that those differences may matter for district outcomes. We are far from knowing how best to design a teacher compensation system, and the optimal system will likely vary across contexts. Yet modest changes to the shape of teacher salary schedules could probably attract broad support in many communities. And because step-and-lane salary schedules are so ubiquitous, even modest improvements to their design could have large aggregate benefits for teachers, students, and schools. 94 References Akiba, M., Chiu, Y.- L., Shimizu, K. , & Liang, G. (2012). Teacher salary and national achievement: A cross-national analysis of 30 countries. International Jo urnal of Educational Research, 53, 171 -1 81 . https://doi. org/10. 1016/ j.ijer.2012.03.007 Angrist, J. D., & Guryan, J. (200 8). 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Jo urnal of Public Economics, 100, 61 -7 8. https://doi.org/1 0. 1016/ j .jp ubeco.201 3.01 .006 110 Table 1 - Research Questions, Hypotheses, Methods, and Results Support for Re sea rch Question H�eot hesis Proxies Method H�eothe sis? 1. The Prevalence of NIA NIA Des criptive NIA Frontloadin Contract restricti vene ss Two-wa� fixed effects No Teachers ' Union Influence Union service center membershi.Q S2atial autoreg re ssi on• No Regulatory flexibility on salary spending Regre ss ion No discontinui!l 2. The Causes of Imperfect Information Adm inistrat or:tea cher ratio Two-wa� fixed effects No Frontloading about Teacher Quali� Contractual restrictions on teacher evaluation Two-wa� fixed effects No � ....... ....... Seg mentation between elem entary and Geography-by-year sec onda!}'. teacher labor markets fixed effects Yes VJ Competition for Teachers Neighbori ng district sala r� schedules S2atial autoreg re ssi on• Limited Regulatory flexibility on salary spending Regre ss ion Limited discontinui!l Better hiring Credentialing rates of newly hired teachers Lagged dependent Yes 3. The Conseq ue nces of variable Frontloading Better student outc omes Standardized test scores Two-wa� fixed effects No Hi � her s e endin � NIA Two-wa� fixed effects Yes a These hypotheses are tested in a single analysis below. b These hypotheses are tested in a single analysis below. - - N Table 2 - Measures of Salary Schedule Frontloading Measure Relative Experience Premium ( AREP ) Five-Yea r Loading (A s ) Gini Loading ( A G ) Ca l cu l at i on salary 11 - salary 1 salary 21 - salary 11 ---"'- 10 "'--------""" l """ O ___ X 100 salary 11 - salary 1 10 salary 6 - salary 1 - - - - - - - X 100 salary 30 - salary 1 L�=l salary 5 30 X 100 L s =l salary 5 Descr i pt i on The additional average annual experience raises teachers are given in their first dec ade compared to teachers in their seco nd decade, expre ssed as a percentage of the average raises given in the first dec ade . Front l oad i ng Back l oad i ng Cr i ter i on Cr i ter i on AR EP > o AREP < o The percentage of all raises (up to A s > 17 .2 A s < 17 .2 step 30 ) recei ved by teachers in th eir first five years . Of total sala ry paid out across step s A G > 16.67 A G < 16.67 of the salary schedule, the percentage paid out in the first five ste s. Table 3 - Correlations Between Frontloading Measures REP 5-Year Gini Relative Experience Premium 1.00 5-Year Loading 0.80 *** 1.00 Gini Loading 0.34*** 0.46*** 1.00 Note. Includes 758 district salary schedules in 20 16-20 17. + p<. 1, * p<.05, ** p<.01, *** p<. 00 1 113 Table 4 - Standardized Account Code Structure Codes Defining Expenditure Variables Ex p enditure Cate g or y All Operations Subsets of Spending on All Operations Teacher Sa laries Teacher Pensions Health and Welf are Benefi ts for Certifi cated Staff Activity Codes Included All All All All Object Codes Included 10 00- 7999 11 00 3101 3401 General Administration 7000- I 000- 7999 7999 Codes Excluded Goals 710 0-7 19 9 (Spending on behalf of other agencies ), 8 I 00 (Community services) Functions 5000-5 999 (Community services), 8500 (Facilities acquisition and construction) Objects 6000-6499, 6501 -6999 (Capital outlay, except equipment replacement ), 7430-7439 (Debt service), 3701- 3702 (Retiree benefi ts) Resource 7690 (CalSTRS contributions from the state) Funds 9 & 62 (District-operated charter schools ) No te. Codes taken from the 2019 California School Accounting Manual. 114 Notes Day-to-day spending on the instruction of students. Si mila r to the CDE's Current Expense of Education. Table 5 - CBA Items Used to Estimate Overall Restrictiveness Associ ation Rights 1. Association members or presidents are promised leave. 2. The contract specifies an amount of release time for the association per year. 3. The contract specifies who pays for general association release time. 4. The association president (or designee) gets additional leave time. 5. The contract specifies who pays for the association president' s leave. 6. The contract specifies the total number of days of release time the association president receives per year. 7. 2: 10 days 8. 2: 20 days 9. 2: 40 days 10. The association president receives full-time leave. Com pensation 11. Members receive a bonus for having a PhD/EdD. Class Size 12. The contract addresses class size. 13. The contract specifies a particular class size. 14. The district must balance class sizes within a specific period of time. 15. The district must balance class sizes within three weeks of the stat of the year or semester. 16. The district must take action if the class size is exceeded. 17. The district must take action by a specific time if class size is exceeded. 18. Class size actions be taken within three weeks 19. Specific actions must be taken if class size is exceeded. Evaluation 20. Permanent members to use an alternative evaluation process with satisfactory prior performa nce. 21. Permanent members can use an alternative evaluation process. Grievances 22. The board does not make final/binding decisions on grievances. 23 . Grievances do not go to the board. 24. Grievances can go to arbitration. 25. Arbitration is the final stage in the grievance process. 26. Grievance arbitration is binding . Non-Teaching Duties 27. There are restrictions on the length and/or number of faculty meetings. 28. There are time constraints on faculty meetings. 29. There are constraints in the number of faculty meetings. Transfers and Vacancies 30. Seniority is addressed as a factor in who is voluntarily transferre d. 31. Seniority is a factor in who is voluntarily transferred at least when all else is equal. 32. There are limits on the frequency with which members may be involuntarily transferre d. 33. The CBA outlines specific causes for which a member may be involuntarily transfe rred. Sch ool Days and Ho urs 34. The CBA specifies the length of the school day in instructional minutes. 115 Table 6 - Items used in Evaluation Subarea Contract Restrictiveness Measure 1. CBA specifies that probationa ry/non-tenured teachers must have a pre-obs ervation me eting with their evaluator 2. CBA requires probationa ry teachers to have advance notice for any of their formal evaluation observations 3. CBA requires greater than 2 days' notice 4. CBA requires greater than 1 weeks ' notice or agree upon in advan ce 5. If they get advance not ice, there is NO clause permitting additional unannounced observations 6. CBA specifies the length of formal observations 7. CBA specifies a time limit within post-obs ervation meetings must occur after observations 8. CBA specifies that post-obs ervation meetings must occur within 5 days 9. CBA specifies how many formal observations the district can have for tenured faculty 10. CBA specifies that district can have greater than one observation of tenured faculty 11. CBA specifies that district can have greater than two observations of tenured faculty 12. CBA allows for Education Code standard evaluation period for NCLB highly qualified teachers of every 5 yea rs, and no more frequently 13. CBA allows permanent/tenured members in the district to use an alternative evaluation process for satisfactory evaluation and performance 14. CBA allows permanent/tenured members in the district to use an alternative evaluation process 15. CBA specifies how many formal observations the district can have for probationa ry/non-tenured faculty 16. CBA outlines a minimum number of observations that must occur before a member recei ves an unsatisfactory evaluation 17. CBA puts a time limit on a teacher 's reply rights 18. Reply time limit is greater than or equal to 10 days 19. Reply time limit is greater than or equal to 15 days 20. CBA does not restrict teachers with negative evaluation from gaining a sala ry step in the following year 21. CBA s p ecifies that negative evaluations can be removed from p ersonnel files 116 Table 7 - Summary Statistics N Mean SD Min Max =1 if elementary district 10667 0.52 0. 50 0 1 =1 if high school district 10667 0. 09 0.29 0 1 = 1 if unified district 10667 0. 39 0. 49 0 1 Enrollment 10667 7162.70 23952. 86 5 727227 = 1 if declining enrollment 10649 0. 55 0. 50 0 1 ¾SPED 10422 9.61 4.0 5 0.00 97.60 ¾ELL 10506 20.36 17. 93 0.00 100 ¾F RL 10617 51 . 86 26.34 0.00 100 % Black 10667 3.35 5.55 0.00 76. 19 % Hispanic 10667 41 .89 28.42 0.00 100 Number of teaching days 10667 179.71 1.26 163 194 Highest entry step on salary schedule 10629 11 .18 6. 88 1 45 Administrators per Teach er 10667 0. 08 0.04 0.00 1.00 Median teacher experience in district 10665 9.44 3. 54 1 29 BA+60 Salaries (Thousands of 2017 Dollars) Step 1 Salary 10667 50 .21 5.7 5 30.77 80 .48 Step 30 Salary 10667 80 .31 12.76 36 .1 5 140.05 BA +60 Frontloading Me asures Relative Experience Premium 10667 58.48 28.1 3 -147.60 100 5-Year 10667 33.44 9.33 0.00 100 Gini 10667 12.70 0.70 10.29 16.67 Contract Restrictiveness Overall 1793 0.00 1.00 -3.44 2.80 Evaluations 1793 0.00 1.00 -3.26 2.79 Newly Hired Te achers % wlo full credential (non-hard-to-staf f) 7484 18.47 22.32 0.00 100 % w/o full credential (hard-to-staf f) 6201 30.47 29.16 0.00 100 Average Years of Experience 95 86 3.72 3. 09 1.00 50 .0 0 Per-Pupil Expenditures (201 7 Dollars) Total 10667 10365 .41 35 94.01 581 5.1 0 58547. 91 Teacher salaries 10667 383 6.43 914.72 1387 . 88 15 853 .21 Teacher pensions 10667 392. 44 119.7 4 0.00 18 11. 42 Certificated health & welfare benefits 10667 614. 49 269.72 0.00 4106. 83 General administration 10667 794.22 582.47 15 8.24 10291.43 Achievement Me asures % proficient or advanced in math 96 78 44.70 18.40 0.00 100 % proficient or advanced in ELA 96 86 49.3 7 17.05 3.00 100 Mean math achievement 9632 0.12 0.89 -2. 61 3. 98 Mean ELA achievement 9640 0.12 0.86 -2. 87 2.99 Note. Data in this table combines annual observations of943 unique districts from 2003 -2004 through 20 16-20 17. Hard-to-staff teachers are th ose with math, science, or spec ial education authoriza tio ns. Staff credential data were not made public from 2009-20 10 through 20 11 -20 12. 117 Table 8 - Absolute Changes in Frontloading 10th 25th 50 th 75th 90th Mean Min %ile %ile %ile %ile %ile Max REP 13.71 0.00 0.00 0.01 4.99 17.63 39. 14 202.34 5-Year 5.01 0.00 0.00 0.01 2.29 6.53 12.22 82.76 Gini 0.31 0.00 0.00 0.02 0.17 0.40 0. 78 5.1 6 Note. Figures are absolute values of differ enc es between minimum and maximum frontloading for 916 districts obse rved at least twice between 2003 -2004 and 20 16-20 17. 11 8 Table 9 - Salary Schedule Structure as a Function of CBA Restricti veness and Teacher Experience CBA Restricti vene ss Step 1 Sala ry (20 17 Dollars) ( 1) (2) -62.32 -147.60 (83.23) (193.05) Median Teacher -228.00 *** -227.10 *** Prior Experience (3 7 .05) (36. 73) Step 30 Salary (20 17 Dollars) (3) (4 ) 10 2.15 30 2.86 (163.99) (376.66) -403 .94 *** -406 .06 *** (77.73) (77.05) Frontloading (Standardized ) REP 5-Yea r Gini (5) (6) (7) (8) (9) (10 ) -0.03 -0.0 1 -0.0 2 0.0 l -0.0 l -0.03 (0 .02) (0 .05) (0 .02) (0 .04) (0 .01) (0 .0 2) 0.00 0.00 (0 .01) (0 .01) 0.00 0.00 (0 .01) (0 .01) -0.00 -0.00 (0 .01) (0 .01) Restricti vene ss 10. 47 -24.63 -0.00 -0.00 0.00 (0.0 0 ) x Experience ( 22.05 ) (42.58) (0.0 1) (0.00 ) Adj. R-sq. 0.97 0.97 0.97 0.97 0.9 1 0.9 1 0.9 2 0.9 2 0.88 Districts 49 1 49 1 49 1 49 1 49 1 49 1 49 1 49 1 49 1 Obs ervations 1681 1681 1681 1681 1681 1681 1681 1681 1681 0.88 49 1 1681 Note. Standard errors clustered on districts in parent heses. All models control for th e natural log of district enrollment; whether the district has declining enrollment; the shares of district students who are Black, Hispa nic, and eligible for free or red uced-price lunch; the number of teaching days in the yea r; and district and yea r fix ed eff ects . All predictors are lagged by one year except for CBA restrictive ness and th e number of teaching days. + p<. l, * p<.05, ** p<.01, *** p<.00 1 119 - Table 10 - Salary Schedule Structure as a Function of CBA Restrictiveness and Teacher Experience, by Outcome Level CBA Restrict. Below (1) 228.28' (10 2. 19 ) Step 1 Salary Step 30 Sa lary Frontloading ( Standardized ) (20 17 Dollars) (20 17 Dollars) REP 5- Year Gini Ab ove Below Ab ove Below Above Below Above BelowAb oveBelow A boveBelow AboveBelowAb oveB elowA boveB elowAbove ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) ( 7 ) ( 8 ) ( 9 ) ( 10 ) ( 11 ) ( 12 ) ( 13 ) ( 14 ) ( 15 ) (1 6 ) ( 17 ) ( 18 ) (1 9 ) ( 20 ) -29 4.51' 415.88 + -582.36' 394.53' -1 59.08 491.61 -295.19 -0.01 0.01 -0.00 0.01 0.00 0.01 0.0 2 0.0 6 -0.03 ' 0.01 -0.06" -0. 01 (132.7 9) (243 .44) (261.00 ) (168.76) (28 0.38 ) (473.38) (440.66 ) (0.0 2 ) (0.01 ) (0.03) (0.0 2 ) (0.0 2 ) (0.0 2 ) (0.03 ) (0.05 ) (0.01 ) (0.01 ) (0.0 2 ) (0.03) Median Teacher -12 6.82 *** -281.94 ***-12 3.19*** -273.34 *** -244. 71 **-424.03 *** -243.88** -4 21.65*** -0.01 0.00 -0.01 0.00 0.00 -0.00 0.00 -0.0 0 0.0 0 -0.00 0.0 0 -0.00 Prior Experience (36.74) (54.0 7) (36.69) (53.57 ) (75.5 1) (10 8.32 ) (75.21 ) (10 7.94) (0.01 ) (0.00 ) (0.01 ) (0.00 ) (0.00 ) (0.01 ) (0.00 ) (0.01 ) (0.01 ) (0.01 ) (0.01 ) (0.01 ) Restrict. -22.98 35.03 -12 .17 16.54 -0.00 -0.00 -0.00 -0.01 o.o o + o.o o x Experience (25.18 ) (28.53 ) (50.66 ) (51.87 ) (0 .00 ) (0.00 ) (0.00 ) (0.01 ) (0.0 0 ) (0 .00 ) Adj . R- sq. 0.87 0.95 0.87 0.95 0.9 2 0.9 3 0.9 2 0.9 3 0.89 0.96 0.89 0.96 0.89 0.85 0.89 0.85 0.88 0.95 0.88 0.95 Districts 248 26 1 248 26 1 246 263 246 263 252 242 252 242 244 246 244 246 250 242 250 242 Observations 784 800 784 800 781 810 781 810 824 8 I 5 824 815 818 823 8 I 8 823 823 823 823 823 Note. Standard errors clustered on districts in parent heses. All models control for the natural log of district enrollment; whether the district has declining enrollment; the shares of district students who are Black, Hispanic, and eligible for free or red uced -price lunch; the number of teaching days in the yea r; and district and year fix ed eff ec ts . All pre dictors are lagg ed by one yea r except for CBA restricti vene ss and the number of teach ing days. Sample sizes differ across outc omes beca use dividing the original estimation sample in different ways results in different numbers of observations that are unique within f i xed effect cells . The se singleton observations are dropped (Correia, 20 15). +p<.l, * p<.05, ** p<.01, *** p<.00 1 Table 11 - Salary Schedule Structure as a Function of Monitoring Intensity Panel A Administrators 2er 100 Teachers Observations Districts Adj. R-sq. Panel B Evaluation Restrictiveness Observations Districts Adj. R-sq. Salary {Thousands of 201 7 Dollars 2 Step 1 Step 30 0 2 {2 2 -7. 92 -21.46 {1 1. 87 2 {1 9.44} 9117 9117 864 864 0.97 0. 96 {6 2 {7 2 62. 94 233.62 + {78.39 2 {130.00 2 16 81 16 81 491 491 0.97 0. 96 Frontloading {Standardized} REP 5-Year Gini {3 2 {4 2 {5 2 o. oo + 0.00 -0.00 {0.00 2 {0.00 2 {0.00 2 9117 9117 9117 864 864 864 0.92 0.87 0.91 {8 2 {9 2 {10 2 -0.00 -0.00 0.02 {0.02 2 {0.01 2 {0.01 2 16 81 16 81 16 81 491 491 491 0.91 0.92 0.88 Note. Standard errors clustered on districts in parent hes es. All models control for the natural log of district enrollment; whether the district has declining enrollment; the shares of district students who are Black, Hispa nic, and eligible for free or red uced-price lunch; the number of teaching days in the yea r; and district and yea r fix ed eff ects . All control varia bles are me asured in the previous year except for number of teaching days. Frontloading me asures have a standard deviation of one across all districts and years . + p<. 1, * p<.05, ** p<.01, *** p<. 00 1 121 Table 12 - Salary Schedule Structure as a Function of Monitoring Intensity by District Type Panel A Administrators per 100 Teachers x Unified X High Observations Districts Adj. R-sg. Panel B Evaluation Restrictiveness x Unified X High Observations Districts Adj. R-sg. Salary (2017 Dollars) Step 1 Step 30 (1) (2) 2.96 -23.15 (12.11) (24.41) -5 5.3 5 + -21. 09 (28.41 ) (38.99) 62.88 151.2 7 + (3 8.86) (78.93) 9117 9117 864 864 0.97 0. 96 (6) (7) 12 8.71 38 8.67 + (141.17) (201.06) -109 .48 -199 .25 (176.70) (263.11) -18. 85 -574. 53 (265. 14) (723. 81) 16 81 16 81 491 491 0.97 0. 96 Frontloading (Standardized) REP 5- Year Gini (3) (4) (5) 0.01 + 0.01 0.00 (0.00) (0.01) (0.00) -0.01 + -0.02 + -0.01 (0.00) (0.01) (0.01) -0.01 -0.01 -0.00 (0.00) (0.01) (0.01) 9117 9117 9117 864 864 864 0.92 0.87 0.91 (8) (9) (10 ) -0.00 0.01 0.01 (0.04) (0.02) (0.01) 0.00 -0.02 -0.02 (0.04) (0.03) (0.02) -0.03 0.02 -0.02 (0.04) (0.05) (0.03) 16 81 16 81 16 81 491 491 491 0.91 0.92 0.88 Note. Standard errors clustered on districts in parent heses . All models control for the natural log of district enrollment; whether the district has decli ning enrollment; th e shares of district students who are Bla ck, Hispanic, and eligible for free or red uced-price lunch; the number of teaching days in the yea r; and district and yea r fix ed eff ects . All control variables are me asured in the previous year except for number of teaching days. Frontloading me asures have a standard deviation of one across all districts and years . + p<. l, * p<.05, ** p<.01, *** p<.00 1 122 Table 13 - Salary Schedule Differences Between High School and Elementary Districts Salary (2017 Dollars) Frontloading (Standardized) Step 1 Step 30 REP 5-Year Gini (1) (2) (3) (4) (5) HS District (Reference Group 16 65.42 *** 2871.63 * 0.20 + 0.24 * 0.03 = Elementary Districts) (499.35 ) (1164.37) (0.11) (0.10) (0.09) Natural Log of Enrollment 707.19 ** 1986.7 5 *** 0.16 ** 0.05 -0.13 * (250.04) (55 9. 54) (0.06) (0. 05 ) (0. 05 ) 1 =Declining Enrollment -10. 09 65.3 7 0.01 0.01 -0.04 (187.65) (425.36) (0.06) (0. 05 ) (0.04) %Hispanic -2. 09 28.36 -0.01 -0.00 -0.01 (26.44) (48.30) (0.00) (0.00) (0.00) %Black -11 8.39 37.17 -0.03* -0.03* -0.03* (83.78) (16 6.53 ) (0.01) (0.01) (0.01) ¾FRL -16.27 -36. 57 0.01 0.00 0.00 (16. 45) (30.89) (0.00) (0.00) (0.00) Teaching 262.39 *** 507.82*** -0.01 -0.01 -0.00 Days {77.63 2 {1 49.72 2 {0.03 2 {0.02 2 {0.02 2 Observations 50 95 50 95 50 95 50 95 50 95 Districts 508 508 508 508 508 Elem-HS Stacks 93 93 93 93 93 Adj. R-sg. 0.72 0.75 0.46 0. 50 0.46 Note. Standard errors clustered on districts in parent heses. Elem entary districts weighted by the percentage of elem entary district enrollment in their HS-el em entary stack they represent. All models include cluster-by-year fixed eff ects . All control varia bles are me asured in the previous year except for service days for returning teache rs. Frontloading mea sures have a standard deviation of one across all districts and yea rs. + p<. l, * p<.05, ** p<.01, *** p<.00 1 123 Table 14 - Salary Levels with Spatial Spillovers Ster 1 {1 2 { 2 2 Geo graphic 0.32 *** Spatial Lag (0 .0 4) Se rvice Center 0.7 1 *** Spatial Lag (0. 06) Natural Log 1382.60 ** 1206.60 ** of Enrollment (477.32) (454.27) 1 =Decli ning -61.33 -72.11 Enrollment (55.91) (54.29) %Hispan ic 7.11 7.75 (9.03) (8.53) %Black 12.21 19.53 (35.22) (33.95) %FRL -10.8 2 * -8.60 * (4.65) (4.25) Teaching 288.26 *** 274.10 *** Da�s { 20.50 2 {1 9.32 2 Within R-sq. 0. 42 0.63 Districts 502 502 Obs ervations 45 1 8 45 1 8 Salary { 20 17 Dollars 2 { 3 2 { 4 2 0.20 *** 0.32 *** (0 .0 4) (0 .0 4) 0.6 2 *** (0. 06) 1157.46 ** 1678.64 * (447.13) (793.97) -62.86 -269.82 ** (54.24) (93.15) 8.97 28.59 + (8.43) (14.75) 14.44 23.03 (33.07) (77.19) -8.or -17.01 * (4.22) (6.91) Ster 30 { 5 2 { 6 2 0. 17 *** (0 .04) 0.7 4 *** 0.66 *** (0. 06) (0 .06) 1413.66 + 1311.85 + (723.61) (712.71) -281.30 ** -281.02 ** (89.99) (89.61) 21.28 23_94 + (13.58) (13.44) 35.07 25.45 (75.21) (74.43) -15.99 * -14.61 * (6.40) (6.20) 277 .38 *** 493.40 *** 460 .63 *** 467.0 2 *** {1 9.38 2 {38. 12 2 { 35.99 2 {3 6.0 3 2 0.6 2 0.40 0.6 2 0.6 2 502 502 502 502 45 1 8 45 1 8 45 1 8 45 1 8 Note. Standard errors clustered on districts in parent heses. All models control for district and yea r fixed eff ects . Controls are me asured in the previous yea r except for service days for returning teachers . + p<. 1, * p<.05, ** p<.01, *** p<. 00 1 124 Table 15 - Frontloading (Standardized) with Spatial Spillovers Frontloading (Standardize ) REP 5-Year Gini ( 1) (2) (3) (4) (5) (6) (7) (8) (9) Geo graphic 0.03 0.0 2 0.0 2 0.03 -0. 13 * -0. 13 * Spatial Lag (0 .03) (0 .03) (0 .0 2) (0 .0 2) (0.05) (0 .05) Se rvice Center 0.0 2 0.0 1 -0.20 * -0.2 1 * 0.0 4 0.06 Spatial Lag (0.05) (0.05) (0. 10 ) (0. 10 ) (0 .06) (0 .06) Natural Log of 0.2 1 0.2 1 0.2 1 0. 16 0.15 0.15 0.07 0.07 0.07 Enrollment (0. 17) (0. 17) (0. 17) (0. 16) (0. 16) (0. 16) (0.05) (0 .05) (0 .05) 1 =Decli ning Enrollment %Hispan ic %Black %FRL 0.0 1 0.0 1 0.0 1 (0 .0 1) (0 .0 1) (0 .0 1) -0.00 -0.00 -0.00 (0. 00) (0. 00) (0. 00) 0.00 0.00 0.00 (0. 00) (0. 00) (0. 00) 0.00 0.00 0.00 (0. 00) (0. 00) (0. 00) 0.0 1 0.00 O.o l 0.0 1 0.0 1 0.0 1 (0 .0 1) (0 .0 1) (0 .0 1) (0 .0 1) (0 .01) (0 .01) -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 (0. 00) (0. 00) (0. 00) (0. 00) (0 .00) (0 .00) 0.0 1 0.0 1 0.0 1 -0.00 -0.00 -0.00 (0 .0 1) (0 .0 1) (0 .0 1) (0 .0 1) (0 .01) (0 .01) -0.00 -0.00 -0.00 0.00 0.00 0.00 (0. 00) (0. 00) (0. 00) (0. 00) (0 .00) (0 .00) Teaching -0.00 -0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 Days (0.00 ) (0.00 ) (0.00 ) (0.00 ) (0.00 ) (0.00 ) (0.00 ) (0 .00 ) (0 .00 ) Within R-sq. 0.0 1 0.0 1 0.0 1 0.0 1 0.0 1 0.0 1 0.00 0.00 0.00 Districts 502 502 502 502 502 502 502 502 502 Obs ervations 4518 4518 4518 4518 4518 4518 4518 4518 4518 Note. Standard errors clustered on districts in parent heses. All models control for district and yea r fixed eff ects . Controls are me asured in the previous yea r except for service days for returning teachers . + p<. l, * p<.05, ** p<.01, *** p<.00 1 125 Table 16 - Parametric Regression Discontinuity Estimates of Salary Schedule Features (1) (2 ) (3) (4) (5) (6 ) (7 ) (8 ) (9) (1 0 ) (1 1 ) (1 2 ) Salaries (Thousands of 2 0 17 Dollar s) Step l Salary, -0.346 -1 .875 0.0 64 -0.565 -1. 132 -0.9 09 -0.956 -1 .773 0.12 9 0. 894 3.490 2.648 BA+60 (l.633) (2.383 ) (3. 10 0 ) (3.018 ) (1.869) (2.7 71) (3.512) (3.396) (2.8 28 ) (3.903 ) (4.613) (4.471) Step 30 Salary, BA +60 -3 .385 -7.6 40 + -4.4 27 -5.035 -5.301 + -5.6 98 -8.5 45 -8.6 60 -5.236 -5 .15 3 -6.93 8 -5.3 11 (2.759) (4. 10 4) (5.445) (5.312) (3.110 ) (4.713) (6.125) (6.0 14) (4.795 ) (7.141 ) (8.854) (8.536 ) Fron tloading (Standardi zed) REP, 0. 19 0.0 4 0. 14 0.23 0. 15 0.0 2 0.27 0.40 0.2 2 -0.07 -0.32 -0.23 BA+60 (0. 16 ) (0.23) (0.3 1) (0.3 1) (0. 17 ) (0.26 ) (0.36 ) (0.36 ) (0.26 ) (0.43 ) (0. 57) (0.58 ) 5- Year, 0.05 0.01 0.23 0.27 0.0 2 0.0 7 0.50 0.53 0.27 0.37 0. 16 0. 19 BA+60 (0. 16 ) (0.23) (0.30 ) (0.30 ) (0. 18) (0.26 ) (0.34 ) (0.35 ) (0.25 ) (0.41 ) (0.54 ) (0.56 ) Gini, 0.32 + 0.5 2' 0.4 4 0.40 0.40' 0.4 4 0.75' 0.61 + 0. 61' 0.66 1.42' 1.05 + BA +60 (0. 16 ) (0.2 4) (0.33 ) (0.30 ) (0. 19 ) (0.28 ) (0.38 ) (0.35 ) (0.28 ) (0.4 7) (0.65 ) (0.58 ) Controls X X X Bandwid th 55 55 55 55 35 35 35 35 15 15 15 15 Degree of Polynomial l 2 3 3 l 2 3 3 l 2 3 3 Districts 681 681 681 680 560 560 560 559 244 244 244 244 Note. Heteroskedasticity-robust standard errors in parentheses. Each coeffic ient is an estimate from a separate regression. Contro ls, when present, include th e natural log of district enrollment; whether the district has declining enrollment; the shares of district students who are Black, Hispanic, and eligible for free or reduced -price lunch; and the number of teaching days in th e year. All control variables are measured in the previous year except for number of teaching days. Salaries are adjusted using the comparable wage index. + p<. l , * p<. 05, ** p<.0 1, *** p<. 00 1 126 Table 17 - Predicting the Percentage of Newly Hired Teachers without a Full Credential Step 1 Sa lary (Thousands ) Step I Sa lary x Creditable Prior Experience REP REP x Creditable Prior Experience 5- Year Loading 5- Year x Creditable Prior Experience Gini Loading Gini x Creditable Prior Experience Max. Creditable Prior Experience Math, Science, or Special Education Other (1) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) ( 7 ) ( 8 ) ( 9 ) ( 10 ) ( 11 ) (1 2 ) ( 13 ) (1 4 ) (1 5 ) 0. 14 -0.36" -0. 11 0. 14 -0.37" -0. 12 0. 18 -0.32' -0.09 0.66" -0. 18' -0. 18 0.65" -0. 19' -0. 19 (0.35 ) (0. 12) (0. 19 ) (0.36 ) (0. 12) (0. 19 ) (0.35 ) (0. 13) (0. 19 ) (0.20 ) (0.0 7) (0. 13) (0.21 ) (0.0 7) (0. 13) -0.0 2 + (0.01 ) -1 .64 -1 .64" -0.53 ( 1.62 ) (0.52 ) (0.98 ) -0. 10 (0.0 7) -0.0 2 + (0.01 ) -0. 71 -1 .68'" -0.76 (1.34) (0.50 ) (0.89 ) -0.09 (0.0 6) -0.0 2 + (0.01 ) -0.63 -0.45 -0.59 (1.94) (0.56 ) (0.91 ) 0.0 2 (0.0 7) -0.00 (0.01 ) -0.34 -0.6 4 + -1 .49' (0.9 3) (0.36 ) (0.71 ) 0.08 (0.06 ) 0.00 (0.01 ) -0 .51 -0.88" -1 .58" (0.91 ) (0.3 1) (0.61 ) 0.07 (0.05 ) (1 6 ) (1 7 ) ( 18 ) 0.65" -0. 18' -0.20 (0.2 0 ) (0.08 ) (0. 13) -0.00 (0.01 ) 0. 77 0.0 6 -1 .85' (0.9 9) (0.37 ) (0.7 4) 0. 18" (0. 06) 0.0 3 -0.08 0.6 0 + 0.0 3 -0.09 0.54 + 0.0 3 -0.07 0.48 -0.0 l 0.01 -0. 16 -0.01 0.00 -0. 12 -0.0 I -0.00 0.29 (0. 11 ) (0. 06) (0.32) (0. 11 ) (0. 06) (0.30 ) (0. 11 ) (0. 06) (0. 47) (0. 09) (0.05 ) (0.22 ) (0. 09) (0.05 ) (0.2 1) (0. 09) (0.05 ) (0. 27) District FE X X X X X X Lagged DV X X X X X X X X X X X X Adj . R- sq. 0.25 0. 18 0. 19 0.25 0. 19 0. 19 0.25 0. 18 0. 18 0.43 0.34 0.34 0.43 0.34 0.34 0.4 3 0.34 0.34 Districts 622 622 622 622 622 622 622 622 622 622 622 622 622 622 622 622 622 622 Observations 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 Note. Standard errors clustered on districts in parentheses. Frontloading measures have a standard deviation of one across all districts and years . The outcome is the percentage of newly hired teachers in the district that lack a full credential, and models are estimated separately for teachers with math, science, or special education teachers ( columns 1-9) and all other teachers ( columns 10 -18). All models control for the natural log of district enrollment; whether the district has declining enrollment; the shares of district students who are Black, Hispanic, English learne rs, and eligible for free or reduced-price lunch and special education services; the number of teaching days in the year; and labor market-by-year fixed eff ects. Salaries are expressed in thousands of 20 17 dollars. Salaries are centered at $30 ,000 and frontloading measures are centered at zero. + p<.l, * p<.05, ** p<.0 1, *** p<.00 1 Table 18 - Predicting New Teacher Hires' Experience Years of Prior Teaching Ex2erience for New!� Hired Teachers (1) (2) (3) (4) (5) (6) (7) (8) (9) Step 1 Salary 0.0 4 0.0 4 *** 0.0 2 0.03 0.0 4 *** 0.0 2 0.03 0.03 ** 0.0 2 (Thousa nds) (0 .03) (0 .0 1) (0 .0 2) (0 .03) (0 .0 1) (0 .02) (0 .03) (0 .01) (0 .02) Step 1 Salary x Creditable o.oo + o.oo + o.oo + Prior Experience (0. 00) (0 .00) (0 .00) REP 0.09 o.or 0.0 4 (0. 09) (0 .0 4) (0. 07) REP x Creditable 0.00 Prior Experience (0 .0 1) 5-Year Loading -0.0 2 0.06 0.00 (0. 07) (0 .0 4) (0 .08) 5-Year x Creditable 0.0 1 Prior Experience (0 .01) G ini Loading 0.08 0.03 0.08 (0 .12) (0 .05) (0 .09) Gini x Creditable -0.0 1 Prior Experience (0 .01) Max. Creditable 0.0 2 + 0.0 2 ** -0.03 0.0 2 + 0.0 2 ** -0.03 0.0 2 + 0.0 2 ** -0.06 Prior Experience (0 .0 1) (0 .0 1) (0 .03) (0 .0 1) (0 .0 1) (0 .03) (0 .01) (0 .01) (0 .04) District FE X X X Lagged DY X X X X X X Adj. R-sq. 0.26 0.18 0.18 0.26 0.18 0.18 0.26 0.18 0.18 Districts 798 798 798 798 798 798 798 798 798 Obs ervations 7610 7610 7610 7610 7610 7610 7610 7610 7610 Note. Standard errors clustered on districts in parent heses. Frontloading measure s have a standard deviation of one across all districts and yea rs. All models control for the natural log of district enrollment; whether the district has declining enrollment; the shares of district students who are Black, Hispanic, English learne rs, and eligible for free or red uced -price lunch and specia l education servic es; the number of teaching days in the yea r; and labor market-by yea r fixed eff ec ts . Salaries are adjusted using the comparable wage index and expre ssed in thousands of20 17 dolla rs. Salaries are expre ssed in thousands of 20 17 dolla rs. Salaries are centered at $30 ,000 and frontloading me asures are centered at zero such that in the models with interactions the coef fic ient on maximum creditable prior experience can be interpreted as the relationship between creditable prior experience and th e outcome when starting salaries are $30,000 (roughly th e minimum typically observed in California during this time) and the salary schedule is neither frontloaded nor backloade d. + p<. 1, * p<.05, ** p<.01, *** p<.00 1 12 8 Table 19-Predicting the Percentage of Newly Hired Teachers without a Full Credential, Quadratic Models Math, Science, or S12ecial Education Other { 1 2 { 2 2 {32 { 4 2 {5 2 { 6 2 {72 {8 2 {9 2 {10 2 {11 2 0 2 2 Step l Salary 0.30 -0 .3 1 ** 0.27 -0.32 ** 0.2 4 -0.33 ** 0.6 2 ** -0. l 7* 0.60 ** -0. 17 * 0.65 ** -0. 16 * (Thousands ) (0.34 ) (0. 12) (0.34 ) (0. 12) (0.35 ) (0.13) (0.20 ) (0.0 7) (0. 19 ) (0.0 7) (0.21 ) (0.08 ) REP -2.43 -2_03 + 0. 18 -0. 17 (l.91) (1.0 9) (1.26 ) (0. 87) REP 2 0.34 0. 11 -0.23 -0. 14 (0 .61) (0 .29) (0 .35) (0 .20 ) 5- Year -1 .27 -1 .86 + -3 .86 + -1 .46 + Loading (3.0 4) (l.l l ) (2.00 ) (0.7 4) 5- Year 2 0. 10 0.0 4 0.5 1' 0. 13 (0.34 ) (0.23) (0.25 ) (0.14 ) Gini 8.53 -5.0 6 1.07 3.62 Loading (7.99) (4.33) (3.74) (3.49) Gini 2 0.85 -0.40 0.03 0.3 1 (0.7 2 ) (0.3 7) (0.37 ) (0.30 ) Max. Creditable 0.0 3 -0.08 0.0 3 -0.09 0.0 3 -0.07 -0. 01 0.01 -0.01 0.00 -0.01 0.01 Prior Experience (0. 11 ) (0.0 6) (0. 11 ) (0.0 6) (0. 11 ) (0.0 6) (0.0 9) (0.05 ) (0.08 ) (0.05 ) (0.09 ) (0.05 ) District FE X X X X X X La ed DV X X X X X X Adj . R- sq. 0.25 0. 18 0.25 0. 18 0.25 0. 18 0.43 0.34 0.43 0.34 0.43 0.34 Districts 622 622 622 622 622 622 622 622 622 622 622 622 Observations 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 Note. Standard errors clustered on districts in parentheses. Frontloading measure s have a standard deviation of one acro ss all districts and years. All models control for the natural log of district enrollment; whether the district has declining enrollment; the shares of district students who are Black, Hispanic, English learne rs, and eligible for free or reduced-price lunch and special education servic es; the number of teaching days in the year; and labor market-by- year fixed eff ects . Salaries are expre ssed in thousands of 20 17 dollars . Frontloading measures are centered at zero such th e main effect of frontloading measures can be interpreted as th e relationship between frontloading and the outcome when th e salary schedule is neither frontloaded nor backloaded. + p<. 1, * p<.05, ** p<.0 1, *** p<. 00 1 129 Table 20 - Student Achievement as a Function of Salary Schedule Structure (District FE Models) Math English/L anguage Arts %age Proficient Standardized Score %age Proficient Standardized Score {1 2 { 2 2 { 3 2 { 4 2 { 5 2 { 6 2 { 7 2 { 8 2 { 9 2 { 10 2 { 11 2 { 12 2 Step 1 Salary 0.2 1 * 0.20 * 0. 17 * 0.0 1 * 0.0 1 * 0.0 1 + 0.10 + 0. 10 0.08 0.0 1 + 0.0 1 + 0.00 (Thousands) (0. 09) (0. 09) (0.08) (0. 00) (0. 00) (0. 00) (0. 06) (0 .06) (0 .06) (0 .00) (0 .00) (0. 00) REP 0.8 2 * 0.0 4 * 0.7 4 * 0.03 * (0 .39) (0 .0 2) (0 .3 1) (0 .01) 5-Year 0.30 0.0 2 0.18 0.0 1 Loading (0.27) (0 .0 1) (0 .22) (0 .01) Gini 0.59 0.03 0.34 0.0 2 Loading (0.46 2 { 0.0 2 2 { 0.34 2 { 0.01 2 Adj. R-sq. 0.90 0.90 0.90 0.88 0.88 0.88 0.93 0.93 0.93 0.9 4 0.9 4 0.9 4 Districts 872 872 872 872 872 872 873 873 873 873 873 873 Obs ervations 9208 9208 9208 9208 9208 9208 9213 9213 9213 9213 9213 9213 Note. Standard errors clustered on districts in parent heses. Frontloading measure s have a standard deviation of one across all districts and yea rs. All models control for the natural log of district enrollment; whether the district has declining enrollment; the shares of district students who are Black, Hispanic, English learne rs, and eligible for free or reduced-price lunch and specia l education servic es; th e number of teaching days in the yea r; and district and labor market-by-year fix ed eff ects . Salaries are expre ssed in thousands of 20 17 dolla rs. Standardized scores are distric ts' mean sca le scores standardized to have a unit standard deviation across districts each yea r. + p<. 1, * p<.05, ** p<.01, *** p<.00 1 130 Table 21 - Standardized Student Achievement as a Function of Salary Schedule Structure, by Student Achievement Level (Di strict FE Models) Bel ow Above BA+6 0 (1 ) (2) Step 1 Salary -0.00 0.0 1 * (Thousands) (0 .0 1) (0 .0 1) REP 5-Year Loading 0.0 1 0.0 2 (0 .0 2) (0 .0 2) Math Bel ow Above (3) (4 ) -0.00 0.0 1 * (0 .0 1) (0 .0 1) -0.0 1 0.0 2 (0 .0 1) (0 .03) Bel ow Above (5) (6) -0.00 0.0 1 * (0. 00) (0 .0 1) English/L anguage Arts Bel ow Above Below Above Below Above (7) (8) (9) (1 0 ) (1 1) (1 2) -o.oo o.oi • -o.oo o.o 1 • -o.oo o.o 1 + (0. 00) (0 .00) (0 .00) (0 .00) (0 .00) (0. 00) 0.0 1 0.03 + (0 .0 2) (0 .02) -0.00 0.0 1 (0 .01) (0 .02) Gini 0.0 1 -0.0 1 0.0 1 0.0 2 Loading (0.0 2) (0.03 ) (0 .02 ) (0.0 2) Adj. R-sq. 0.65 0.88 0.65 0.88 0.65 0.88 0.77 0.93 0.77 0.93 0.77 0.93 Districts 555 560 555 560 555 560 504 535 504 535 504 535 Obs ervations 4578 4488 4578 4488 4578 4488 4439 464 1 4439 464 1 4439 464 1 Note. Standard errors clustered on districts in parent heses. Frontloading measure s have a standard deviation of one across all districts and yea rs. All models control for the natural log of district enrollment; whether the district has declining enrollment; the shares of district students who are Black, Hispanic, English learne rs, and eligible for free or red uced -price lunch and specia l education servic es; the number of teaching days in the yea r; and district and labor market-by-year fix ed eff ects . Salaries are expre ssed in th ousan ds of 20 17 dolla rs. Standardized scores are distric ts ' mean sca le scores standardized to have a unit standard deviation across districts each yea r. + p<. l, * p<.05, ** p<.01, *** p<.00 1 131 - Table 22 - Resource Allocation Measures as a Function of Salary Sched ule Structure (District FE Models) Per-Pupil Spending (Inverse Hyperbolic Sine ) Step 30 Salary All Operational Teacher Sa laries Teacher Pensions Certifi cated Health & Welfare General Administration BA+60 (I ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) ( 7 ) ( 8 ) ( 9 ) (1 0 ) (1 1 ) (1 2 ) (1 3 ) (1 4 ) (1 5 ) (1 6 ) (1 7) (1 8 ) Step I Salary 1.1 0 2'" I .0 71 '" 1.434'" 0.01 0'"0 .01 1 '"0. DI 1'"0.01 5'"0 .01 5'"0 .01 6'"0 .01 5'"0.0 15'"0.0 16'" 0.0 04 0.0 04 0.005 0.008'" 0.0 08'"0.008'" (Thousands ) (0. 082 ) (0.0 91) (0.0 61) (0.0 0 1) (0.0 0 1) (0.0 0 1) (0.0 0 1) (0.0 0 1) (0.0 0 1) (0.0 0 1) (0.00 1) (0.00 1) (0.0 03 ) (0.0 03 ) (0.0 04 ) (0.0 02 ) (0.0 02 ) (0.0 02 ) REP 5- Year Loading -2. 735••· (0.343 ) -2.250 *** (0.32 2 ) -0.00 1 (0.0 05 ) 0.0 0 1 (0.0 04 ) 0.0 03 (0.0 06 ) 0.0 0 1 (0.0 06 ) 0.0 06 (0.0 06 ) 0.0 04 (0.0 06 ) 0.00 1 (0.0 2 1) -0.0 04 (0.0 09 ) -0.0 07 (0. 007) 0.0 05 (0.0 06 ) Gini -6.257 *** -0.0 18* -0.0 25** -0.0 24 ** -0 .018 -0. 002 Lo ading ( 0. 260 ) ( 0. 007 ) ( 0. 009 ) (0 .0 09) ( 0.0 25) ( 0. 009 ) Adj . R- sq. 0.98 0.98 0.9 9 0.9 2 0.9 2 0.9 2 0.87 0.87 0.87 0.91 0.91 0.91 0.85 0.85 0.85 0.9 0 0.9 0 0.9 0 Districts 910 910 910 910 910 910 910 910 910 910 910 910 910 910 910 910 910 910 Observations 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 10 175 1017 5 1017 5 1017 5 Note. Standard errors clustered on districts in parent heses. Frontloading me asures have a standard deviation of one across all districts and yea rs. All models control for the natural log of district enrollment; wheth er the district has declining enrollment; the shares of district students who are Black, Hispa nic, English lea rners, and eligible for free or red uce d-price lunch and spec ial education servic es; the number of teaching days in the yea r; and district and labor market-by-year fix ed eff ects . Salaries are expre ssed in thousan ds of 20 17 dollars . + p<. l, * p<.05, ** p<.01, *** p<.00 1 Figures Figure 1 - Example Salary Schedule Lanes 100000 - C'U 0 C ..... 80000 � 0 N - � C'U C'U ti) ..... 60000 � 0 N I co � 0 N 40000 0 Ramona City Unified (BA+60) , , , , , 5 , , , , , , ,-- , 10 ·- �-- ' , I 15 Step ,- ,-- ' ,-- ' ,-- ' Paradise Unified (BA+60) 20 25 30 Figure 1. Example salary schedule lanes. Salaries for teachers with a bachelor's degree (BA) and 60 additional units i n two California d istricts in 20 1 6-20 1 7. 133 Figure 2 - Conceptual Framework Labor Market Factors R02: The Ca uses oi F ronll oading , ' 1 Spatial \ I Rel ationships I with ot her \ Districts I ' , +!- R01: The Prevalence of Fronll oading Fro ntload ing + + R03: The Consequen ces of Frontloading Expenditures + r------ 1 Teacher 1 + Recruitment 1 and Retention 1 I Student Outcomes Moderating District Factors: reso urce levels, student disadvantage, teacher experience, etc. Figure 2. Conceptual framework. Circles indicate factors causi ng front loaded ness and squares are effects of frontloading. Dashed lines indicate mediators and th e box at the bottom indicates potential moderating factors . Arrows indicate theoretical causa l relationship s. 134 Figure 3 - CTA Service Centers er ice C nter Council Di trict • I Redding 1 Redwood 3 Chi o 4 Fe ther RiH!r Capua! Golden G te 5 6 7 lcosta Deha So urce: California Teachers Association Figure 3 . CTA service centers. 23 an Gorgom _4 an Die o 25 lmpenal 26 Higher l::du lion ( talev. Ide ) 135 Figure 4 -Av erage Teacher Salary by Step 90000 - ns 0 C 80000 ..... """" 0 N - � 70000 ns V, C1' Cl ns 60000 - C1' 50000 / ✓ • • jY .... •·•· .. ...... . • ••• • -•·· • · · · · · .......... ...... _. .......... ♦ ............ ....... .. . 1 2 3 4 5 6 7 8 9 1 0 11 12 1 3 14 15 16 1 7 18 1 9 20 21 22 23 24 25 26 27 28 29 30 Step 1 - - - - - • - - - - 200 3-200 4 - - • - - 201 2- 201 3 201 6-2 01 7 Figure 4. Averag e salary levels. FTE- weighted. Taken from J-90 data files. 136 Figure 5 - The Distribution of Salary Schedule Frontloading Cl) t5 ·c Cl Q) 0) cu C Q) CJ I.... Q) 0... ''J 1 .0 0.5 0.0 I -100 -50 0 50 1 00 m_ , _ -___:::- _ vs __.___,__ ____ =============== ======� .- � 0 20 40 60 80 100 �rn- . -=::- -=- -� -�-- � - .....:::::::- _ -_ -__, _ _ --1 ____.___ _ _ , I� 10 12 1 4 16 18 Percentage Fif!ur e 5. Distribution of fro ntlo ading measures for California dist ricts in 201 6-2017. N = 758 . Vertical lines ind icate value at which schedules ar e neit her frontloaded nor backlo aded by a given measure. The REP is the extent to wh ich the fi rst 1 0 raises on the salary schedu le are larger than th e second 1 0, exp ressed as a percentage of the first 1 0. The 5-year measure is the percentage of all raises between steps 1 and 30 that accumulate in the first 5 raises. The G in i measur e is the the percentage of aggregate salary earned across all 30 steps earn ed across the first 5 steps. For details about fr o ntlo ading measures, see Table 1 . 137 Figure 6 - The Distribution of Salary Schedule Frontloading (Standardized) 50 w 40 CJ ·c o 30 Q) CJ) .S 20 C Q) � Q) o.. 10 0 -8 -6 Backloaded Frontloaded -4 REP -2 0 2 Standard Deviations 5-Year 4 6 8 Gi ni l Figure 6. Distribution of standardiz ed fro ntlo ading measures for Calif ornia dist ricts in 20 16-201 7. N = 758. Meas ures are stand ardized to have a stand ard deviation and centered so that a value of zero indicates a sdi edule that is n either fr ontloaded nor backloaded . The REP is the extent to which the first 1 0 raises o n the salary sdi edule are larger than the second 10 , expressed as a percenta9e of the firs t 10. Th e 5-year measure is t percentage of all raises bet ween steps 1 an d 30 that accumulate in the first 5 raises. The Gin i measure 1s the the percentage of aggregate salary earned across all 30 steps ear ned across the fi rst 5 steps. Fo r details abo ut frontload ing meas u res, see Table 1 . 138 Figure 7 - Changes in Average Salaries at Various Steps � 2 ta ni V, Q> 0 C) ta I.. Q> � -2 ta Q> 0:: C: -4 Q> C) C: ta -6 � 0 Q> C) ta -8 - C: Q> (J I.. � -1 0 Recession St art 1 04- 05 06-07 Step 1 I !I · .. I · • �- � ..... , ... . '" ........... . , --- -4� \s .. ,, ... ,, .. - ,, .. ,, . .. , , ·-. \ ·. . \ -._ \ 11 -.. 08-09 10-1 1 School Year � .. . � 12-1 3 14-1 5 16-1 7 - St ep 10 ·· · · •·· · · St ep 20 - ,._ · Step 30 J Figure 7, Changes in average salaries at various steps, FTE-weighted and indexed to 2006-2007, 139 Figure 8 - Frontloading over Time ,-.. 3.0 REP Cl) C (59.9) (59 .9) (59.6) (58.8) (59.3) (57.8) (58.0) (57.9 ) (58.0 ) (58. 1 ) (58.5) (57. 1 ) (56.3) 0 2. 1 3 2.1 3 2.12 2.09 2. 1 1 2.06 2.06 2.06 2.06 2.07 2.08 2.03 2.00 :;::; 2.0 • • • • • • • • • • • • • cu "> 1 .73 1.76 1.75 1.76 1. 8 1 .76 1 .74 1 .73 1 .7 1 1 .73 1 .72 1 .73 1.71 1.68 Q) 1 . 0 (33.4) (33.6) (33 .6) (33.7) (3 .8) (33.7) (33. 5) (33.4) (33.2) (33.4) (33.3) (33 .4) (33.2) (32.9) 0 5- Year I "'O I .... 0.0 cu "'O I C 2 -1.0 I Cf) I � -2 .0 Recession Start: "'O I � - 3.0 I +:: I C 0 -4 .0 I I LL � -5 .0 Gini I cu I .... � -6.0 -5.67 -5.68 -5.66 -5.70 -5 ,j7 0 -5.72 -5.65 -5.69 -5.69 -5.71 -5.71 -5.71 -5.69 -5.71 <( (1 2.7) (12.7) ( 1 2.7) (12.7) ( 1 .7) (1 2.7) (12.7) ( 12.7) (12.7) (1 2.7) (12.7) (12.7) (12.7) ( 1 2.7) 03-04 05-06 07-08 09-1 0 11-1 2 13-14 15-16 04-05 06-07 08-09 1 0-11 12-1 3 14-1 5 16-17 School Year Figure 8. Average frontload ing over time in California d istricts. Measur es are standardized to have a unit standard devi ati on and centered so that a value of zero in dicates a schedule that is neither frontl oaded nor backloaded . Unstandardized values in parentheses . The REP is the extent to which the first 1 0 raises on the salary schedule are larger than the second 1 0, expressed as a perce ntage of the first 1 0. The 5-year measure is the percentage of all raises between steps 1 and 30 that accu mulate in the first 5 raises. The Gini measure is the percentage of all salary earn ed across all 30 steps earned across the fi rst 5 steps. For detai ls about frontloading measures, see Table 1. 140 Figure 9 - Changes in Frontloading between 2003-2004 and 2016-2017 rJ) t5 ·c 0 -1 00 -50 0 50 100 15(-40 REP -20 0 20 5-Year 40 60 -6 -4 -2 0 Gini Figure 9. Cha nges in frontload ing between 2003-2004 a nd 201 6-201 7 for California districts. Includes 659 districts observed in both years. 2 Positive (negative) values indic ate more (less) frontloadin g in 201 6-201 7 compared to 2003-2004. The REP is the extent to which the fi rst 10 raises on the sa lary sched ule are la rger tha n the second 1 0 , expressed as a percentage of the first 10. The 5-year measure is the percenta ge of all ra ises between steps 1 and 30 that accumulate in the first 5 raises. he Gini measure is the percenta ge of all salary earned across 30 step s earned across the first 5 steps. For deta ils about frontload ing measures, see Table 1. 141 Figure 10 - Distribution of Unduplicated Pupil Percentages 40 - 30 - ·.:::: cr.i 20 - 0 10 - �✓ "' 0 !� 0 ... ..... <� Jil ... 20 ,./ - . -- � iii .. - - - - - - " / .,. v - - 40 60 - "" "" .. v ... - - Unduplicated Pupil Percentage Figure 10. Un d upl icated pupil percentages i n 2016-2017 . Gray line is kern el de nsity. 142 - .... - .... ... i--- ..- � � - 1Jr - - 80 100 Figure 11 - Teacher Salaries and District Unduplicated Pupil Percentages r--. T"" 0 N I " District 130000 � 11 0000 Step 30 0 N 0 co � 90000 co ,_ co co Cl) ,_ Q) .c 70000 � 50000 � 30000 X Step 1 0 X •• • Cond itional Mean Cubic Fit X " 20 X . • ·x x· X " x "� . )( X 40 60 Unduplicated Pupil Percentage 95% CI X X 80 100 Figu re 11. Salaries for teachers with a BA and 60 units in 20 1 6-20 1 7. District marker size is proportional to FTE on sched ule . Cond itional mean marker size is proport ional to the number of d istricts represented . Salaries are adjusted using the comparable wage index. Salaries greate r than $ 1 30,000 not shown . 143 Figure 12 - Frontloading and Unduplicated Pupil Percentages 4 2 0 -2 4 2 0 -2 -4 -6 -8 0 0 0 20 20 • District 20 40 60 40 60 • Co nditiona l Mean Cubic Fit 40 60 Unduplicated Pupil Percentage 80 80 95% CI 80 1 00 1 00 1 00 :;o m "'O Figure 12. Standard ized frontloading of sa laries for teachers with a BA and 60 units in 20 16-20 17 . District marker size is proportional to FTE on sched ule . Conditional mean marker s ize is proportional to the number of d istricts represented . Values more ( less) than four standard deviations from zero not shown for the REP and 5-year measure (Gini measure). 144 Figure 13 - Regression Discontinuity Estimates of Salary Levels Over Time en '- � 0 0 20000 t-- ..... 0 N .!!!. C1l 2: 10000 a, u C a, "O 0 .;:::: C 0 u ;;R. 0 0 CJ) -1 0000 "O C C1l a, E � -20000 w 0 0::: Step 1, BA+60 Step 30, BA+60 I ◄► 0 ·� � II I• 20 13-2014 • 2014-2015 ■ 20 15-2016 ... 2016-2011 1 Figure 13 . Regression discontinuity estimates of salary levels over time. Models are estimated separately for each year, include 519 districts observed on the same side of the 55% UP threshold in all four years, and control for cubic polynomials of the UP fit separately on each side of the threshold. Salaries are adjusted using the comparable wage index. 145 Figure 14 - Regression Discontinuity Estimates of Frontloading Over Time <J QJ .!:::! <J co <J C: 1 co - if) Cl) ro .5 C: - QJ QJ 0 (.) C: QJ <J <+= -.5 C: - 0 u :::R 0 0 (j) <J C: 1 co - Ol .5 <J co .5 0 - :;::::; C: 0 0 QJ co E -.5 - -� w 0 0::: REP 5-Year ◄► � ◄► n " ·� I Gini " 0 1• ◄► I I• 20 1 3-2014 • 201 4-201 5 ■ 20 1 5-201 6 .... 20 1 6-201 7 •II> Figure 14 . Regression discontinuity estimates of frontloading over time. Models are estimated separately for each year, include 519 districts observed on the same side of the 55% UP threshold in all four years, and control for cubic polynomials of the UP fit separately on each side of the threshold. Salaries are adj usted using the comparable wage index. 146 Appendix Figure Al -T he Distribution of Raises Across Salary Schedule Steps -- en ro 0 0 0 en "'O C ro en :J 0 ..c f-- 0.. Q) +-' (/) en :J 0 "> � Cl. E 0 Q) en ro Ci::'. 10- 8 - 6- �: *. • •••••• l l l iii 1 il l . : . 1111 • .!. 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 1 8 19 20 21 22 23 24 25 26 27 28 29 30 10- 8- 6- • • .. �: • ��ft f � •• Uil i iii iii iii iL il 10 - 8- 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 1 8 19 20 21 22 23 24 25 26 27 28 29 30 . . . . : • I t �HHt . . . . . HUUilll!i 111 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 1 8 19 20 21 22 23 24 25 26 27 28 29 30 Step OJ :t> + w 0 OJ :t> + 0) 0 Figure A 1. Box plots of raises at each step of the salary schedule for Ca lifornia districts in 20 16-20 1 7 . Boxes cover the interquartile range (IQR), horizonta l lines withi n boxes indicate the median , and whiskers span va lues within 1.5 IQRs of the nearer quart i le. Raises over $10,000 not shown . 147 Figure A2 - The FTE-Weighted Distribution of Salary Schedule Frontloading Cl) t5 ·c Cl Q) 0) cu C Q) CJ I.... Q) 0... 2 0 ] 1 .5 1 .0 0.5 0.0 I -100 - ----+--1 � -� -50 0 50 1 00 m_ . _ _ l(S ___.________,__ ____ -:::... ---=-------=-------=-------=------::=....---=-------=-------=---- � . • � 0 20 40 60 80 100 i� J- . ---.----- --.-- -------.- ___._ -- , - � - �- . - 10 12 14 16 18 Percentage Figure A2. FTE-weighted distri buti o n of frontload ing measures for California d istricts in 20 1 6-201 7. N = 758 . Vertical lines ind icate value at which sched ules are neit her fr ontlo aded no r backload ed by a given measure. The REP is the ext ent to which the first 1 0 raises on the salary schedule are larger than the second 1 0, expressed as a percentage of the first 1 0. The 5-year measur e is the percentage of all raises betw een steps 1 and 30 that accumulate in the fi rst 5 raises. The Gini measure is the percentage of aggregate salary earned across all 30 steps earn ed across the fi rs t 5 st eps. Fo r d etails abo ut frontload in g measures, see Table 1 . 14 8 Figure A3 -T eacher Salaries and Unduplicated Pupil Shares without CWI Adj ustment, BA+60 ,.._ ...... 0 N <O ...... 0 N 0 <O + <( 130000 110000 90000 � cu 70000 .... Q) .c (.) cu � 50000 30000 )( District X Step 30 X X . . ')( . Step 1 0 • Conditional Mean Cubic Fit X X x x< X x.; .. • .x � � XX X 20 X X X X 40 60 Unduplicated Pupil Percentage 95% CI 80 100 Figure A3. Salaries for teachers with a BA and 60 units in 201 6-20 17. District marke r size is proportional to FTE on schedule. Conditional mean marker size is proportional to the number of districts represented . 14 9 Table Al - Salary Levels with Spatial Spillovers Using Inverse Dista nce Weighting for Geographic Proximity Ste12 1 (1) (2) Geo graphic 0.66 *** Spatial Lag (0. 06) Se rvice Center 0.7 1 *** Spatial Lag (0. 06) Natural Log 1843.35 *** 1206.60 ** of Enrollment (473.42) (454.27) 1 =Decli ning -78.73 -72.11 Enrollment (54.13) (54.29) %Hispan ic -2.23 7.75 (8.76) (8.53) %Black 4.72 19.53 (34.36) (33.95) %FRL -9.16 * -8.60 * (4.38) (4.25) Teaching 289.21 *** 274.10 *** Da�s {1 8.85 2 {1 9.32 2 Within R-sq. 0. 44 0.63 Districts 502 502 Obs ervations 45 1 8 45 1 8 Salary (20 17 Dollars) (3) (4) 0.40 *** 0.66 *** (0. 06) (0. 07) 0.5 1 *** (0. 06) 1487.4 1 ** 2546.3 1 ** (452.20) (778.07) -74.27 -272.59 ** (53.61) (91. 14) 2.79 12.18 (8.41) (14.46) 10 .11 12.19 (32.70) (76.52) -7.68 + -15.51 * (4.16) (6.66) 279.69 *** 497.28 *** {1 8.63 2 { 36.00 2 0.60 0. 42 502 502 45 1 8 45 1 8 Ste12 30 (5) (6) 0.36 *** (0 .07) 0.7 4 *** 0.57 *** (0. 06) (0 .06) 1413.66 + 1852.70 ** (723.61) (718.04) -281.30 ** -280.97 ** (89.99) (89.03) 21.28 15.30 (13.58) (13.55) 35.07 20.0 2 (75.21) (73.87) -15.99 * -14.25 * (6.40) (6.22) 460.63 *** 472.34 *** {35.99 2 {3 5.24 2 0.6 2 0.60 502 502 45 1 8 45 1 8 Note. Standard errors clustered on districts in parent heses. All models control for district and yea r fixed eff ects . Controls are me asured in the previous yea r except for service days for returning teachers . The inverse distance weighting matrix for geog raphic proximity is tru ncated to districts within 50 miles and spe ctral normalized. + p<. 1, * p<.05, ** p<.01, *** p<. 00 1 150 Table A2 - Frontloading (Standardized) with Spatial Spi llovers Usi ng Inverse Di stance Weighting Frontloading (Standardized} Geo graphic Spatial Lag Se rvice Center Spatial Lag Natural Log of Enrollment 1 =Decli ning Enrollment %Hispanic %Black ¾FRL REP 0 2 (22 (32 -0.20 -0.2 1 (0 .22) (0 .22) 0.0 2 0.0 2 (0.05) (0.05) 0.2 1 0.2 1 0.2 1 (0. 17) (0. 17) (0. 17) 0.0 1 0.0 1 0.0 1 (0 .0 1) (0 .0 1) (0 .0 1) -0.00 -0.00 -0.00 (0. 00) (0. 00) (0. 00) 0.00 0.00 0.00 (0. 00) (0. 00) (0. 00) 0.00 0.00 0.00 (0. 00) (0. 00) (0. 00) 5-Year Gini (42 (52 (62 {72 (82 (92 -0.00 0.06 0.13 0.11 (0. l 8) (0. l 8) (0 .18) (0 .19) -0.20 * -0.20 * 0.0 4 0.03 (0. 10 ) (0. 10 ) (0 .06) (0 .06) 0. 16 0.15 0.15 -0.0 1 -0.0 1 -0.0 1 (0. 16) (0. 16) (0. 16) (0. 06) (0 .06) (0 .06) 0.0 1 0.00 0.00 -0.0 1 -0.0 1 -0.0 1 (0 .0 1) (0 .0 1) (0 .0 1) (0 .0 1) (0 .01) (0 .01) -0.00 -0.00 -0.00 0.00 0.00 0.00 (0. 00) (0. 00) (0. 00) (0. 00) (0 .00) (0 .00) 0.0 1 0.0 1 0.0 1 0.00 0.00 0.00 (0 .0 1) (0 .0 1) (0 .0 1) (0 .0 1) (0 .01) (0 .01) -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 (0. 00) (0. 00) (0. 00) (0. 00) (0 .00) (0 .00) Teaching -0.00 -0.00 -0.00 0.00 0.00 -0.00 -0.00 -0.00 -0.00 Days (0.00 2 (0.00 2 (0.00 2 (0.00 2 (0.00 2 (0.00 2 (0.00 2 (0.00 2 (0.00 2 Within R-sq. O.ol 0.0 1 0.0 1 0.0 1 0.0 1 0.0 1 0.00 0.00 0.00 Districts 502 502 502 502 502 502 502 502 502 Obs ervations 4518 4518 4518 4518 4518 4518 4518 4518 4518 Note. Standard errors clustered on districts in parent heses. All models control for district and yea r fixed eff ects . Controls are me asured in the previous yea r except for service days for returning teachers . The inverse distance weighting matrix for geog raphic proximity is tru ncated to districts within 50 miles and spe ctral normalized. + p<. l, * p<.05, ** p<.01, *** p<.00 1 151 Table A3 - Salary Sched ule Structure with Spatial Spillovers with District -Specific Quadratic Time Trends Salary Frontloading (20 17 Dollars) (Standardized) Step 1 Step 30 REP 5-Year Gini {1 2 { 22 { 32 { 42 { 52 Geo graphic Spatial Lag 0.28 * 0.16 *** 0.06 -0.0 1 -0.0 2 (0. 12) (0 .0 4) (0.05) (0. 14) (0 .07) Se rvice Center Spatial Lag 0.65 *** 0.66 *** 0.0 2 -0.95 0.07 (0. 06) (0. 06) (0.27) (1.57) (0 .91) Natural Log of Enrollment -3827.62 * 986.05 -0. 14 + -0.3 1 -0.4 1 (1789.32) (10 43.12) (0. 09) (0. 47) (0 .54) 1 =Decli ning Enrollment -161.69 + -167.59 * -0.00 -0.0 1 -0.0 1 (87.26) (71 .97) (0 .0 1) (0 .0 2) (0 .03) %Hispanic -8.57 1.96 -0.00 -0.0 2 -0.00 (10.9 0) (1 1 .68) (0. 00) (0 .03) (0 .01) %Black -28.09 -122.56 + 0.0 1 0.0 4 0.0 1 (39.58) (64.20) (0 .0 1) (0. 06) (0 .01) ¾FRL 3.00 0.70 0.00 0.00 0.00 (3.25) (5.23) (0. 00) (0 .0 1) (0 .00) Teaching Days 224.35 *** 425.15 *** -0.00 -0.0 2 -0.00 {24.462 {3 2.81} {0.0 1} {0.0 42 {0.00 2 Within R-sq. 0.33 0.29 0.00 0.00 0.00 Districts 502 502 502 502 502 Obs ervations 4518 4518 4518 4518 4518 Note. Standard errors clustered on districts in parent heses. All models control for district and yea r fixed effects and district- specific quadratic time trends. Controls are me asured in the previous year except for service days for returning teache rs. + p<. 1, * p<.05, ** p<.01, *** p<. 00 1 152 Table A4 - Salary Schedule Structure with Spatial Spillovers (Spatial Durbin Models) Sa lary Frontloading (20 17 Dollars) (Standardized ) Step I Step 30 REP 5-Y ear Gini {12 { 2 2 {32 { 4 2 { 5 2 Geographic Spatial Lag Outcome 0. 19'" 0. 16'" 0.0 3 0.0 3 -0. 13' (0.0 4) (0.03) (0.03) (0.0 2 ) (0.05 ) Natural Log -2101 .49 + -2604 .83 -0.07 -0.05 0.01 of Enrollment ( 1208. 17) ( 16 40.48 ) (0.2 2 ) (0.23) (0. 17) l = Declining -68.57 -1 2.79 0.01 0.0 0 -0. 01 Enrollment (11 7.06 ) (179.94) (0.0 2 ) (0.0 2 ) (0.0 2 ) %Hispanic 44.92' 37.42 0.0 0 0.0 0 0.0 0 (21 .04) (29 .91) (0.0 0 ) (0.0 0 ) (0.0 0 ) %Black 88.15 151. 09 0.0 0 0.0 0 0.01 (61.69) (96.37) (0.01 ) (0.01 ) (0.01 ) ¾FRL -8.53 -29.5r 0.0 0 0.0 0 0.0 0 (8.65 ) (15 .27) (0.0 0 ) (0.0 0 ) (0.0 0 ) Teaching -2.43 49.59 -0.00 0.0 0 -0.00 Days (32.28 ) (55 .06 ) (0.0 0 ) (0.0 0 ) (0.0 0 ) Service Center Spatial Lag Outcome 0.6 4'" 0.68'" -0.0 2 -0.29' -0. 01 (0.0 6) (0.0 6) (0.0 6) (0. 12) (0.0 7) Natural Log 781.84 136 2.37 -0.0 2 -0.45 -0. 17 of Enrollment (1926.30 ) (3029 .52) (0.2 9) (0.38 ) (0.3 1) ! = Declining 11 4.42 393.94 -0.03 -0.0 4 -0. 01 Enrollment (256.0 3) (446.15 ) (0.0 4) (0.05 ) (0.0 4) %Hispanic -32.45 -9.00 -0. 01 -0. 01 + -0. 01 (37.23 ) (68.13) (0.01 ) (0.01 ) (0.0 0 ) %Black -3 3.85 -7 2.71 0.01 0.0 0 0.0 2 (185.21) (282.0 4) (0.0 4) (0.03) (0.0 2 ) ¾FRL -3 .90 18.77 -0.00 -0. 01 -0 .01' (18.57 ) (33.08 ) (0.0 0 ) (0.0 0 ) (0.0 0 ) Teaching -14 5.26' -300.08' 0.0 0 -0.00 0.0 0 Da ys (69.16 ) (136.0 0 ) (0.01 ) (0.01 ) (0.01 ) Within R- sq. 0.6 2 0.6 2 0.01 0.01 0.0 0 Districts 502 502 502 502 502 Observations 4518 4518 4518 4518 4518 Note. Standard errors clustered on districts in parentheses. All models control for district and year fixed effects and th e district's own values of time-varying predictors. Controls are measured in th e previous year except for service days for returning teache rs. + p<. l , * p<. 05, ** p<.0 1, *** p<. 00 1 153 Table A5 - Parametric Regression Discontinuity Estimates of Salary Schedule Structure without CWI Adju stment (I ) (2) (3) (4) (5) (6) (7) (8) (9) (1 0 ) (1 1 ) (1 2 ) Salaries (Thousands o/ 2 0 17 Dolla rs) Step 1 Salary, -0.7 48 -3 .522" -3 .0 84 + -2.383 + -1 .928' -3 .686' -2.891 -1 .935 -3 .403 ' -1 .285 -0.534 0. 416 BA+60 (0. 866) (1.273 ) (1.697) (1.432 ) (0. 967) (1.469) (1.959 ) (1.632 ) (1.466) (2.257 ) (2.79 1) (2.341 ) Step 30 Salary, BA+60 -3 .964* -1 0.208 *** -9. 520 * - 7.929 ** -6.4 96** -10.19 2 ** -11. 188* -8.47 1 ** -1 0.57 4 ** - 7.917 -12 . 11 l + - 7. 746 (1.982 ) (2. 897) (3.843) (2.8 48) (2.232 ) (3.2 97) (4.365 ) (3.262 ) (3.325) (5.15 6) (7.0 16 ) (5.0 90 ) Fron tloading (Standardi zed) REP, 0 .19 0 .04 0 .14 0 .23 0 .15 0 .0 2 0 .27 0.40 0 .22 -0 .07 -0 .32 -0 .23 BA+60 (0. 16 ) (0.23) (0.3 1) (0.3 1) (0. 17 ) (0.26 ) (0.36 ) (0.36 ) (0.26 ) (0.43 ) (0. 57) (0.58 ) 5- Year, 0.05 0.01 0.23 0.27 0.0 2 0.0 7 0.50 0.53 0.27 0.37 0. 16 0. 19 BA+60 (0. 16 ) (0.23) (0.30 ) (0.30 ) (0. 18) (0.26 ) (0.34 ) (0.35 ) (0.25 ) (0.41 ) (0.54 ) (0.56 ) Gini, 0,32 + 0.5 2' 0.4 4 0.40 0.40' 0.4 4 0.75' 0.61 + 0. 61' 0.66 1.42' 1.05 + BA+60 (0. 16 ) (0.2 4) (0.33 ) (0.30 ) (0. 19 ) (0.28 ) (0.38 ) (0.35 ) (0.28 ) (0.4 7) (0.65 ) (0.58 ) Controls X X X Bandwidth 55 55 55 55 35 35 35 35 15 15 15 15 Degree of Polynomial I 2 3 3 1 2 3 3 1 2 3 3 Districts 681 681 681 680 560 560 560 559 244 244 244 244 Note. Heteroskedasticity-robust standard errors in parentheses. Contro ls, when present, include th e natural log of district enrollment; whether the district has declining enrollment; the shares of district students who are Black, Hispanic, and eligible for free or reduced-price lunch; and the number of teaching days in the year. All control variables are measured in th e previous year except for number of teaching days. + p<. l , * p<.05, ** p<.0 1, *** p<. 00 1 154 Table A6 - Nonparametric Regression Discontinuity Estimates of Salary Schedule Features Sa laries ( Thousands of 20 17 Dollars ) Frontloadin g (Standardized ) Step l Step 30 REP 5- Year Gini BA +60 (l) (2) (3) (4) (5) (6) (7) (8) (9) (10) Robust RD 1.514 2.2 2 1 -6.9 96 -5.0 03 0. 139 -0.326 0.430 0. 15 4 0. 890 + 0_955 + Estimate (3 .184 ) ( 3.643 ) (5.148 ) (7 .472 ) (0 .368 ) (0 .559 ) (0 .384 ) ( 0.530 ) ( 0.525 ) (0 .528 ) Order of Local Polynomial 1 2 I 2 I 2 1 2 1 2 BandwidthBelow Cutoff 12.77 16.46 19.06 17.14 15. 23 14.13 12.19 14.44 10 .88 21 .02 Observations Below Cutoff 95 121 148 128 11 4 10 6 89 10 9 82 15 3 Bandwid th Ab ove Cutoff 12.77 16.46 19.06 17.14 15. 23 14.13 12.19 14.44 10 .88 21 .02 Observations Above Cutoff 111 148 17 4 15 0 132 121 10 3 125 91 19 0 Note. Heteroskedasticity-robust standard errors in parent heses. Local polynomials are constructed using triangular kernel weights and bandwidth s sel ected to optimize mean square error of th e resulting point estimate s. Point estimates are bias-co rrected using local quadratic regre ssi on. Estimates are obtained using the rdrobu st command in Stata (Calonico, Catta neo, Farrell, & Titiunik, 20 l 7). Salaries are adjusted using the comparable wage index . + p<. l, * p<.05, ** p<.01, *** p<.00 1 155 Table A 7 - Student Achievement as a Function of Salary Schedule Structure with District- Specific Cubic Time Trends Math English/L anguage Arts %age Proficient Standardized Score %age Proficient Standardized Score {1 2 { 2 2 { 3 2 { 4 2 { 5 2 { 6 2 { 7 2 { 8 2 { 9 2 { 10 2 { 11 2 { 12 2 Step 1 Salary 0.03 0.0 2 0.03 0.00 0.00 0.00 -0.00 -0.00 -0.0 1 -0.00 -0.00 -0.00 (Thousa nds) (0.08) (0. 09) (0.08) (0. 00) (0. 00) (0. 00) (0.05) (0 .06) (0 .05) (0 .00) (0 .00) (0. 00) REP -0. 13 -0.0 1 0. 22 0.0 2 (0.29) (0 .0 1) (0.28) (0 .01) 5-Year -0. 10 -0.0 1 0.0 2 0.0 1 Loading (0 .30 ) (0 .0 1) (0 .25) (0 .01) Gini -0.0 1 -0.00 0. 12 0.0 1 Loading { 0.40 2 { 0.0 2 2 { 0.26 2 { 0.01 2 Adj. R-sq. 0.95 0.95 0.95 0.95 0.95 0.95 0.97 0.97 0.97 0.97 0.97 0.97 Districts 872 872 872 872 872 872 873 873 873 873 873 873 Obs ervations 9208 9208 9208 9208 9208 9208 9213 9213 9213 9213 9213 9213 Note. Standard errors clustered on districts in parent heses. Frontloading measure s have a standard deviation of one across all districts and yea rs. All models control for the natural log of district enrollment; whether the district has declining enrollment; the shares of district students who are Black, Hispa nic, English lea rne rs, and eligible for free or red uced -price lunch and specia l education servic es; the number of teaching days in the yea r; district and labor market-by-year fix ed eff ects ; and district- specific cubic time trends. Salaries are expre ssed in thousands of 20 17 dolla rs. Standardized scores are mean sca le scores standardized to have a unit standard deviation across districts each yea r. + p<. l, * p<.05, ** p<.01, *** p<.00 1 156 - Table A8 - Predicting the Percentage of Newly Hired Teachers without a Full Credential Controlling for Step 30 Salary Step l Salary (Thousands ) Step l Salary x Creditable Prior Experience Step 30 Sa lary (Thousands ) REP REP x Creditable Prior Experience 5- Year Loading 5- Year x Creditable Prior Experience Gini Loading Gini x Creditable Prior Experience Max. Creditable Prior Experience District FE Lagged DV Adj . R- sq. Districts Observations Math, Science, or Special Education ( 1 ) (2 ) (3 ) (4 ) ( 5 ) (6 ) (7 ) ( 8 ) ( 9 ) 0.47 -0. 16 -0. 15 0.38 -0. 16 -0. 16 0.01 -0.06 0. 13 (0.51 ) (0. 14) (0. 18) (0.50 ) (0. 14) (0. 18) (0.7 2 ) (0.26 ) (0.30 ) -0.00 (0.01 ) 0.0 0 (0.01 ) -0.0 2 + (0.01 ) Other (1 0 ) (1 1 ) ( 12 ) (13 ) (1 4 ) (15 ) 0.80 ** -0. 11 -0.2 1 + 0.80 ** -0.09 -0. 19 (0.26 ) (0.09 ) (0.12 ) (0.26 ) (0.09 ) (0.12 ) 0.01 (0.01 ) 0.01 (0.01 ) (1 6 ) (1 7) (1 8 ) 0.6 0 -0.2 2 -0.27 (0.41 ) (0. 17 ) (0.20 ) -0.00 (0.01 ) -0. 16 -0. 15 + -0. 15 + -0.09 -0. 16' -0. 16' 0. 11 -0. 17 -0. 15 -0. 13 -0.06 -0.06 -0. 16 -0.09 + -0.08 0.0 3 0.0 3 0.05 (0.26 ) (0.08 ) (0.08 ) (0.2 7) (0.08 ) (0.08 ) (0.39 ) (0. 15 ) (0. 15 ) (0. 14) (0.05 ) (0.05 ) (0. 15 ) (0.05 ) (0.05 ) (0.2 2 ) (0. 10 ) (0. 10 ) -2.18 -2.22··· -l.1 4 (1.85) (0.6 4) (1.05 ) 0.0 3 -0.09 -0. 10 (0.0 7) 0. 15 -0.90 -2.28'" -1 .47 (1.58) (0.6 0 ) (0.95 ) 0.0 3 -0.09 -0.08 (0.0 6) 0.01 0. 12 -l.74 -1 .72 (3.33) (1.29 ) (1.41) 0.01 (0.0 7) 0.0 3 -0.07 0.45 (0. 11 ) (0. 06) (0. 62) (0. 11 ) (0. 06) (0.59) (0. 11 ) (0. 06) (0. 47) X X X X X X X X X 0.25 0. 18 0. 19 0.25 0. 19 0. 19 0.25 0. 18 0. 18 622 622 622 622 622 622 622 622 622 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 415 6 -0.88 -0.89 * -l.80 * (1.1 6) (0.43 ) (0.71 ) -0. 01 0.08 (0.05 ) 0.00 -0.6 4 + -1.04 -1 .22" -1 .96" (1.20 ) (0.37 ) (0.63 ) -0.01 -0.00 0.07 (0.05 ) -0.57 (0.08 ) (0.05 ) (0.37) (0.08 ) (0.05 ) (0.38 ) X X X X X X 0.43 0.34 0.34 0.43 0.34 0.34 622 622 622 622 622 622 415 6 415 6 415 6 415 6 415 6 415 6 0.9 9 0.28 -1 .47 (1.87) (0.9 0 ) (1.03 ) 0. 18** (0. 06) -0. 01 0.01 I. 10' (0. 09) (0.05 ) (0.45 ) X 0.4 3 622 415 6 X 0.34 622 415 6 X 0.34 622 415 6 Note. Standard errors clustered on districts in parent heses. Frontloading measures have a standard deviation of one across all districts and years. The outcome is the percentage of newly hired teachers in the district that lack a full credential, and models are estimated separately for teachers with math, science, or specia l education teachers ( columns 1- 9) and all other teachers ( columns 10 -18 ). All models control for the natural log of district enrollment; whether the district has declining enrollment; the shares of district students who are Black, Hispa nic, English learners, and eligible for free or reduced-price lunch and specia l education services; the number of teaching days in the year; and labor market by-year fi xed eff ects. Salaries are expressed in thousands of 20 17 dollars. Salaries are centered at $30,000 and frontloading measures are centered at zero such that in the models with interactions the coeffic ient on maximum creditable prior experience can be interpreted as the relationship between creditab le prior experience and the outcome when starting salaries are $30,000 (roughly the minimum typically observed in California during this time) and the salary schedule is neither frontloaded nor backloaded. + p<.l, * p<.05, ** p<.01, *** p<.00 1 Table A9 - Achievement as a Function of Salary Schedule Structure, Quadratic Models Step 1 Salary Thousands REP REP 2 5- Year Loading 5- Year 2 Gini Loading Math English/Lang uage Arts __ o/o_ a _ g _ e _ P _ ro _ fi _ ci _ e _ nt __ S _ ta _ n _ da _ r _ di _ ze _ d _ S _ c _ o _ re ___ o/c _o � ag � e _ P _ r _ o fi_, c _ ie _ n _ t _ Standardized Score ( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) ( 7 ) ( 8 ) ( 9 ) ( 10 ) ( 11 ) ( 12 ) 0.20· 0. 21· 0_ 14 + 0.01 * 0.01 * 0.01 0.0 9 0. 10 + 0.06 0.01 + 0.01 + 0.00 (0.0 9) (0.0 9) (0.08 ) (0.0 0 ) (0.0 0 ) (0.0 0 ) (0.0 6) (0.0 6) (0.06 ) (0.00 ) (0.00 ) (0.00 ) 1.38* (0.6 9) -0.2 2 (0. 19 ) 1 _ 15 + (0. 59) -0. 14 + (0.0 7) -3 .81 * ( 1.69) o.or (0.0 4) -0. 01 (0.01 ) 0.0 4 (0.03) -0.00 (0.0 0 ) -0. 17 * (0.0 9) 1.36'' (0.46 ) -0.2 4 + (0.13) 0.35 (0.51 ) -0.03 (0.0 7) -1 .68 ( 1.41) 0.06" (0.0 2 ) -0.01 + (0.01 ) 0.0 2 (0.0 2 ) -0.00 (0.00 ) -0.07 (0.06 ) Gini 2 -0.4 4' -0.0 2' -0.20 -0.01 ( 0. 19 ) ( 0.01 ) ( 0.14 ) ( 0.01 ) Adj . R- sq. 0.9 0 0.9 0 0.9 0 0.88 0.88 0.88 0.9 3 0.9 3 0.93 0.9 4 0.9 4 0.9 4 Districts 872 872 872 872 872 872 873 873 873 873 873 873 Observations 9208 9208 9208 9208 9208 9208 92 13 92 13 92 13 92 13 92 13 92 13 Note. Standard errors clustered on districts in parent heses. Frontloading measure s have a standard deviation of one across all districts and yea rs. All models control for the natural log of district enrollment; whether the district has declining enrollment; the shares of district students who are Black, Hispa nic, English learners, and eligible for free or red uced -price lunch and specia l education servic es; the number of teaching days in the yea r; and district and labor market-by-year fix ed eff ects . Salaries are expre ssed in thousands of2017 dolla rs. Standardized scores are distric ts ' mean sca le scores standardized to have a unit standard deviation across districts each yea r. Frontloading me asures are centered at zero such the main effect of frontloading measures be interpreted as the relationship between frontloading th e outcome when th e salary schedule is neither frontloaded nor backloade d. + p<. l, * p<.05, ** p<.01, *** p<.00 1 15 8 Table A 10 - Resource Allocation Measures as a Function of Salary Schedule Structure, Quadratic Models Per-Pu12il S12ending {Inverse H�12erb olic Si ne} Step 30 Certifi cated Health & Sa lar� {Thousands } All O12era tional Teacher Sa laries Teacher Pensions Welfare General Administration {I l {2 } {3} (4) (5 ) (6) (7) (8) (9) (1 0 ) (1 1) (1 2 ) {1 3} {1 4} {1 5 } {1 6} {1 7} {1 8} Step l Salary 1.085 *** 1.067 *** l.461 *** 0.0 lo *** 0. 01 1 *** 0.012 *** 0.0 15 *** 0.0 15 *** 0.0 16*** 0.0 15 *** 0.0 15 *** 0.0 16*** 0. 004 0. 004 0.0 05 0.0 08 *** 0.0 08 *** 0.0 09 *** (Thousands ) (0.083 ) (0.0 91) (0.0 60 ) (0.0 0 1) (0.0 0 1) (0.0 0 1) (0.0 0 1) (0.0 0 I) (0.0 0 I) (0.0 0 l) (0.00 1) (0.00 l) (0.0 03 ) (0.0 03 ) (0.0 04 ) (0.0 02 ) (0.0 02 ) (0.0 02 ) REP -1 .393*** 0.0 06 0. 01 1 0.012 0.0 26 -0.0 07 (0.345 ) (0. 009) (0.0 08 ) (0. 009) (0.0 24 ) (0.0 10 ) R£ p 2 -0.608''' -0.0 03 -0.0 03 -0. 002 -0.0 12 -0.0 00 (0. 101 ) (0.0 03 ) (0.0 03 ) (0.0 03 ) (0.008 ) (0.0 03 ) 5- Year -2.842 *** 0.0 13 + 0.0 26 ** 0.039 *** 0.005 -0.0 15 - Loading (0.488 ) (0.0 08 ) (0. 009) (0.0 09) (0.0 23 ) (0.014 ) 5- Year 2 0.0 93 -0. 002' -0. 004' -0.005 '" -0.00 1 0.0 03 + (0. 079) (0.0 0 1) (0.0 02 ) (0. 002 ) (0.0 03 ) (0.0 02 ) Gini -2.540'" 0.0 21 -0.0 26 -0.0 29 0.0 23 0.0 72" Loading (0.7 00 ) (0.0 37) (0.0 47) (0.0 44) (0.0 49) (0.0 25) Gini 2 0.386 *** 0.0 04 -0.0 00 -0.0 00 0.0 04 0.0 08 ** {0.0 73} {0.0 03 } {0. 004} {0. 004} {0. 007 } {0.0 03 } Adj . R- sq. 0.98 0.98 0.9 9 0.9 2 0.9 2 0.9 2 0.87 0.87 0.87 0.91 0.91 0.91 0.85 0.85 0.85 0.9 0 0.9 0 0.9 0 Districts 910 910 910 910 910 910 910 910 910 910 910 910 910 910 910 910 910 910 Observations 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 1017 5 Note. Standard errors clustered on districts in parent heses. Frontloading measures have a standard deviation of one across all districts and years. All models control for the natural log of district enrollment; whether the district has decli ning enrollment; the shares of district students who are Black, Hispanic, English learners, and eligible for free or reduced-price lunch and specia l education services; the number of teaching days in the year; and district and labor market-by-year fi xed eff ects. Sa laries are expressed in thousands of 20 17 dollars. Frontloading measures are centered at zero such that the main effect of frontloading measures can be interpreted as the relationship between frontloading and the outcome when the salary schedule is neither frontloaded nor backloaded. + p<.I, * p<.05, ** p<.01, *** p<.00 1

Abstract (if available)

Abstract Most teachers are paid according to salary schedules in which teachers are placed in “lanes” based on their education level and advance up “steps” of their lane as they accumulate experience. In theory salary schedules that are “frontloaded,” letting teachers attain the highest salaries quickly, allow districts to more effectively recruit and retain teachers. However, little empirical evidence supports that proposition and it is unclear why, if frontloaded schedules are more effective, backloaded schedules remain common. I extend this literature using a 14-years of district-level data from California, including detailed data on the contents of districts’ contracts with their teachers’ unions and the composition of their salary schedules. These data allow me to (i) assess the prevalence of teacher salary schedule frontloading, (ii) test theoretical explanations for salary frontloadedness, and (iii) evaluate the relationship between salary frontloadedness and districts’ hiring outcomes, student achievement, and spending patterns. While teacher salary schedules in California are heavily frontloaded in how they distribute annual raises, they vary substantially in their degree of frontloadedness. I find no evidence supporting common theoretical arguments that backloaded salary schedules are the result of teachers’ union influence or administrators’ inability to monitor teacher performance effectively. Instead, frontloading appears to be driven at least in part by competition for new teachers. Indeed, frontloaded salary schedules appear to be helpful in recruiting better-credentialed teachers, though they also appear costly for districts and are not associated with improved student achievement. These findings contribute to our understanding of teacher labor markets and of administrative dynamics in districts. Given their ubiquity, understanding the economics and politics of teacher salary schedules is important to effective policymaking.

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Asset Metadata

Creator Bruno, Paul (author)

Core Title Loaded questions: the prevalence, causes, and consequences of teacher salary schedule frontloading

School Rossier School of Education

Degree Doctor of Philosophy

Degree Program Urban Education Policy

Publication Date 06/02/2020

Defense Date 04/22/2020

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag OAI-PMH Harvest,teacher compensation,teacher labor markets,teachers’ unions

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Polikoff, Morgan (committee chair), Strunk, Katharine (committee chair), Goldhaber, Dan (committee member), McCarthy, TJ (committee member)

Creator Email paulbruno@gmail.com,pbruno@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-314699

Unique identifier UC11663373

Identifier etd-BrunoPaul-8560.pdf (filename),usctheses-c89-314699 (legacy record id)

Legacy Identifier etd-BrunoPaul-8560.pdf

Dmrecord 314699

Document Type Dissertation

Rights Bruno, Paul

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA