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Children’s travel behavior in journeys to school

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Children’s travel behavior in journeys to school

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Content CHILDREN’S TRAVEL BEHAVIOR IN JOURNEYS TO SCHOOL by Sylvia Ying He A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (POLICY, PLANNING AND DEVELOPMENT) August 2012 Copyright 2012 Sylvia Ying He ii ACKNOWLEDGEMENTS This dissertation has been funded by the Eisenhower Transportation Fellowship from the U.S. Department of Transportation and USC Dissertation Completion Fellowship. My transformation from student to scholar has been an exciting and fruitful journey, yet completing my doctorate is just the beginning of another voyage. I owe my greatest gratitude to my dissertation committee. In particular, I am indebted to my adviser, Prof. Genevieve Giuliano, for having taught me to be critical and to dare to challenge the conventional notions, an attitude that I will keep for the rest of my academic life. I would like to thank my mentor, Prof. Harry Richardson, who has provided me a great opportunity to be his teaching assistant and shown me what excellence in teaching really means. I thank Prof. Chris Redfearn for having pushed me hard to search for an engaging research topic and innovative research methods. I appreciate the valuable time from Prof. Geert Ridder, who has suggested many useful econometric methods and helped me improve my modeling skills. Many faculty and staff members at USC have inspired me. I would especially like to thank James Moore, Lisa Schweitzer, MaryAnn Murphy, Marlon Boarnet, Vivian Wu, and Terry Cooper. They have shown me how to conduct research, to present at seminars, to write academic articles, to think philosophically, and to self reflect. The doctoral program has been joyful because of the company of my colleagues, friends, and family. In particular, I am grateful to my wonderful colleagues from USC and McMaster: Darren Scott, Ellen Shiau, Ajay Agarwal, Ruben Mercado, Karen King, and Lingqian Hu. They have lent me their ears and offered their help when I needed them the most. Lastly, a heartfelt thank you goes to my parents. My graduate studies would have not been possible without their great support and understanding. This dissertation is dedicated to them for their endless love and encouragement. iii TABLE OF CONTENTS ACKNOWLEDGEMENTS ......................................................................................................... ii LIST OF TABLES ....................................................................................................................... v LIST OF FIGURES ................................................................................................................... vii ABSTRACT... ............................................................................................................................ viii CHAPTER 1 INTRODUCTION ................................................................................................ 1 1.1 Motivations .................................................................................................................... 1 1.2 Land Price and School Quality ....................................................................................... 4 1.3 School Choice and Site-Based Management .................................................................. 6 1.4 Implementation of School Choice Policy ....................................................................... 8 1.5 Travel Behaviors under School Choice Policy ............................................................... 9 1.6 Significance and Contributions .................................................................................... 12 1.7 Dissertation Structure ................................................................................................... 14 1.7.1 Essay one: How much do parents pay for school quality? .................................... 14 1.7.2 Essay two: Are parents willing to incur longer trips for better school quality? .... 15 1.7.3 Essay three: Do parental work arrangements and location affect a child’s journey to school? ............................................................................................................. 17 Chapter 1 References ............................................................................................................... 19 CHAPTER 2 HOW MUCH DO PARENTS PAY FOR SCHOOL QUALITY? .................. 24 2.1 Introduction .................................................................................................................. 24 2.2 Literature Review ......................................................................................................... 27 2.3 Methodology and Model Specification ........................................................................ 30 2.3.1 Multilevel estimation of hedonic price: A three-level model ................................ 31 2.3.2 Model specification .............................................................................................. 35 2.4 Study Area and Descriptive Analysis ........................................................................... 39 2.5 Results .......................................................................................................................... 43 2.6 Conclusion ................................................................................................................... 53 Chapter 2 References ............................................................................................................... 56 CHAPTER 3 ARE PARENTS WILLING TO INCUR LONGER TRIPS FOR BETTER SCHOOL QUALITY? ....................................................................................... 61 3.1 Introduction .................................................................................................................. 61 3.2 Literature Review ......................................................................................................... 63 3.3 Data and Methodology ................................................................................................. 66 3.3.1 Data sources ......................................................................................................... 66 3.3.2 Methodology ........................................................................................................ 68 3.4 Models ......................................................................................................................... 74 3.4.1 Model specification .............................................................................................. 74 3.4.2 Selection of variables ........................................................................................... 77 3.4.3 Descriptive analysis .............................................................................................. 85 iv 3.5 Results .......................................................................................................................... 88 3.6 Conclusion ................................................................................................................... 94 Chapter 3 References ............................................................................................................... 98 CHAPTER 4 DO PARENTAL WORK ARRANGEMENTS AND LOCATION INFLUENCE A CHILD’S JOURNEY TO SCHOOL? ................................ 102 4.1 Introduction ................................................................................................................ 102 4.2 Theoretical Framework and Empirics ........................................................................ 104 4.2.1 Theoretical framework of time geography.......................................................... 104 4.2.2 Empirics of temporal synchronization and spatial coordination ......................... 105 4.3 Methodology .............................................................................................................. 107 4.3.1 Study area and data............................................................................................. 107 4.3.2 Defining escort-mode (EM) choices ................................................................... 110 4.4 Models ....................................................................................................................... 115 4.5 Results ........................................................................................................................ 124 4.6 Conclusion ................................................................................................................. 129 Chapter 4 References ............................................................................................................. 132 CHAPTER 5 CONCLUSION ................................................................................................. 135 Chapter 5 References ............................................................................................................. 142 COMPREHENSIVE REFERENCES .................................................................................... 143 v LIST OF TABLES Table 1.1: Arguments for and against school choice ...................................................................... 8 Table 1.2: School choice and travel distance (median) ................................................................ 12 Table 2.1: Three-level data in the research setting of school capitalization study ........................ 35 Table 2.2: Variable definitions and data Sources ......................................................................... 38 Table 2.3: Summary of house price and school statistics of 24 school districts in Orange County (in order of house price) ............................................................................................. 42 Table 2.4: Results of ANOVA analysis ....................................................................................... 43 Table 2.5: Statistic summary of variables (N=30,699) ................................................................. 44 Table 2.6: Comparison of results from OLS and multilevel estimation (N=30,669) (standard errors in parenthesis) .................................................................................................. 49 Table 2.7: t test on the equality of means of estimates from multilevel and OLS estimation ....... 50 Table 2.8: Results from multilevel analysis with random coefficient of the test score ................. 51 Table 2.9: Premiums of test score at district level ........................................................................ 53 Table 3.1: Summary of the size of choice sets ............................................................................. 73 Table 3.2: Variable definitions ..................................................................................................... 76 Table 3.3: Proportion of neighborhood schools, nearest schools, and out-of-district schools actually chosen ........................................................................................................... 78 Table 3.4: Test scores for school districts .................................................................................... 80 Table 3.5: Summary of school density (number of schools within 10 mile radius from home).... 82 Table 3.6: Summary of selective household mobility indicators of students attending K-12 public schools ....................................................................................................................... 84 Table 3.7: Descriptive analysis: the attributes of the chosen alternatives and the decision makers ................................................................................................................................... 87 Table 3.8: Estimation results for school destination choice models ............................................. 92 Table 4.1: Escort decision by household structure ..................................................................... 109 vi Table 4.2: Escort-mode decision analysis (row percentage in brackets) .................................... 111 Table 4.3: Escort-mode choice alternatives, by household type ................................................. 114 Table 4.4: Definition of variables .............................................................................................. 118 Table 4.5: Descriptive statistics, by household structures .......................................................... 122 Table 4.6: Estimation results for dual-earner households (Reference group: driven by mother, EM2) ........................................................................................................................ 128 vii LIST OF FIGURES Figure 1.1: Mode of arrival to school for students age 5-18, 2001 RHTS .................................... 10 Figure 1.2: Mode of travel to school by distance for students age 5-18, 2001 RHTS .................. 11 Figure 2.1: Twenty four elementary and unified school districts in Orange County .................... 39 Figure 2.2: Academic Performance Index (API) of 382 elementary schools in Orange County, 2001 ........................................................................................................................... 40 Figure 3.1: Search radius of elementary school travelers ............................................................. 72 Figure 3.2: Search radius of high school travelers........................................................................ 73 Figure 3.3: School choice and median travel distance (in mile) ................................................... 78 Figure 4.1: Mode choice summary (N=3,172) ........................................................................... 108 viii ABSTRACT Trips to school are increasingly undertaken in automobiles. While much research has been conducted regarding the neighborhood built environment and safe routes to school, very little has looked at school policies and intra-household dynamics. These factors can indeed influence children’s travel behavior in journeys to school. First, school quality is capitalized in residential house prices. Low income households often live in low-performing districts. Open enrollment allows students to transfer out of their neighborhood schools when seats are available. When these options are exercised, children living in low-performing districts may travel longer distances in order to attend good quality schools, compared to children living in high-performing districts. Secondly, at the household level, women have increased their participation in the labor market while remaining the primary caretaker of children. Their workplace location may affect their children’s escort and mode choice decision as well. Thus far, our understanding of children’s increased travel distance and reliance on automobile has largely been disconnected from the context of school choice and intra-household constraints. This dissertation links journeys to school with these institutional and household factors. In my dissertation, I examine the school quality capitalization effect in land values using hedonic pricing models, and I explain children’s travel behavior by looking at school choice and intra-household scheduling constraints using activity-based transportation models. By considering the spatial relationship between home, school, and workplace in the Los Angeles region, I answer the following questions: 1) How much do parents pay for school quality? 2) Are parents willing to incur longer trips for better school quality? and 3) Do parental work arrangements and location affect a child’s journey to school? These answers will help us understand why distance to school and car use have increased in recent decades and how school choice is connected to active commuting. 1 CHAPTER 1 INTRODUCTION 1.1 Motivations In the United States, trips to school have been increasingly undertaken in automobiles. The percentage of children age 6-12 who travel thusly has increased from 15% in 1969 to 50% in 2001. An outcome of increased travel distance and car dependency is that children miss an important part of physical exercise outside their classrooms (Tudor-Locke et al. 2001). Walking to school can be an important part of children’s daily physical activities and a complementary part of in-school physical education classes (Tudor-Locke et al. 2001). Although there is no formal study of its kind conducted in the U.S., a study based in Russia suggested that this proportion of active commuting is the primary source of physical activity, accounting for roughly between 40%-50% (Tudor-Locke et al. 2001). Moreover, it is postulated that children who are car dependent may continue this behavior into adulthood, thereby limiting their alternative travel modes (Tudor-Locke et al. 2001, Roberts 1996). With such plausible behavioral consequences, some researchers suggest that it is important to provide exposure to alternative travel mode choices at early ages (Tudor-Locke et al. 2001, McMillan 2005). Children’s increasing reliance on automobile is resulted from several social and institutional changes. First, the increasing traffic and neighborhood environment has reduced the safety for pedestrians and bicyclists (Staunton et al. 2003, Boarnet et al. 2005, Lin and Chang 2010). Second, the average distance to school has increased (Waygood and Kitamura 2009, McDonald 2008a, McMillan 2007). Approximately 75% of children traveled a mile or more to school in 2001, compared to 54.8% in 1969 (NHTS Brief 2008). This stems partially from the decentralization of activities that caused declining level of school density (Ewing et al. 2004). Third, women’s increasing participation in the labor market and the growing number of dual 2 earner households have caused more school trips embedded in the commute, which is often undertaken by car (McDonald 2008a). Fourth, school policies have changed, allowing parents to exercise the right to leave the neighborhood school (Wilson et al. 2010, Yang et al. 2012). A number of national and local school transportation programs have been implemented to address some of the aforementioned issues. For example, to address the road and personal safety issues, transportation and urban planners have endeavored to create safer and more walkable neighborhoods. Positive results from empirical studies show that children are more likely to commute “actively” (i.e., walking or biking) to school in pedestrian and bicycle friendly neighborhoods (Staunton et al. 2003, Boarnet et al. 2005, Lin and Chang 2010). Such urban form elements, nonetheless, would have less impact on children’s mode choice when other factors are included (e.g., travel distance) (Bradshaw 1995, DiGuiseppi et al. 1998, McMillan 2007, Yarlagadda and Srinivasan 2008). Among the less examined factors, school variables are one aspect that deserves further examination (Sirard and Slater 2008). Under this category is school choice policy, which allows parents to opt out their neighborhood schools. This option can directly affect travel distance because if no intradistrict and interdistrict transfers were allowed, all students attending public schools would be assigned to the neighborhood schools, implying short travel distances. Although it has been postulated that school quality and parental school choice have caused long distance trips (Bradshaw 1995), there are only limited documentations regarding the effects of these school variables on travel behavior (Ewing et al. 2004, Wilson et al. 2007, Wilson et al. 2010). Under school choice policy, school quality is not the only reason why parents opt out the neighborhood schools; rather, they may choose a school based on the proximity to their workplace. Nowadays, there are an increasing number of working mothers in the labor force. 3 Meanwhile, many of them retain the primary responsibility of child care. While full time mothers may choose the neighborhood school for proximity, the same reason is applied for working mothers. They may choose a school closer to their workplace, which could be far away from home, resulting in a longer travel distance for the children. The role of school choice policy, of course, is inseparable from the built environment and land use patterns. If there is no disparity in the spatial distribution of school quality and other characteristics, distance between the school and home would be the primary consideration in parental school choice. However, the distribution of school quality in most U.S. metropolitan areas is far from homogeneous. Under the rent bidding mechanism (Alonso 1964), rich households will bid out poor households and locate themselves in proximity to quality public schools and other public services. School choice policy is most relevant to those living in places with low quality schools because higher income households have more choices – they can go to good local schools, or even better private or charter schools. That being said, a long travel distance to school is a natural outcome of school choice policy, the design of which stems from an unequal distribution of land values and school quality. This dissertation contemplates to stitch several otherwise separate dimensions in the urban systems and to provide a fuller picture of the current school transportation landscape for us to better understand children’s changing travel behavior in journeys to school. The objectives of this dissertation can be summarized as: 1. To understand why travel distance and car use has increased 2. To understand the role of school quality in school choice and children’s travel distance 3. To understand how parents make decisions regarding children’s means of travel to school 4 1.2 Land Price and School Quality Tiebout (1956) Theory states that households will sort themselves into jurisdictions that provide similarly needed public services, the process of which results in neighborhoods that share not only relatively homogenous spatial but also social and economic characteristics. Land value under this urban economics framework reflects both housing and location characteristics as well as the level of public service (Black 1999, Barrow 2002). In other words, different types of public service can be capitalized in house price (Hilber and Mayer 2009). A direct result from education capitalization is an unequal spatial distribution of school quality coincided with a similar spatial distribution of land prices. It is known the spatial distribution of school quality in the U.S. is not homogeneous. High income families that can afford to live in a good school district buy themselves the proximity to good schools, whereas low income families are usually locked in low performing districts (Betts et al. 2000). The inequality of school quality can be further enlarged by continuous funding discrepancy because some studies show that there is a strong correlation between school inputs and outputs (Nechyba and Strauss 1998). Revenues of most school districts in the U.S. are closely tied with property tax (Barrow and Rouse 2004). Districts with expensive properties usually translate into high revenues. In some cases, services provided by school districts of high quality are valued even in excess of the higher tax rate they levy (Bogart and Cromwell 1997). To break the unequal funding between the good and poor performing districts, two major education reforms have been enacted in California. The first reform is Proposition 13, which capped local property taxes at 1 percent and restricted annual increases in assessed property value to 2 percent per year, after California Supreme Court ruled in Serrano v. Priest that a property-tax based public education finance system was unconstitutional as school district funding was disproportionately favoring the affluent and wealthy. Since Proposition 13 was enacted in 1978, 5 California has equalized the base revenue limit which determines a fixed spending level for all school districts. California’s school finance system has two important impacts on household location choice (Bayer 2000). First, because local property taxes are fixed at a rate of 1 percent, residential location decision of households are not affected by variation in property tax rates, which differentiates California from most other states. Second, since voters’ preference cannot directly impact either school district expenditures or property tax rates, household preferences for school quality can be primarily realized by the sorting process across districts (Bayer 2000, Dynarski et al. 1989). Albeit Proposition 13 and subsequent legislation tried to reduce these inequalities in school finance, substantial and continuing performance gaps still remain. Betts et al. (2000) point out that “[t]he centralization of funding of school districts that resulted from Proposition 13 and related court judgments has not fully equalized resources across districts and schools” (p. 10). Distribution of student socioeconomics and the resulting inequities in school resources may contribute to variations in academic performance (Betts et al. 2000). The other major education reform after Proposition 13 is school choice policy. This open enrollment program provides more choices of school, especially for those living in low- performing neighborhoods. School choice policy was designed to provide more education opportunities and to improve school performance by lessening the association between residential location and school assignment (Schneider et al. 1997, Ryan and Heise 2002). While this policy has two objectives: to improve both the efficiency and equity of the public education market (Hastings et al. 2005), “[t]he core principle of school choice is an equitable one, as school choice grants poorer students an opportunity—the chance to choose their own schools—that is now reserved for wealthier students” (Ryan and Heise 2002, p. 2051). People hoped that by giving students from low-performing districts the opportunity to go to a school of a better quality and/or 6 a different socioeconomic composition, they could have substantial academic improvements. Under school choice policy, several national school choice plans had been implemented, such as intra-district and inter-district transfers, charter schools, and vouchers. 1.3 School Choice and Site-Based Management First became available in California between 1985 and 1990, school choice policy was designed with consideration of children’s learning styles (Odden 1991): “One issue related to school choice is the linkage of choice with site-based management of schools. Many argue that if wide discretion is given to education professionals to implement strategies designed to achieve student performance goals, then parents should be given a choice in selecting schools on the basis of their preference for particular education philosophies or the learning styles of their children” (p. 110). Here the “site-based management” implies the mobility of student composition, allowing the mixture of students from different neighborhoods and potentially different socioeconomic backgrounds. Three forms of “site-based management” schools are available in California— charter schools, private schools, intradistrict and interdistrict transfers. The first form is charter schools, which also receive public funds as conventional public schools. Charter schools are opened to students regardless of their residential district. They are accountable to the public but not necessarily to a local school district (Odden 1991). They are created when a group of parents, teachers and community leaders petition a local school board or county board of education for a charter to open an independent school to serve their community (California Charter Schools Association, 2012). Since the legislation was passed in 1992, the number of approved charter schools has increased annually. As of July 2001, about 350 charter schools were operating in California (Ed-Data 2010). The number of operating charter schools has grown to 746 in 2008-09 (California Department of Education 2009). One of the reasons why 7 charter schools have gained growing interest is their academic accountability, which can be proved by the strong student academic improvements reported by the California Charter Schools Association. The second type is private schools, which are often considered superior to public schools (Chubb and Moe 1990). Private schools are opened and attended by choice, even though they have been available long before site based management. As private schools charge tuition, households with more than one child can actually save money by paying higher rent and moving to a good school catchment area instead of sending their children to private schools (Gibbons and Machin, 2003). In contrast to the rising enrollment of charter schools, private schools have lost enrollments since 2000 in the Los Angeles region. Whether the newly available “site-based management” public schools are the substitute for private schools is still unknown. The third form is the intradistrict and interdistrict transfers, or open enrollment policy. Open enrollment is widely available in California. According to Los Angeles County Office of Education, all 80 school districts in Los Angeles County allow for transfers in and out of the district. Students can apply for schools in districts that participate in this choice program. However, seats are not guaranteed for all applicants if applications exceed the capacity and the admission will be decided by random drawing, with priority given to those whose siblings are already enrolled or those whose parents work in the district. One of the most critical criteria in allowing a transfer is the difference in school characteristics between the district of residence and the accepting district. If a student’s application is denied, an appeal can be filed when “the student has expressed a genuine interest in an educational class or program which is both available and beneficial to the student, which cannot be reasonably provided by the district of residence, and the student is in fact eligible for, and has committed to taking or has been accepted into, the 8 desired class or program” (Los Angeles County Office of Education 2010). This form of site- based management—intradistrict and interdistrict transfers—will be the focus in this dissertation. 1.4 Implementation of School Choice Policy Since its inauguration, the school choice policy has encountered support and challenges. Bierlein et al. (1993) summarized the arguments from both the advocates’ and critics’ perspectives (Table 1.1). For example, one challenging aspect of the implementation of the choice plans is transportation. Without proper assistance, the effectiveness of this policy will be questioned because low-income families usually have low car ownership and would probably find it very difficult to travel very far to attend better schools (Bierlein et al 1993, Dillon 2008, He 2011). Table 1.1: Arguments for and against school choice Advocates Critics Choice is a way to achieve equal educational opportunities for poor and minority youngsters. There is no convincing evidence that competition will improve schools or pupil achievement. Choice can rescue children from bad schools. The children most in need—those without supportive, capable parents—will likely be left with the worst choices. Competition for students and money will force schools to improve and be more accountable. Choice will work against low-income families unless transportation is provided; money spent on buses is better spent in the classroom. Children have different learning needs and, therefore, need different teaching options. Private school choice will drain money from already needy public schools. By choosing a school, parents will be more involved in, and committed to, their child’s education. Choice is a red herring that diverts the public’s attention from the need to adequately finance public schools. Choice can promote voluntary desegregation. Encouraging student transfers will undercut efforts to increase school-community ties. Choice will force schools/districts to streamline their bureaucracies. Choice will lead to a higher level of professionalism and expertise among teachers. Choice should involve a variety of options for parents, including the ability to use state funds for private and religious schools. Source: Bierlein et al. (1993), p. 25 9 Based on an analysis of the history and current status of the open enrollment programs across the U.S., Bierlein et al. (1993) summarized several points of the existing state programs: 1. Each state program has had steady growth, although the participation rate is still low. Highest participation rates have occurred in programs that have existed the longest, signaling the positive effect of awareness. 2. Neither devastating effects nor vast improvements have occurred since the beginning of the choice programs. Opponents of these programs feared a large scaled transfer from poor schools, leading to school abandonment and closures, teacher unemployment, and district bankruptcies; advocates for the choice programs predicted students in the choice program would have improvements over academic achievement, parent involvement and satisfaction. However, neither of these predictions came true. 3. Parents are satisfied with the choice program. The reasons why they apply for the choice program are school quality, although proximity is also frequently cited. Although the school choice plans are still limited in scope, participating parents are satisfied (Bierlein et al. 1993, Ryan and Heise 2002). Moreover, long waiting lists in some study areas (e.g., Boston and Rochester) suggested that the participation rate will rise when there are more spaces available (Ryan and Heise 2002). The increasing popularity of school choice policy has also been witnessed in the Los Angeles area, which is reflected by the demand for inter- district transfers (Los Angeles County Office of Education 2010). 1.5 Travel Behaviors under School Choice Policy This dissertation draws travel diaries from the 2001 SCAG Post Census Regional Household Travel Survey (RHTS) of the Los Angeles region. The dominant travel mode to school in this region is private vehicle, followed by walking. Figure 1.1 shows that, among students age 5-18, 10 more than 60% travel by private vehicle, about 20-25% on foot or by bicycle, and slightly more than 12% by school bus; few students travel by transit bus or by subway. Figure 1.1: Mode of arrival to school for students age 5-18, 2001 RHTS Non-motorized modes become less popular as travel distance increases. Figure 1.2 reports the frequency of trips in different travel distances and modes. In this figure, the distribution of the major modes shows that about 50% of school trips less than a half mile are made by walking or biking, and the rate decreases with distance. When the trip length is more than 2 miles, the rate drops to only 15%. Travel by school bus or local bus account for a small percentage for short distance trips, but the mode share of bus rise to almost 20% for trips of more than 2 miles. Private vehicle is used by the majority of trips, accounting for 44.39% of the mode share even for trips of less than a half mile. When the distance is greater than 1 mile, almost 70% of trips are made by private vehicles. 0% 10% 20% 30% 40% 50% 60% 70% Walk Bike School bus Transit Private vehicle K - 6th Grade 7th - 12th Grade 11 Figure 1.2: Mode of travel to school by distance for students age 5-18, 2001 RHTS Given this trend in school choice policy, more parents and children who exercise this option will have different travel behaviors, especially with respect to active commuting. Because school choice policy allows parents to choose a non-neighborhood school, students who have the opportunity to leave their neighborhood schools are prone to travel greater distances and use different travel modes other than walking or biking compared with those attending neighborhood schools (Yang et al. 2012, Wilson et al. 2007). From the RHTS survey, travel distance is found to be strongly related to school choice as well. There is a sizable difference in travel distance between those who exercise the school choice option and those who attend the local schools (Table 1.2). For elementary school trips, the median travel distance for those who transfer out of the district is 3.83 miles, compared to an average of 0.35 miles for those who choose the neighborhood schools and 1.14 miles who attend other schools within the home district. For high school trips, this distance disparity is also significant. The median travel distance of students who exercised the inter-district transfer option is 4.53 miles, versus 1.09 miles and 2.50 miles for students who choose schools in the first two categories. Due to the strong relationship between school choice and travel distance, we have a 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% <1/2 mile 1/2 – 1 mile 1 – 2 miles >= 2 miles Private Vehicle Bus Walk/Bike 12 reason to believe that school choice policy can have a major impact on children’s travel behavior by allowing parents to choose from more school choices. Table 1.2: School choice and travel distance (median) School Category Elementary School Trips High School Trips percentage Travel distance (mile) percentage Travel distance (mile) Neighborhood school 46% .35 62% 1.09 Other schools within district 44% 1.14 26% 2.50 Schools out of district 10% 3.83 12% 4.53 1.6 Significance and Contributions Journeys to school have become a major urban planning concern. Children are increasingly traveling by car rather than walking and traveling longer distance to school, hence engaging in less physical activity and contributing to congestion and pollution. There is an urgent call for our attention to reduce car dependency among children and adolescents. Researchers have endeavored to discover other important factors so as to provide innovative policies and programs to encourage walking/biking. Among these factors, some researchers believe that redesigning the built environment can provide a pedestrian and bicycle friendly and safe path to school and increase active commuting (Lin and Chang 2010). The exercise during students’ journeys to school complements students’ limited in-school physical education classes and improves students’ wellbeing (Tudor-Locke et al. 2001). However, are these changes in the neighborhood and school routes sufficient to influence students’ mode choice? To better understand children’s travel behaviors, more studies with school variables are needed. Sirard and Slater (2008) reviewed over a hundred papers on active commuting. They summarized most variables used in the related literature. These variables were categorized into three groups: policy level, neighborhood level, and parent/family level. Whilst most of the 13 variables fell into the latter two categories, few variables have been identified in the policy category: the only four variables that have been tested included construction date, size, physical education class during the week, and if a school discourages walking to school (WTS). Their review suggested that other policy level variables (i.e., school busing policies, school choice, and school locations) as well as the interactions of these with neighborhood and parent/family level variables need to be further examined. Studies considering policy level variables are still limited (Sirard and Slater 2008). This research will help fill this gap by accounting for school quality and the school choice policy. Although both academic performance and location have been identified in the education literature as the two most cited factors in parental school choice (Petronio 1995, Glazerman 1998, Calvo 2007, Burgess et al. 2009, Denessen et al. 2005, Kleitz et al. 2000, West et al. 1998, Armor and Peiser 1998, Coldron and Boulton 1991), the variable of academic performance and parents’ workplace has been largely missing in school transportation studies, thus preventing us from a deeper understanding of the effect of school choice policy on travel behavior. My study shows that explaining children’s travel behavior is complex and that our current efforts in promoting active commuting have largely neglected school location and characteristics (McDonald 2008a, Ewing et al. 2004, Yarlagadda and Srinivasan 2008) as well as intra-household dynamics. Long travel distance is a result of parental school choice in a region where public school resources are distributed unequally (Betts et al. 2000) and a result of parent- child schedule coordination. Just because a child lives within walking distance of a school does not mean the child will walk there, or even that the child will attend that school. A further examination of how parents choose a school and how they decide the children’s means of travel to school may help explain the discouraging school transportation statistics—increased travel 14 distances, increased car use, and decreased rate of active commuting to school (NHTS Brief 2008). 1.7 Dissertation Structure This dissertation will first evaluate the land value capitalization effect of public education in order to understand why high income families bid for residential location close to good public schools and how low income families may take advantage of school choice policy to get better public education by traveling far from home. Then it will examine, when different public schools are available, how parents gauge travel distance and school quality in their school choice decision. Conditional on this choice, this research will lastly examine how escort decision and mode choice are determined. 1.7.1 Essay one: How much do parents pay for school quality? In the first essay, I estimate how much homebuyers are willing to pay for school quality. In California, there exists a significant spatial disparity in public school quality. Parents choose their home close to good schools to ensure that their children an opportunity to receive quality education. The bidding for proximity can lead to a pattern of spatial distribution where households with similar socioeconomic status and willingness-to-pay for school quality cluster together. During this sorting process, administrative, political, and statistical boundaries are formed. Households and their dwellings are expected to be more homogeneous inside and more heterogeneous across these boundaries. Extensive studies have used the hedonic model, which describes house price as the sum of several housing and neighborhood characteristics, to estimate homebuyers’ willingness-to-pay for school quality. Various estimation approaches differ from each other by one fundamental— 15 the assumption of the data structure. The traditional estimation of the hedonic model applies ordinary least squares (OLS) estimation (Leech and Campos 2003). This estimation method is under criticism for the possible autocorrelation of the error terms. To address this issue, a number of different methods have been applied in capitalization studies, such as boundary discontinuity design (Black 1999), generalized least squares models (Haurin and Brasington 1996), and nonparametric models (Gibbons and Machin 2003). However, none of these capitalization studies have framed the house prices in a hierarchical structure (Giuliano et al. 2010), which is indeed capable of picking up unobserved spatial contextual interactions of individual objects from the same spatial units and addressing the mixed level of variation in house prices within and across boundaries. This essay adopts a hierarchical (i.e., three-level) framework, where each house is considered to be nested in the neighborhood and school district. I estimate how much homebuyers are willing to pay for school quality using residential housing prices in Orange County, California in 2001. The estimation results show that proximity to a good school increases housing prices significantly. A 10% increase in school quality, as measured by the Academic Performance Index (API) score, will raise housing prices by approximately 2.3%. In addition to house-level variables, several neighborhood and district variables such as median household income, expenditure per student and percentage of minority students in a school district also have strong effects. 1.7.2 Essay two: Are parents willing to incur longer trips for better school quality? Like many other large metropolitan areas, the Los Angeles region has significant spatial variation in public school quality and land values. Households that can afford to pay price premiums may locate themselves closer to good quality schools. The proximity to good schools guarantees admission while reducing commute costs. In contrast, households in the lower income brackets 16 may take advantage of the open enrollment policy in the California public school system, which entitles students to transfer out of their neighborhood school when seats are available. School choice policy gives parents the option of “shopping for the best product for their child from among a variety of public schooling options” (Dodenhoff 2007). When faced with a seemingly unlimited set of school choice, how do parents choose the right school? The education literature suggests that when parents choose a school, both location and characteristics are considered. However, the trade-off between distance and school quality has not been well understood. When this option is exercised, households living in low-performing districts may be more prone to longer travel in search of good quality schools compared to households in high-performing districts. However, whether the travelers are able to attend school in a district other than their residential district may depend on various factors such as the inter-district transfer policy and mobility constraints. This essay fulfills this gap by modeling K-12 school destination choice using an activity- based approach. I will examine to what extent school location and quality affects children’s destination choices. My hypothesis is that the better the school quality, the more likely the school will be chosen as a destination among all the feasible choices. Since the home location is fixed, the chosen school will determine a student’s travel distance, which has been frequently shown to have a great influence on travel mode. It is expected that students living in good school districts are less likely to choose a non-residential district school. The results show that, even when the option of intradistrict and interdistrict transfer is available, the largest proportion of students attend the neighborhood schools, which echoes the conventional practice of school assignments. Moreover, the outcomes show that both school quality and location are influential in parental school choice. First of all, school quality matters: parents are willing to incur longer distance trips for better quality schools. Second, distance 17 matters: the nearest school has a much higher probability of being selected whilst out of district schools have a much lower probability of being selected. Several interaction terms turn out highly significant, signaling people’s heterogeneous preference for school attributes: students from the lowest performing districts have a higher probability of leaving the residential district by exercising the inter-district transfer option; travelers from the densest school area and lowest performing districts consider distance as a greater impedance. After controlling for the residential area’s school quality and school density, different racial groups have no significant different preference for distance, boundary effect, and school quality. 1.7.3 Essay three: Do parental work arrangements and location affect a child’s journey to school? In the United States, the share of children age 6 to 12 who travel to school by private vehicle has increased significantly in the past decades. Much research on school transportation has been conducted to identify what factors influence children’s mode choice and how to incorporate the information into urban design and transportation engineering. However, information of the parents as the real choice maker has rarely been taken into account. A child’s mode to school is influenced by the parent(s). Children of 6 to 12 years are dependent upon parental choices; the parent decides whether the child is escorted to school or travels by himself/herself. Thus an increasing share of auto trips may reflect parental choices and constraints. For example, women’s increased labor force participation (and the time constraints working imposes on household travel needs) may be as important as travel distance. Although a dependent child’s mode choice depends on parental choice, the decisions of escort and travel mode are usually modeled as separate decisions with most studies focused on mode choice. In fact, the child’s mode and whether the child is escorted by a parent (or other caretaker) are related. For example, children 18 who are escorted to school are most likely to be dropped off or picked up by car, whereas those who travel independently are more likely to use modes such as walking, biking, and bus. To study the escort-mode joint decision, it is important to consider intra-household bundling constraints, which can be defined as the scheduling and spatial constraints that determine whether a household member is able to join another member during an activity. Applying this concept to school trips, whether a parent can escort their children to school may depend on the parent’s scheduling and spatial constraints, e.g. work schedule and job location. The scheduling constraints have only recently been addressed: parental employment and flexibility of work hours are significant factors in escort and/or mode choice of children’s school trips (McDonalds 2008a, Vovsha and Petersen 2005, Yarlagadda and Srinivasan 2008). Spatial constraints, nonetheless, have not been accounted for. This essay presents a first attempt in bringing both scheduling and spatial variables derived from the parent’s work arrangement and workplace in modeling escort-mode decisions of school trips. The outcomes in this paper demonstrate that the parent’s, especially the mother’s increasing work hours and more distant job location result in an increased likelihood of several alternative escort-mode choices. Mothers who work longer hours and farther away from home are less likely to escort their children in car. These trips have been substituted by alternative escort choices such as escorted by fathers and by siblings, or alternative mode choices such as active commuting and busing. More importantly, the estimates of the spatial coordination variables suggest that the parent-child joint trip can be made easier if the child attend a school closer to the parent’s workplace. This decision may facilitate the escorting trip and childcare outside school hours but at the same time may result in a child’s longer travel distance and a different mode choice than those who travel independently. 19 Chapter 1 References Alonso W. 1964, Location and Land Use. Cambridge, MA: Harvard University Press. Armor D. J., and Peiser B. M. 1998, Interdistrict choice in Massachusetts. In P. E. Peterson and B. C. Hassel (Eds.), Learning from School Choice. Washington, DC: Brookings Institution Press. Barrow L. 2002, School choice through relocation: evidence from the Washington, D.C. area. 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Tudor-Locke C., Ainsworth B.E., and Popkin B.M. 2001, Active commute to school: An overlooked source of childrens’ physical activity. Sports Medicine, 31, 309-313. Vovsha P. and Peterson E. 2005, Escorting children to school: Statistical analysis and applied modeling approach. Transportation Research Record: Journal of the Transportation Research Board, 1921, 131-140. Waygood E.O.D. and Kitamura R. 2009, Children in a rail-based developed area of Japan: Travel patterns, independence, and exercise. Transportation Research Record: Journal of the Transportation Research Board, 2125, 36-43. Weimer D.L. and Wolkoff M.J. 2001, School performance and housing values: Using non- contiguous district and incorporation boundaries to identify school effects. National Tax Journal, 54, 231-253. West A., Pennell H. and Noden P. 1998, School admissions: Increasing equity, accountability and transparency. British Journal of Educational Studies, 46, 188-200. Wilson E.J., Wilson R., Krizek K.J. 2007, The implication of school choice on travel behavior and environmental emissions. Transportation Research Part D, 12, 506-518. 23 Wilson E.J., Marshall J., Wilson R., and Krizek K.J. 2010, By foot, bus or car: Children’s school travel and school choice policy. Environment and Planning A, 42, 2168-2185. Yang Y., Abbott B., and Schlossberg M. 2012, The Influence of school choice policy on active school commuting: A case study of a middle-sized school district in Oregon. Environment and Planning A (forthcoming). Yarlagadda A.K. and Srinivasan S. 2008, Modeling children’s school travel mode and parental escort decisions. Transportation, 35, 201-218. 24 CHAPTER 2 HOW MUCH DO PARENTS PAY FOR SCHOOL QUALITY? A Multilevel Estimation of School Quality Capitalization in Residential Housing Price 2.1 Introduction The largest public fiscal undertaking in California is kindergarten through twelfth grade (K-12) public education (Odden 1991). The state is the major source of revenue for California’s schools, a total of $68.6 billion dollars or a total spending per pupil of $11,584 (California Governor’s Budget Summary 2007-2008). In fact, the state role in California is much higher than the national average. For the fiscal year 2007-08, state revenues accounted for 61.3% compared to the national average of 48.3% (National Center for Education Statistics 2010). The reason for public school’s dependence on the state government is the implementation of an important property taxation policy, Proposition 13, which capped local property taxes at 1 percent and restricted annual increases in assessed property value to 2 percent per year. Proposition 13 was drafted after Serrano v. Priest, in which California Supreme Court ruled that a property-tax based public education finance system was unconstitutional as school district funding was disproportionately favoring the affluent and wealthy. Since Proposition 13 was enacted in 1978, California has equalized the base revenue limit, which determines a fixed spending level for all school districts. California’s school finance system has two important impacts on household location choice (Bayer 2000). First, because local property taxes are fixed at a rate of 1 percent, residential location decision of households are not affected by variation in property tax rates, which differentiates California from most other states. Second, since preferences of the voters in each district cannot directly impact either school district expenditures or property tax rates, household preferences for school quality can be realized mainly through the sorting process across districts (Bayer 2000, Dynarski et al. 1989). The sorting results in a cluster 25 of relatively homogeneous households in terms of their preferences for school quality within the same district. Home buyers are aware of school quality when they make the purchase decision (Weimer and Wolkoff 2001). Parents value various characteristics of a school and view school quality in different ways (Barrow 2002, Barrow and Rouse 2004, Black 1999, Brasington 1999, Calvo 2007, Downes and Zabel 2002, Rothstein 2006). Indicators of school quality may include test scores, reputation, per pupil expenditures, and peer group effect, etc (Downes and Zabel 2002, Brasington 1999, Rothstein 2006). Among the numerous studies, the most widely used and consistent indicator is test scores. Although test scores may reflect the socioeconomic status of the students rather than learning experience, this indicator is still a good measure of quality because it still signals academic achievement. Moreover, it is publicly available and it is often the only tangible evidence of quality that many parents have (Calvo 2007). Parents choose their home location close to good schools to ensure their children’s admittance (Barrow 2002, Calvo 2007, Nechyba and Strauss 1998). Houses within attendance zones of high quality schools are often priced higher than comparable houses outside the attendance boundaries, all else equal (Black 1999, Bogart and Cromwell, 1997). The rent bidding process for proximity results in the spatial distribution where households with similar socioeconomic status and willingness-to-pay for public education cluster together (Alonso 1964). Therefore, spatial information such as house prices and household attributes are expected to be more homogeneous within and more heterogeneous across different geographic and administrative boundaries. The intrinsic spatial variation in this measurable information, in turn, reflects the spatial variation in people’s attitudes and preferences as well as various administrative and political contextual issues (Fotheringham et al. 2002). The level of such preference may vary from place to place. 26 This spatial variation and the potential interactions of spatial objects imposes some challenges to the application of hedonic analysis (Rosen 1974) in estimating the marginal effect of a particular housing or neighborhood variable on the price of land (Black 1999, Reback 2005, Thorsnes and Reifel 2007). The traditional estimation of hedonic model (i.e., OLS estimation) is a global estimation approach (Fotheringham et al. 2002). By assuming all observations are independent, OLS fits a single relationship for all the data, which can lead to misleading interpretations of local relationships (Fotheringham et al. 2002). When subgroups of data are analyzed separately, the results may show an opposite sign to those when data are analyzed at the aggregation level, which is referred to Simpson’s Paradox (Simpson 1951, Fotheringham et al. 2002). One alternative estimation method addresses the spatial dependent problem by focusing on a relatively homogeneous group by drawing data from a restricted geographic area or using locally weighted estimation approach (Black 1999, Gibbons and Machin 2003). This type of local estimation (Fotheringham et al. 2002) controls for the contextual effects through 1) sampling from a small area and thus collinearity issue among global variables for a small geography incurs, or 2) assigning a spatial dummy variables. Either way, the local estimation approach does not estimate a general trend to fit the data; thus limiting our understanding of the capitalization effect from the regional perspective. The multilevel estimation can be considered an intermediate level estimation. The multilevel models consider interactions of variables at different regimes and levels; hence it can be a good compromise between global and local models (Páez and Scott 2004). This paper adopts the multilevel model recommended for spatial data of hierarchical structure (Fotheringham et al. 2002, Páez and Scott 2004) to estimate the effect of elementary school quality on house price in Orange County, California of 2001. Due to strong spatial interactions among individual objects 27 within the boundary, the multilevel model structure is expected to better accommodate such contextual effects than the OLS estimation. 2.2 Literature Review The traditional estimation of the hedonic price is the ordinary least squares (OLS) estimation (Leech and Campos 2003). The traditional estimation is often criticized because of plausible autocorrelation of the error terms in housing data (Can and Megbolugbe 1997, Fingleton 2006, Giuliano et al. 2010, Orford 2000, Thériault et al. 2006). OLS assumes independence of its error terms. This assumption, nonetheless, is often violated in studies using spatial data, which are spatially dependent by nature (Fotheringham et al. 2000, Páez et al 2008). Spatial dependence (or spatial autocorrelation) states that spatial observations nearby are more likely to share similar attributes and influence each other than distant observations (Anselin 1989, Goodchild 1992). Spatial autocorrelation and dependence can be traced back to the first law of geography: "[e]verything is related to everything else, but near things are more related than distant things" (Tobler 1970, p.236). If we ignore a positive autocorrelation, the confidence interval calculated based on an independence assumption would be too narrow, hence we may run into a risk of type I error (rejecting a null hypothesis of no causal relationship that should not be rejected), thus erroneously concluding with a significant difference between two samples (Fotheringham et al. 2000). Alternatives to the OLS estimation have been developed in capitalization studies, including generalized least squares (GLS) (Haurin and Brasington 1996), boundary discontinuity design (Black 1999, Bayer et al. 2007), and non- and semi-parametric/locally weighted regression (Gibbons and Machin 2003, Redfearn 2009), geospatial models (Haider and Miller 2000, Bourassa et al. 2010), and multilevel (Giuliano et al. 2010). 28 As Bourassa et al. 2010 noted, empirical studies in different study area will result in varied magnitudes of effects. The elasticity of house prices with respect to public school quality (the majority of which are measured by test scores or public proficiency passage) is frequently shown to be inelastic: 0.15 (Brasington 2007), 0.21 (Brasington 2002), 0.27 in Figlio and Lucas (2004), 0.20 (Hite et al. 2001), 0.5 (Black 1996). A few studies, however, presented an elastic number such as 1.1 (Downes and Zabel 2002) and 6.7 (Gibbons and Machin 2003). The variation in the elasticity is possibly a consequence of the different approaches adopted. For example, with 1991 single-family house prices in 134 jurisdictions in Ohio’s six largest MSAs, Haurin and Brasington (1996) applied generalized least squares (GLS) to test for the capitalization effect of two local public services: the passage rate of 9th graders and nominal property tax rate. They regressed house price on housing characteristics, school district dummies, and community and MSA variables. The results showed that 1% increase in passage rate of 9th graders increased a house price of $380-$400, equivalent to one half-percent of the house price at mean. Black (1999) designed a boundary discontinuity regression to evaluate parental valuation of elementary school quality in three suburban counties in Massachusetts from 1993-1995, in which school quality was measured by 4th grade MEAP test scores. Black’s results showed that parents are willing to pay 2.5% more for a house for a 5% increase in test score. Gibbons and Machin (2003) adopted nonparametric estimation to evaluate the effect of primary school performance on property prices in the not well-defined school catchment areas in the London region of U.K. from 1996 to 1999. They found that 1% increase in school performance pushed up property prices by 6.7%. The capitalized costs of public primary education are close to the cost of private education for a one-child family. These various estimation approaches, together with the traditional OLS estimation approach, can be differentiated from each other by one fundamental—the assumption of the data 29 structure. The OLS approach assumes that observations are independent from each other and the error terms are homoskedastic. GLS relaxes such an assumption by allowing a certain degree of correlations between the observations but the model does not have a pre-determined structure of the correlation. The boundary discontinuity approach assumes that the observations are discontinuous across certain boundaries, thus the difference-in-difference approach can be applied when a buffered zone from both sides of the boundary is used to control for variations in the sample. The nonparametric and geospatial models essentially concur with the first law of geography by assuming there is spatial dependence in the data. An observation is influenced by its neighbor observations hence there is a weighting scheme to account for the influence of distance or contiguity. The multilevel approach also agrees upon there is spatial dependence among the observations, but it further assumes that the correlation structure is determined by some sort of a priori boundaries. Multilevel models are often applicable in urban studies because individual objects often cluster at different geographic aggregation levels and these models can account for both individualism and holism (Courgeau 2003). Modeling spatial behavior solely at individual level is prone to atomistic fallacy, whereas modeling solely at aggregate level is prone to ecological fallacy, which refers to the potential erroneous inference of individual behavior based on aggregated spatial data (Alker 1969, Fotheringham et al. 2002, Gehlke and Biehl 1934, Robinson 1935). As a matter of fact, multilevel analysis model has long been used in student performance studies where students are nested under classroom, school, and neighborhood (Bickel 2007, Garner and Raudenbush 1991, Goldstein 1987, Snijders and Bosker 1999). The multilevel approach is able to separate individual effects from place/contextual effects by allowing individual spatial objects to have within-group interactions (Goldstein 1987, Guiliano et al. 2010). A multilevel (or hierarchical regression) model is an extension of the 30 random parameters model (Greene 2002). It considers fixed effects and random effects at multiple levels. At each level, homogeneous errors are assumed because of the relatively homogeneity. The model is structured in a fashion such that the parameter heterogeneity across individual observations or groups can be viewed as stochastic and can be fit by least squares estimation (Greene 2002). The a priori definition of discrete boundary at each aggregation level needs to be justified in multilevel analysis. For social sciences research, these boundaries are usually administrative, political, or statistical boundary. The boundary setting implies that the nature of the spatial process is discontinuous because the spatial behavior may change when the boundary is redrawn. Hence, it is unrealistic to impose a discrete set of boundaries on most spatial processes. However, the imposition of administrative boundary (e.g., municipal and county boundary) is one exception because the associated policy could affect people’s behavior, which would differ once they cross the boundary (Fotheringham et al. 2002). The concept of neighborhood and school district boundaries has been applied in both housing and education studies (Bourassa et al. 2010, Goldstein 1987, Garner and Raudenbush 1991). For example, the boundary of the relatively homogeneous neighborhoods has been used to define submarkets in housing studies (Bourassa et al. 2010); the boundary of school district has been used to show the strong boundary effects in school capitalization (Bayer et al. 2007, Black 1999, Bogart and Cromwell 1997, Kane et al. 2003, 2006). 2.3 Methodology and Model Specification The hedonic analysis assumes that the house price is the sum of several housing and neighborhood characteristics (Des Rosiers et al. 2000, Goodman and Thibodeau 2003, Vadali and Sohn 2001). When the school district variables are included, the basic model is 31 ) , , ( ln i i i i D N H f price  2.1 where H i is structure attributes of the i th house; N i is neighborhood variables; and D i is school district variables. The purpose of this research is to test whether school quality affects residential house prices using the multilevel estimation for the hedonic analysis. In view of spatial dependence and the clustered nature of spatial data, this paper assumes a hierarchical structure of the housing observations. This paper hypothesizes that, when homebuyers purchase their house, factors at different spatial levels are taken into account, ranging from housing attributes, to neighborhood characteristics, to school district information. Thus, a three-level analysis framework (i.e., house, neighborhood, and school district) is adopted. The geographic level of municipality is not included here because it is not necessarily equivalent to the boundary of local government’s jurisdiction (Ihlanfeldt 2007); it may provide minimal information regarding local school spending beyond the school district level. Therefore, homebuyers may not pay attention to the boundary of municipalities as much as they do for neighborhood and school district. 2.3.1 Multilevel estimation of hedonic price: A three-level model Multilevel model (or hierarchical model) originates from linear mixed model (LMM), in which both fixed and random effects associated with one or more random factors can be included (West et al. 2007). Fixed effects, also called regression coefficients, describe the relationship between the dependent variable and the independent variables for the entire population at individual (lowest) level. Random effects, which can be modeled as random intercepts or as random coefficients, represent random deviations from the relationships described by fixed effects. The residuals from LMM are normally distributed but are not necessarily independent or have constant variance (Eq. 2) (West et al. 2007). LMM is suitable for data sets where the dependent 32 variable are clustered, longitudinal, or repeated-measures in nature. From a hierarchical linear modeling (HLM) perspective (Raudenbush and Bryk 2002), LMM handles multi-levels of data, hence the name of multilevel or hierarchical model (West et al. 2007). In other words, multilevel model can capture the change in variance at different aggregation levels and timeframes. It allows the means of the intercepts or coefficients to vary with measured covariates (Greene 2002). Following the notation from West et al. (2007): i i i i i Z u X Y      2.2 where the first term is fixed factors, the second and third terms are random factors. In random intercepts models, the Z matrix would simply be a column of 1’s. It is assumed that the q random effects in the u vector follow a multivariate normal distribution ) , 0 ( ~ D N u i . It is also assumed that the n i residuals in the i  vector for a given observation i are random variables that follow a multivariate normal distribution ) , 0 ( ~ i i R N  ; where the variance-covariance matrices D and R are respectively defined as:                 2 , 2 , 1 , 2 2 2 2 , 1 , 1 2 , 1 2 1 ) ( uq uq u uq u uq u u u u uq u u u u i u Var D                 2.3                 2 , 2 , 1 , 2 2 2 2 , 1 , 1 2 , 1 2 1 ) ( n q q n n i i Var R                                 2.4 33 In terms of estimating fixed-effect parameter β and the covariance parameters D  and R  , restricted maximum likelihood (REML) estimation (sometimes called residual maximum likelihood estimation) is preferred over maximum likelihood (ML) estimation because the REML estimates of the covariance parameters θ are unbiased as it accounts for the loss of degrees of freedom that are used to estimate the fixed effects in β (Hox 2002,West et al. 2007). To test if a model specification is better than a simple linear regression, a likelihood ratio test can be used by comparing the likelihood ratios (Eq. 3). The likelihood ratios (LR) test statistic asymptotically follows a χ 2 distribution. The number of degrees of freedom df is obtained from subtracting the number of parameters in the tested model from the number of parameters in the null model β (West et al. 2007). 2 mod mod ~ )) log( 2 ( ) log( 2 ) log( 2 df null el null el L L L L       2.5 A three-level multilevel model will be used to analyze household’s willingness-to-pay for public school quality. This setup will allow us to estimate the proportion variance in house price due to differences between neighborhoods and differences between school districts. Level 1 denotes observations at the most detailed level of the data. It represents the units of analysis in the study. Level 2 observations represent clusters of units (neighborhood). Level 3 represents clusters of Level 2 units (clusters of clusters). Notation and subscript for specifying a three-level model can be found in various forms (Bickel 2007, Hox 2002, Luke 2004, Raudenbush and Bryk 2002, Snijders and Bosker 1999, West et al. 2007). Following the specification of random intercepts three-level model (MLwiN 2010): ijk ijk ijk x y 1 0     ijk jk k ijk u v 0 0 0 0 0        2.6 34 where i level 1 (e.g. house), j level 2 (e.g. census tract) , k level 3 (e.g. school district); k v 0 is the random effect at the school district level, an allowed-to-vary departure from the grand mean; jk u 0 is the random effect at the census tract level, a departure from the school district effect; ijk  is the random effect at the house level, a departure from the census tract effect within a school district; Variance between school districts = Var. ( k v 0 ) = 2 0 v  ; Variance between census tracts within school districts = Var. ( jk u 0 ) = 2 0 u  ; Variance between houses within census tracts within school districts= Var. ( ijk  ) = 2   ; Variance between census tracts = 2 0 2 0 u v    ; Random effects at different levels are assumed to be uncorrelated. The intraclass correlation coefficients (ICCs) (denoted as  below) will be used to measure the proportion of the total random variation due to the variance of the random effects at the aggregate level. It describes the similarity of the responses within a cluster (West et al. 2007). The term intraclass correlation coefficient is called as such because it is equal to the correlation between two randomly drawn micro-units from a macro-unit (Snijders and Bosker 1999). Through the ICCs, we can obtain the proportion variance in house price due to differences between census tracts and between school districts respectively. When the ICC indicator at the neighborhood level is high, it signals that households distinguish public school quality beyond the district level. 35 Proportion variance due to differences between school districts and between tracts: v  = intra-district correlation coefficient (ICC v ) = 2 2 0 2 0 2 0        u v v Proportion variance due to differences between census tracts: u  = intra-tract correlation coefficient (ICC u ) = 2 2 0 2 0 2 0 2 0          u v u v 2.3.2 Model specification The dependent variable is the natural log of residential house price. The explanatory variables are also transformed by the natural log 1 . The log transformation can be considered as the linearization of variables. In addition, the log-log form on both sides of the linear equation has an advantage in that the estimates of the independent variables can be directly interpreted as their respective elasticity effects on the house price. The estimation of this model will be a multilevel approach (Table 2.1). Table 2.1: Three-level data in the research setting of school capitalization study Level of Analysis Hierarchy Boundary Level 1 Unit of analysis House Level 2 Cluster of units Neighborhood (census tract) Level 3 Cluster of clusters School district Level 1 refers to attributes of each individual house, which include structure variables such as lot size and square foot. Besides the structure variables, the school quality of the nearest school of each house is also included as a house level variable. Another important variable at the 1 Because the natural log of 0 will result in a negative infinity, all explanatory variables with a value of 0 are replaced by a very small value (i.e., 0.001). 36 house level is distance to the coast. To many homebuyers, easy access to the beach is a valuable amenity (Giuliano et al. 2010, Ihlanfeldt 2007). A short distance to the coast is expected to increase the value of a house; hence, the estimation of this distance variable is expected to have a negative sign. This paper also assumes that, at the home purchase moment, parents have no intention to exercise the school choice option, meaning that they expect their children to attend the neighborhood school, which is defined as the nearest school within the school district. The school quality is approximated by a proficiency score—the Academic Performance Index (API). The API score first became available on July 1, 1999. This score measures a school’s academic performance and growth based on test scores of students in Grades 2 through 11 who participate in the Standardized Testing and Reporting (STAR) Program and the California High School Exit Examination. API scores are calculated by the California Department of Education (CDE) and disseminated directly to schools and districts. The API scores also are posted on the CDE’s and most schools’ web sites, making the API one of the most commonly used measures of academic performance. Level 2 and Level 3 refers to the neighborhood and district level, respectively. The analysis unit of neighborhood level is proxied by census tracts. At the neighborhood level, several variables from Census are included, such as population density, composition of major ethnic population (i.e., Whites, African Americans, and Hispanics), and median household income. At the school district level, information such as weighted API score, expenditure per pupil and the number of pupil per teacher is added (Ihlanfeldt 2007, Hilber and Mayer, 2009, Brasington, 1999, Kane et al. 2006, Kane and Staiger, 2002, Bayer et al. 2007). Definitions of the dependent and the independent variables as well as their sources are described in Table 2.2. Data from three sources are compiled in order to analyze the capitalization 37 effect of public schools on house price in the year of 2001. House price, location, and unit structure characteristics of the same year are obtained from DataQuick, a nationwide supplier of real estate information and analytics. The attributes of neighborhoods, through the proxy of census tracts, are drawn from U.S. Census 2000. The individual school and school district information is from California Department of Education. Table 2.2: Variable definitions and data Sources Variable Definition Data Sources Dependent variable Price House price DataQuick 2001 Level 1 variables (H) Lot size Lot size DataQuick 2001 Bedroom Number of bedrooms Bathroom Number of bathrooms Square foot Square footage Distance _coastline Distance to coastline (in meter) Calculation in GIS API score API score of the nearest elementary school in the residential district California Dept of Education 2001 Level 2 variables (N) Population density Population density per square mile Census 2000 % White Percentage of Whites % African American Percentage of African Americans % Hispanic Percentage of Hispanics Median age Median age of the population Median income Median household income Level 3 variables (D) Weighted API Weighted Academic Performance Index of the district California Dept of Education 2001 Expenditures Expenditures per pupil (ADA) % English Learner Percent of English learner % of Free Meals Percent of students eligible for free or reduced price meals % of Minority Percent of minority students Class Size Average class size Pupils per Teacher Pupils per teacher ratio 38 39 2.4 Study Area and Descriptive Analysis My analysis area is Orange County, California. It has a population of 2.8 million in twelve unified, twelve elementary, and three high school districts as of 2001. Since the objective of this paper is to examine the capitalization of elementary public schools in house price, only the boundaries of unified and elementary school districts will be used (Figure 2.1) in the following analysis. Some of the best school districts in the Los Angeles region (i.e., Irvine Unified and Los Alamitos Unified) are found in Orange County. Meanwhile districts with less impressive school performance (i.e., Anaheim Elementary and Santa Ana Unified) can also be found in the same county. Figure 2.1: Twenty four elementary and unified school districts in Orange County 40 Figure 2.2: Academic Performance Index (API) of 382 elementary schools in Orange County, 2001 There are a total of 382 elementary schools in 24 elementary and unified districts. While each district has a reputation in its quality education, there is still a noticeable variation in school performance inside most districts, as shown in Figure 2.2. In this figure, the size of each dot (which represents one school) is proportional to its quality as measured by the API score. The spatial distribution of school quality in Orange County is not homogeneous. Generally speaking, school quality within the district is relatively more homogenous than across the county. The standard deviation of API score of most districts is much smaller than that of the County (i.e., 120). Nonetheless, the school quality in some districts has a marked variation (i.e., Tustin Unified, Orange Unified, and Newport-Mesa Unified). For example, the API scores in Orange Unified 41 School District range from 524 to 863. The heterogeneity in school quality is also exhibited in some medium-sized districts. For instance, among the 14 elementary schools in Tustin Unified District, the lowest API score is 553 compared to the highest score of 882, resulting in a standard deviation as large as 121 (Table 2.3). The total number of house price observations in Orange County is 38,120, distributed across the 24 unified or elementary school districts. These houses across different school districts are priced differently, even for houses located within the same district, reflecting the variation of school quality. Districts with the most expensive house prices (i.e., Laguna Beach Unified, Newport-Mesa Unified, and Huntington Beach City Elementary) are often associated with higher API scores, whereas the least expensive districts (i.e., Anaheim Elementary, Santa Ana Unified, and Magnolia Elementary) are mostly associated with lower API scores. At the higher end, for example, the average house price in Laguna Beach Unified District is $776,077, more than double of the county level ($337,484). This is not surprising given the district’s overall outstanding school quality, indicated by a very impressive weighted API score at 868. Towards the lower end of the housing market, for instance, Anaheim Elementary has an average price of $225,824, more than 30% lower than the county average. School quality may play an important role in this district as well because Anaheim’s weighted average API score at 585 is roughly 20% lower than the county level. However, the relationship between average house price and school quality at district level is not necessarily linear because some inexpensive districts, such as Brea- Olinda Unified, Cypress Elementary, Fountain Valley Elementary, and Saddleback Valley Unified, exhibit high API scores. These districts all have weighted API scores of over 800, yet the average house price is only around $300,000. 42 Table 2.3: Summary of house price and school statistics of 24 school districts in Orange County (in order of house price) District Name Num. of houses Percent of total houses Average house price ($) Num. of elementary schools Weighted API score 1 Std. of API scores 2 Laguna Beach Unified 495 1.3 776,077 2 868 21 Newport-Mesa Unified 2,383 6.25 597,624 22 747 113 Huntington Beach City Elementary 1,429 3.75 441,539 7 808 58 Capistrano Unified 5,585 14.65 396,402 31 803 90 Los Alamitos Unified 460 1.21 387,225 6 849 23 Ocean View Elementary 1,144 3 356,691 12 760 80 Tustin Unified 1,708 4.48 352,750 14 742 121 Orange Unified 3,335 8.75 334,887 29 719 118 Irvine Unified 2,263 5.94 333,784 22 872 30 Fountain Valley Elementary 745 1.95 323,731 8 838 27 Saddleback Valley Unified 4,012 10.52 315,285 25 842 44 Placentia-Yorba Linda Unified 2,129 5.58 307,560 19 764 103 Brea-Olinda Unified 427 1.12 305,519 6 828 47 Fullerton Elementary 1,453 3.81 299,378 16 709 112 Cypress Elementary 532 1.4 281,737 10 826 45 Westminster Elementary 872 2.29 258,850 13 696 61 Centralia Elementary 468 1.23 254,673 9 738 75 Buena Park Elementary 504 1.32 242,116 6 698 50 La Habra City Elementary 572 1.5 231,124 7 669 53 Garden Grove Unified 3,111 8.16 229,422 45 691 69 Anaheim Elementary 1,590 4.17 225,824 23 585 61 Magnolia Elementary 409 1.07 221,910 9 634 65 Savanna Elementary 362 0.95 206,080 4 738 47 Santa Ana Unified 2,132 5.59 205,204 35 564 90 TOTAL 38,120 100 337,484 380 722 120 Note: 1. Weighted API score of the district is obtained by weighting each school’s API score by its enrollment using the following formula:     S s s S s s s Enrollment Enrollment API 1 1 * 2. This column shows the standard deviation of school-level API scores by district. 43 2.5 Results After further cleaning the dataset 2 , the final dataset contains 30,669 observations, including single family residences and condominiums. Figure 2.2 and Table 2.3 above show that house prices and the API scores differ across the school districts. ANOVA (analysis of variance), which is a way to decompose the observed variance into components attributable to the sources of variation, is used to test if school district boundaries contribute to a considerable amount of variances in house price and the test score. Results from ANOVA test confirm that the mean of both API score and house price differs significantly across school district boundaries (Table 2.4). This boundary effect contributes to 49% and 20% of the variation in the test score and housing price, respectively. Table 2.4: Results of ANOVA analysis ANOVA analysis of the API score (in natural log) Number of obs. = 30,669 R-squared = 0.4937 Root MSE = .1143 Adj R-squared = 0.4933 Source Partial Sum of Square df Mean Square F Value Prob > F School District 390.3702 23 16.9726 1299.19 0.0000 Residual 400.3469 30645 .0131 Total 790.7171 30668 .0258 ANOVA analysis of house price (in natural log) Number of obs. = 30,669 R-squared = 0.2013 Root MSE = .4503 Adj R-squared = 0.2007 Source Partial Sum of Square df Mean Square F Value Prob > F School District 1565.8195 23 68.0791 335.71 0.0000 Residual 6214.6012 30645 .2028 Total 7780.4207 30668 .2537 2 The following observations are dropped: 1) 0 bedroom, 2) 0 square foot, 3) use code other than single family residence and condominium. 44 Table 2.5: Statistic summary of variables (N=30,699) Mean Median Std. Dev. Min Max Value ($) 313,311.4 269,000 225,052.1 25,000 6,600,000 Lot size 3,699.904 0 10,499.04 0 871,200 Bedroom 2.936 3 .917 0 20 Bathroom 2.047 2 .644 .25 3 8.75 Square foot 1,552.757 1,386 722.159 35 24,187 Distance _coastline (meter) 8.355 8.006 5.009 .000 22.307 API score 754.901 788 112.535 472 922 Population density (per mi 2 ) 7,640.882 6,908.9 4,773.331 16.5 44,453.8 % White 68.529 73.005 17.262 23.050 97.611 % African American 1.567 1.316 1.050 .111 27.287 % Hispanic 24.207 14.378 21.645 1.626 97.507 Median age 35.463 35.2 5.901 21.5 78.8 Median household income ($) 65,865.01 62,388 21,981.34 14,828 163,321 Weighted API 746.855 747 85.321 564 872 Expenditures ($) 6,278.248 6,149 356.489 5,773 8,045 % English Learner 27.755 23.9 19.081 2.2 66.7 % of Free Meals 35.303 33.4 23.608 6.3 84.8 % of Minority 53.797 45.7 22.949 14.9 96.2 Class Size 27.185 27.7 1.704 21.2 28.9 Pupils per Teacher 21.778 21.9 .914 19.6 23.4 The descriptive statistics of variables listed are summarized in Table 2.5. Several variables are summarized here for descriptive purpose but they are not included in the hedonic model. One of them is the weighted API score, obtained by weighting each school’s API score by its enrollment. This variable is not included in the hedonic model because the API score of nearest elementary school captures more disaggregate school information and reflects school premiums in land values more precisely than the weighted API score. That said, the estimate of the school quality variable should be interpreted as a homebuyer’s willingness to pay for proximity to a quality school rather than an entry ticket to a high performing district. The other variables are dropped for collinearity problem. A collinearity check is then conducted for the 3 A quarter bath is usually found in older homes and it usually contains just a toilet or shower stall. 45 covariates. The correlations of variables entering the final model are smaller than 0.6. For example, the percentage of Hispanics is negatively highly correlated with the API score (-0.7841) and the percentage of Whites (-0.6782) and hence dropped. Several district variables (i.e., percentage of English learners, percentage of students qualified for free or reduced price meals, and percentage of minority students) are dropped for collinearity reason as well; they are highly correlated with socioeconomic variables (i.e., percentage of Whites, percentage of Hispanics) and the API score, or correlated among themselves. Regression results from the multilevel and the OLS estimation are summarized in Table 2.6. The first six columns of results are from multilevel estimation in a stepwise modeling sequence (Models 1-6). Each step demonstrates the contributions of the independent variables to the variations in house prices. The last column reports outcomes from the OLS estimation for comparison purpose (Model 7). As mentioned earlier, both dependent and independent variables are transformed by the natural log. Hence, the estimates from this table can also be interpreted as elasticity effects. Model 1 tests the null model with an intercept only. In the model summary part, the LR test calculates a likelihood-ratio to compare the mixed model to ordinary regression. Using the maximum likelihood method, LR test performs a likelihood-ratio test of the null hypothesis that the estimates from the unrestricted and the restricted models are the same. The likelihood ratios (LR) test statistics suggest that for the multilevel mixed-effects linear regression should not be reduced to a simple linear regression. ρ v and ρ u report the proportion variance due to differences between school districts and differences between tracts is 20.23% and 53.53%, respectively. The substantial variations in house prices across the boundaries support a hierarchical analysis. Model 2 tests the three housing structure variables—lot size, number of bedroom, and square footage. The signs of these estimates are positive, as expected. An increase in all these 46 variables raises the house value but square footage has the largest impact: a 10% increase in this variable levels up the house price by 6.6%. The inclusion of these variables, compared to Model 1, largely reduces the variance of residual and the variance of the tract level constant but not much for the variance of the district level constant. Model 3 includes the distance to the coastline. This distance variable influences variations in house price in the expected way. A shorter distance to the coastline boosts the property value significantly. A 10% increase in the distance variable leads to an approximately 1% decrease in the house price. The extra information of the accessibility to the coastline also considerably reduces the variance of the constant terms at both district and tract levels, resulting in a smaller proportion of the house price variance due to the boundary effects. Model 4 adds the last variable at the house level—the API score of the nearest elementary school. As expected, a higher test score of the nearest elementary school is associated with a higher property value. A 10% increase in the school quality raises the house price by 2.9%. The test score variable improves model performance substantially. The absolute value of the log likelihood is improved by 56.5663 (from -3900.72 to -3746.28). Improvements in AIC (Akaike information criterion) and BIC (Bayesian information criterion) (by 111.133 and 102.802, respectively) also strongly support the inclusion of the test score variable. Model 5 includes the density and racial composition information of the neighborhood. These variables further reduce the constant variances at the district and tract levels. The estimates of these variables all have expected signs. The property value will drop in a neighborhood with a higher population density and a higher proportion of African Americans. Meanwhile, a higher proportion of Whites will level up the value in the property. The inclusion of the neighborhood variables also reduces the effects of other independent variables. This is especially noticeable for the test score variable, with estimate changed from .2883 to .2342, meaning that a 10% increase 47 in the school quality will raise the property value by 2.3%. Thus far, all independent variables entered the model are highly significant. Model 6 is the final model with multilevel estimation. The last set of independent variable—district information—is included 4 . Among these variables (i.e., expenditures per pupil, class size, and pupils per teacher), only the expenditure variable is significant. Moreover, this variable has the largest elasticity among all independent variables. A 10% increase in expenditure per pupil will raise the house price almost the same amount, by 9.3%. While the test score is a highly valued indicator of school quality, expenditure is a complementary indicator of school quality. These two indicators are sometimes referred to input and output factors of a school quality (Brasington, 1999). Although some studies showed that school inputs are not valued by parents (Downes and Zabel 2002), this study demonstrates that an additional school spending raises property values (Barrow and Rouse 2004, Nechyba and Strauss 1998, Brasington 1999). With the addition information from the district level, estimates of other independent variables appear stable and consistent with results from Model 5. Model 7 keeps the same variables but adopts the OLS estimation instead. It should be noted that when multilevel analysis is reduced to a simple one-level analysis, the regression is essentially the same the OLS regression. The model has an adjusted R 2 of .6491 means that approximately 65% of the variation in house prices can be explained by the independent variables. Compared to the estimates from Model 1-6 of the multilevel approach, some estimates from the OLS estimation are quite different. For example, the elasticity of the test score is up from .2340 4 Another multilevel model with these three levels of variables is also estimated but the hierarchical order of neighborhood and school district is flipped. This separate model is estimated to test if the sign and magnitude of the API estimate are significantly different than those estimated from the original hierarchy. The results show that the API estimate (.2324) is consistent; the most noticeable differences occur for two variables: percentage Whites (.1760) and expenditures per student (.6932). 48 (Model 5) to .3294, whereas expenditure is down from .9309 (Model 6) to .7223. The variable of class size also becomes significant in from the OLS estimation. The fact that more variables turned significant in the OLS estimation may plausibly be associated with the risk of type I error (rejecting a null hypothesis of no causal relationship, which should not be rejected) due to the autocorrelation in the variables (Fotheringham et al. 2000). The superiority between the two estimation approaches can be measured by the AIC and BIC measures, a lower value of which signifies a better model fit. The result shows that the multilevel approach is better than the OLS estimation. In fact, the LR test from Model 6, which essentially compares Model 6 and Model 7, also rejects the linear regression (Chi square=5601.07). 49 Table 2.6: Comparison of results from OLS and multilevel estimation (N=30,669) (standard errors in parenthesis) Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Multilevel Estimation OLS Constant 12.5322 *** (.0495) 7.6415 *** (.0605) 8.4676 *** (.0766) 6.6215 *** (.1813) 6.9518 *** (.2365) -2.6349 (3.1056) -.9424 ** (.4010) Level 1 Lot size .0073 *** (.0002) .0074 *** (.0002) .0074 *** (.0002) .0074 *** (.0002) .0074 *** (.0002) .0076 *** (.0002) Bedroom .0688 *** (.0040) .0691 *** (.0040) .0687 *** (.0040) .0695 *** (.0040) .0695 *** (.0040) .0551 *** (.0042) Square Foot .6606 *** (.0059) .6637 *** (.0059) .6599 *** (.0059) .6576 *** (.0058) .6578 *** (.0058) .7294 *** (.0057) Distance_ coastline -.0930 *** (.0062) -.0965 *** (.0061) -.0918 *** (.0059) -.0897 *** (.0059) -.0971 *** (.0021) API score .2883 *** (.0257) .2342 *** (.0259) .2340 *** (.0258) .3294 *** (.0139) Level 2 Population density -.0488 *** (.0083) -.0487 *** (.0083) -.0544 *** (.0030) % White .1098 *** (.0302) .1107 *** (.0301) .1266 *** (.0082) % African American -.0862 *** (.0104) -.0842 *** (.0105) -.0703 *** (.0033) Level 3 Expenditures .9309 *** (.3015) .7223 *** (.0357) Class Size .1076 (.2737) .0880 *** (.0304) Pupils per Teacher .3454 (.4809) .0537 (.0470) MODEL SUMMARY Variance of District Level constant .0539 (.0176) .0462 (.0144) .0235 (.0076) .0176 (.0058) .0096 (.0033) .0073 (.0026) NA Variance of Census Tract Level constant .0887 (.0054) .0309 (.0020) .0250 (.0016) .0212 (.0014) .0165 (.0011) .0165 (.0011) NA Variance of residual .1238 (.0010) .0709 (.0006) .0708 (.0006) .0707 (.0006) .0707 (.0006) .0707 (.0006) .0890 (.0007) Log Likelihood -12565.82 -3900.72 -3802.85 -3746.28 -3674.90 -3670.77 -6471.31 AIC 25139.64 7815.443 7621.693 7510.56 7373.794 7371.545 12968.62 BIC 25172.97 7873.76 7688.341 7585.539 7473.766 7496.51 13076.92 Wald χ 2 NA 23483.82 23991.53 24371.01 25033.79 25072.52 56741.60 Prob > χ 2 NA 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 LR Test χ ’2 19846.19 15560.04 9443.65 7363.56 5999.07 5601.07 NA Prob > χ ’2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 NA ρ v 0.2023 0.3122 0.1974 0.1607 0.0992 0.0772 NA ρ u 0.5353 0.5209 0.4068 0.3543 0.2696 0.2519 NA Adjusted R 2 NA NA NA NA NA NA 0.6491 Note: *** indicates significance at 99% level, ** indicates significance at 95% level, * indicates significance at 90% level. 50 Using the estimates and standard errors from the hedonic analysis, t test is then conducted to compare if the coefficient estimates from the multilevel approach (i.e., Model 6) are different from those from the OLS estimation (i.e., Model 7), which is considered as the benchmark (Table 2.7). It shows that the multilevel approach produces three estimates significantly different from the OLS estimates, including the number of bedroom, square footage, and the test score. These variables belong to Level 1, which are house level variables. All estimates at Level 2 and 3 are not significantly different from the OLS estimates. The t test statistics suggests that OLS estimation may cause biased estimates for disaggregate variables. For aggregate variables, nonetheless, this conventional practice seems to be able to generate reasonable results. Table 2.7: t test on the equality of means of estimates from multilevel and OLS estimation Variable Multilevel Estimate Std Err Std Dev OLS Estimate t Pr(|T| > |t|) Lot size .0074 0.0002 0.0422 .0076 -0.8302 0.4064 Bedroom .0695 0.0040 0.7043 .0551 3.5806 0.0003 *** Square Foot .6578 0.0058 1.0240 .7294 -12.2456 0.0000 *** API score .2340 0.0258 4.5223 .3294 -3.6944 0.0002 *** Distance_ coastline -.0897 0.0059 1.0335 -.0971 1.2539 0.2099 Population density -.0487 0.0083 1.4532 -.0544 0.6869 0.4921 % White .1107 0.0301 5.2641 .1266 -0.5290 0.5968 % African American -.0842 0.0105 1.8347 -.0703 -1.3268 0.1846 Expenditures .9309 0.3015 52.8016 .7223 0.6919 0.4890 Class Size .1076 0.2737 47.9317 .0880 0.0716 0.9429 Pupils per Teacher .3454 0.4809 84.2264 .0537 0.6065 0.5442 Note: *** indicates significance at 99% level. Thus far, models using the multilevel estimation have only allowed intercepts to vary across the district and tract boundaries. The coefficients of the independent variables, however, are fixed. Nonetheless, homebuyers in different districts (or submarkets) may have different willingness to pay for school quality. Those who have a similar willingness to pay are likely to cluster under the same district, which can be accommodated by allowing the slope of the test 51 score variable to vary at the district level. The coefficient of the test score is thusly decomposed into the fixed and the random parts. Another assumption thus far is that the variance for each random effect within a random-effects equation is distinct and covariances are assumed to be zero. To relax this assumption, the covariances are now allowed to be distinct. Equation 2.7 is slightly modified from Equation 2.6: ijk ijk ijk ijk API x y * 1 1 0       ijk jk k ijk u v 0 0 0 0 0        k 1 1 * 1      2.7 Table 2.8: Results from multilevel analysis with random coefficient of the test score Model 8 Coef. Std Err. Constant -.2893 3.0539 Level 1 Lot size .0074 *** .0002 Bedroom .0693 *** .0040 Square Foot .6582 *** .0058 Distance_ coastline -.0898 *** .0059 API score .2381 *** .0409 Level 2 Population density -.0486 *** .0081 % White .1110 *** .0294 % African American -.0798 *** .0103 Level 3 Expenditures .6816 ** .2981 Class Size .0972 .2405 Pupils per Teacher .2912 .4392 MODEL SUMMARY Variance of random effect of API .0158 .0116 Variance of district level constant .6185 .4816 Covariance of API and district level constant -.0986 .0745 Variance of census tract level constant .0157 .0011 Variance of residual .0707 .0006 Log Likelihood -3666.177 AIC 7366.354 BIC 7507.981 52 Result from this estimation is presented in Table 2.8. Decomposing the coefficient of the test score significantly reduces the variance of the district level constant and hence reduces the variance of house price attributable to the district level. Most of the estimates from Model 8 appear consistent with the outcomes from Model 6. The effect of the expenditure per student has the largest reduction, down from .9309 to .6816. This can be interpreted as people’s value of expenditures per pupil is correlated with their value of test scores (Nechyba and Strauss 1998). The value of school expenditures is hence reduced when allowing homebuyers’ willingness to pay for test score to vary across districts. The random effects of the API test score estimated using Model 8 is reported for each school district (Table 2.9). The random coefficient appears uncorrelated with the average house price. In general, homebuyers who can afford to live in the best performing districts do not necessarily pay a higher proportion of the house price for school quality, although households from the lowest performing districts tend to pay less than the average. When combined with the fixed part of the test score coefficient (.2381), the total API coefficients reveal the willingness to pay for test score. The coefficients range from .0556 (Anaheim Elementary) to .4816 (Newport- Mesa Unified). When the grand total house price is taken into account, the absolute values of the school quality premiums have a wide spectrum. For example, the two most expensive school districts, Laguna Beach Unified and Newport-Mesa Unified, are associated with the largest school premiums in absolute term ($3069 and $2878, respectively), whereas some of the least expensive districts (i.e., Anaheim, La Habra City Elementary, and Santa Ana Unified) have the lowest school premiums ($126, $350, and $363, respectively). Some districts that are known for their good quality public education (i.e., Los Alamitos Unified and Irvine Unified) are associated with high premiums close to $1000. On average, homebuyers in Orange County paid a school premium of $789 for a 1% increase in the API score. 53 . Table 2.9: Premiums of test score at district level District Name Average house price ($) Weighted API score Random API coef. Total API coef. Premiums of Test Score ($) Laguna Beach Unified 776,077 868 .1573 0.3954 3068.95 Newport-Mesa Unified 597,624 747 .2435 0.4816 2878.42 Huntington Beach City Elementary 441,539 808 -.0497 0.1884 832.05 Capistrano Unified 396,402 803 -.0122 0.2259 895.65 Los Alamitos Unified 387,225 849 .0192 0.2573 996.50 Ocean View Elementary 356,691 760 -.0203 0.2178 777.03 Tustin Unified 352,750 742 -.0024 0.2357 831.59 Orange Unified 334,887 719 -.0232 0.2149 719.82 Irvine Unified 333,784 872 .0398 0.2779 927.73 Fountain Valley Elementary 323,731 838 -.0880 0.1501 486.06 Saddleback Valley Unified 315,285 842 -.0093 0.2288 721.51 Placentia-Yorba Linda Unified 307,560 764 -.0018 0.2363 726.90 Brea-Olinda Unified 305,519 828 -.0159 0.2222 679.00 Fullerton Elementary 299,378 709 .0768 0.3149 942.87 Cypress Elementary 281,737 826 .0800 0.3181 896.33 Westminster Elementary 258,850 696 -.0902 0.1479 382.95 Centralia Elementary 254,673 738 .0244 0.2625 668.63 Buena Park Elementary 242,116 698 .1155 0.3536 856.23 La Habra City Elementary 231,124 669 -.0869 0.1512 349.56 Garden Grove Unified 229,422 691 -.0492 0.1889 433.48 Anaheim Elementary 225,824 585 -.1825 0.0556 125.66 Magnolia Elementary 221,910 634 -.0055 0.2326 516.26 Savanna Elementary 206,080 738 -.0582 0.1799 370.83 Santa Ana Unified 205,204 564 -.0611 0.1770 363.30 TOTAL 337,484 722 -.0044 0.2337 788.85 2.6 Conclusion A multilevel framework is adopted in this study to account for the hierarchical nature of the spatial data, which appear to have attributes similar to their geographic neighbors (Tobler 1970). This paper assumes that house data are more homogeneous under the same geographic boundaries at both school district and census travel levels. The estimation result of the three-level model outperforms the OLS estimation. The likelihood test confirms that the house- neighborhood- school hierarchy is better than a flat (linear) organization of the data. The result 54 from the final model (Model 8) shows that homebuyers pay a substantial proportion of their house price for school quality, i.e. a 10% increase in the API score of the nearest elementary school levels up the house price by approximately 2.3%. This study may be improved by using a more comprehensive measure of school quality, rather than a single indicator (i.e., the API test score). Based on the publicly available information from the Department of California, information previously available at the district level is now available at the school level, which may facilitate the development of a better indicator for school quality. However, many of these variables are highly correlated with the API test score, such as percentage of Whites (ρ=0.8655), percentage of Hispanics (ρ=-0.9436), percentage of English learners (ρ=-0.9060), percentage of students eligible for free or reduced price meals (ρ=-0.9477), and average education level of the parents (ρ=0.8698). In this sense, the employment of the API score may already capture other aspects of the school quality to a certain degree, although there are possibly other better measurements. The shadow prices estimated by hedonic models reveal homebuyer’s willingness to pay for house characteristics and neighborhood amenities as well as public services. The estimation outcomes shed lights on not only the economic prospects but also the affordability issue in the house market. With respect to school quality, the substantial school premiums of public education presented in this study show that high-performing schools are associated with high land values, which are often bid up by households with high willingness-to-pay for education and certain financial affordability. The heterogeneous distribution of school quality and house price across the school districts has brought up concerns regarding the education opportunities for low-income families, who are more likely to live in less expensive neighborhoods, which are often attached with poor performing schools. 55 The outcomes of this study have two main implications for public policy. First, knowing the high public education premiums paid by homebuyers estimated in this study, we may expect continuing persistence in boundary effect. This boundary effect reflects the common interests and preferences of rent bidders, which in turn reinforces the autonomy of each school district. Social policies that aim to equalize the spatial distribution of the school quality may encounter resistance from the existing land owners if such redistribution suggests the weakening of the boundary effect and the depreciation of the school premiums for which homebuyers have bid with a hefty price. Second, the elasticity for school quality has a considerable variation across the distribution when accounting for the sizable difference in the average house price (i.e., ranging from $205,204 in Santa Ana Unified to $776,077 in Laguna Beach Unified). The absolute value of school premium has a remarkably wide spectrum: swinging from the lowest $126 to highest $3,069. The house price capitalization encourages homeowners to invest in durable public goods (Hilber and Mayer 2009). 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A Destination Choice Modeling Approach 3.1 Introduction Children’s journeys to school have increasingly occurred by car. In 2001, 50% of children age 6- 12 in the United States traveled to school by car, a significant change from 15% in 1969 (NHTS Brief 2008). As a result, a noticeable drop has occurred in children’s travel to school on foot or by bicycle. Walking to school can be an important part of children’s daily physical activities and a complementary part of in-school physical education classes (Tudor-Locke et al. 2001). What explains the change in children’s mode of travel to school? There are three explanations in the literature: 1) decentralization and declining residential density, which increases the average distance between schools; 2) increased traffic and other threats to personal safety when using non-motorized modes; 3) increased rate of employment among women with children (Staunton et al. 2003, Boarnet et al. 2005, Ewing et al. 2004, Lin and Chang 2010, Waygood and Kitamura 2009, McMillan 2007, McDonald 2008a, 2008b, NHTS Brief 2008). All of these are plausible explanations. However, the literature has not examined the role of school quality. It is well known that school quality varies across neighborhoods. Thus a fourth explanation for longer distance to school is the search for school quality, particularly among households residing near poorer quality schools. School choice policy is one cause of increasing travel distances and greater variation in transportation mode choice for journeys to school (Wilson et al. 2010, Yang et al. 2012). It is known that the spatial distribution of school quality in the United States is not homogeneous. Households that can afford to pay price premiums may locate themselves closer to good quality schools. The proximity to good schools guarantees admission while reducing commuting costs. 62 As a result, households with similar socioeconomic status and willingness-to-pay for public education cluster together; and high-income neighborhoods have better schools. There have been several education reforms attempting to break the strong tie between property values and public school quality, and to achieve better equity in public education. However, the situation has not improved significantly. A more recent reform to provide more school options for children is school choice policy. This policy, first available in California between 1985 and 1990, provides more choices for attending school, especially for those living in neighborhoods with low-performing schools. While traditional school assignment systems allocate students to their neighborhood school, the open enrollment program offers students more options through intra-district and inter-district transfer options. When parents are faced with choosing among the neighborhood school, other schools in the district, and out of district schools, how do they make the decision? The most frequently used method in education studies of revealing parental choice entails questionnaires or phone interviews, which ask parents to rank their school choices (Denessen et al 2005, Calvo 2007, Kleitz et al. 2000). However, the results are not based on actual choice behavior and may disguise some true preferences. To examine the link between school choice and observed trips and travel patterns, this paper retrieves data on school trips and identifies the actual choice of school from a regional household travel survey in the Los Angeles region; it models the effect of school attributes on school choice using the destination choice modeling approach. In this approach, the utility function of each destination choice consists of the school alternatives and the parents, who make school choices on behalf of/considering the preferences of their children. The outcomes will give us insights as to how parents, under school choice policies, explore various education opportunities for their children considering school distance and district jurisdiction barriers as 63 well as benefits from alternative public schools. This research may add a different perspective to current literature on understanding the decline of active commuting and the increase in travel distance, by linking travel distance to school quality and school choice. The remainder of this paper is organized as follows. In Section Two, I will review relevant literature on the destination choice method and parent school choice decision making. In Section Three, I will describe the data sources and methodology to delineate the feasible choice set. In Section Four, I will describe the model specifications and selection of the explanatory variables, and provide a descriptive analysis. In Section Five, I will describe the results from the estimations and the model’s predictive power using the estimates. Lastly, I will conclude in Section Six with implications of how school choice policy may affect children’s travel behavior. 3.2 Literature Review A number of detailed studies from the education and urban economics literature have examined which school characteristics parents value the most (Burgess et al. 2009, West et al. 1998, Coldron and Boulton 1991, Denessen et al 2005). In the process of parental choice, different types of parents may have different preferences for schools. Parents choose a school based on a range of factors. For example, they may choose a school based on peer group quality, such as test scores and student characteristics (Rothstein 2006, Brasington and Haurin 2006, Kane et al. 2006). They also may factor racial diversity into school choice decisions, and consider popular schools that are characterized by a high percentage of White students and high test scores (Calvo 2007). Among all the factors, the two most cited factors in school choice are location and academic performance (Calvo 2007, Burgess et al. 2009, Petronio 1995, Glazerman 1998, Black 1999, Nechyba and Strauss 1998, Barrow 2002, Barrow and Rouse 2004, Brasington 1999, Rothstein 2006, Downes and Zabel 2002). 64 The location of a school determines travel distance and travel time; thus it affects the level of convenience regarding school trips. It is suggested as the most important reason for parental school choice (Calvo 2007, Burgess et al. 2009). For example, in Calvo’s (2007) study, parents are shown to use distance from home to school to eliminate most schools. Many parents consider schools to be feasible only if they are located within a certain distance. To rule out schools of the lowest performance, parents also use test scores and reputation (Calvo 2007, Schneider and Buckley 2002). In Burgess et al.’s (2009) survey in England, the two most important factors in parents’ first school choice nomination are: proximity to home and a general good impression of the school, reported by 67.28% and 62.87% of parents respectively. Between these two reasons, location seems to matter even more: the largest percentage (25.56%) of parents choose proximity/ease of travel to be the most important criteria for nominating the school as the first preference. Academic performance is another main reason for school choice (Denessen et al. 2005, Kleitz et al. 2000, West et al. 1998, Armor and Peiser 1998, Coldron and Boulton 1991). Armor and Peiser (1998) studied the inter-district school choice program in Massachusetts. The three most frequently cited criteria for parents to leave for another school district are: academic standards, curriculum, and facilities. Based on Denessen et al.’s (2005) survey in the Netherlands, where there is no assigned local school for children and hence “a total freedom of school choice” (p. 349), quality of education is the leading factor among a list of 17 possible reasons for parental choice. Kleitz et al. (2000) studied parental school choice in North Texas. While different racial/ethnic and income groups have different preferences, there is a common goal for academic excellence by all types of parents. Parents’ preference for educational quality among lower socioeconomic status and racial minority groups is as strong as or even higher than it is among other groups. 65 The measurement of school quality can take various forms (Nechyba and Strauss 1998, Brasington, 1999, Weimer and Wolkoff 2001, Downes and Zabel 2002). Various proficiency scores, such as SAT scores and MEAP test scores, have been widely used as an indicator of school quality (Barrow 2002, Rothstein, 2006). Although test scores may be an imperfect measurement of school quality or student performance improvement, many parents still think test scores are a good measure of quality (Calvo 2007). Part of the reason is that test scores are publicly available, and quite often they are the only tangible evidence of quality that many parents reference (Calvo 2007). Proximity and school quality are valued differently by parents of different socioeconomic status (SES). Due to the distance, when facing the option to attend a better quality school, not every parent will choose to exercise that option. Some findings show that households of low SES are more likely to exercise the option (Calvo 1997). In Calvo’s study based on the Seattle Public School District, where a universal choice plan (no default assignment to neighborhood schools) has been implemented, less than 50% of public school students attended neighborhood schools. A large percentage of students took advantage of the open enrollment policy and traveled farther than the minimum distance to receive public education. More than 60% of travelers lived near low-quality schools, over 52% of whom chose high-quality schools and 45% chose medium- quality schools. Calvo’s study implied that low-income students are more likely to exercise the school choice option. Burgess et al. (2009) revealed an opposite finding. Drawing data from the Millennium Cohort Study, Burgess et al. found that parents of higher SES are more likely to choose a school with a higher ranking in academic quality, whilst lower SES parents are more likely to prefer proximity to the family home over academic performance. In general, they concluded that location matters more than school quality in the process of school choice. 66 Although the school choice program is designed to achieve better equity in public education and aims to provide more choices for students from low-performing districts, consensus has not been reached whether low-income households benefit from school choice programs. Whether a non-neighborhood school will be chosen is determined by parents’ value in school quality, their willingness to travel, and their mobility level. These determinants may vary by families of different socioeconomic status. The objective of this research is to explain the probability of a school being chosen and to examine how school and household characteristics affect school choice. 3.3 Data and Methodology 3.3.1 Data sources The study area of this research is the five-county Los Angeles region. This analysis draws from travel diary data from the 2001 SCAG (Southern California Association of Governments) Post Census Regional Household Travel Survey (RHTS). Taken once every 10 years and covering six counties in the region (i.e., Los Angeles, Orange, Riverside, San Bernardino, Ventura, and Imperial), the RHTS Travel Survey gathers information on where, why, and how people travel. Travelers complete either a 24-hour travel diary for each weekday, or a 48-hour travel dairy for weekends covering a Friday/Saturday or Sunday/Monday period. From Spring 2001 to Spring 2002, travelers from 16,939 households reported a total number of 134,247 trips. Imperial County, because it is a rural county, was excluded from further analysis, leaving 16,024 households in the sample. My sample of school trips was selected based on age and the trip purpose. A trip is selected if and only if the primary or secondary trip purpose was going to school (attending classes) and the age of the traveler was 5-18, a normal age for K-12 students. These school trips were grouped into two types based on whether the students were attending K-6 th or 7 th -12th grade 67 schools as two predefined categories in the survey. Trips related to other grades (i.e., daycare/pre- school, trade/technical, college, postgraduate) are excluded Categorizing the trips as elementary school trips or high school trips is important because students and parents in these two categories potentially base their school preferences on different factors (Lankford et al. 1995, Calvo 2007). It has been shown that the majority of students living near failing schools are willing to travel long distances for better schools (Calvo 2007). In addition, parents pay more attention to alternative and/or subtle measures, such as college attendance rates and reputation, than to the more publicly available measures of academic quality (i.e., average school test scores) (Calvo 2007). Treating these groups separately provides us with more detailed information on the most influential factors in school choice involving each subset of students. At the elementary school level, parents are primarily the decision makers of school choice. For this age group, students’ travels are more dependent on their parents’ schedules and time budgets. At the high school level, parents still may be the key decision makers. However, high school students often can have more input in the selection process because they are more independent and mature than their elementary school counterparts. As a matter of fact, high schools are quite different from elementary schools with respect to their spatial distribution and school characteristics (e.g., larger enrollments, class size, service areas, and test scores). For this reason, the choice sets for both groups are separated in order to disentangle parents’ preferences at each school level. Individual school attribute and location information is obtained from the California Department of Education. 68 3.3.2 Methodology 3.3.2.1 Destination choice approach The destination choice model is a type of location choice model. It is based on discrete consumer choice observed in real markets and random utility theory. Each individual traveler is assumed to have a set of feasible destination choices, which contains the actually chosen destination plus a number of feasible choices. This approach has been used to estimate the effect of variables included in the utility function on the probability a destination alternative will be chosen. The destination choice modeling approach has been used for activities such as shopping and recreation (Scott and He 2012, Fox et al. 2004, Simma and Axhausen 2002). The destination choice model approach applies discrete choice models (Scott and He 2012, Simma and Axhausen 2002, Ettema and Timmermans 2007, Pellegrini et al. 1997, Recker and Kostyniuk 1978, Kitamura and Kermanshah 1984, Koppleman and Hauser 1978, Miller and O'Kelly 1983, Timmermans et al. 1984). For each observation, the utility of taking part in an activity at a specific location depends on the attractiveness of that location, travel distance to that location, and the traveler’s attributes (Burns 1979, Ettema and Timmermans 2007, Scott and He 2012). 3.3.2.2 Matching stated destinations with schools In order to identify which school a student was attending during the RHTS survey, the X, Y coordinates of the school trip destinations are matched within a set of spatially available school opportunities in ArcGIS, a suite consisting of a group of geographic information system (GIS) software. Not all the destinations reported by the travelers match exactly with the school facilities, probably due to fuzziness in reporting the geographic locations and in the geocoding process. Therefore, the nearest school of the correct school type (i.e., elementary school for elementary 69 school students, high school for high school students) was assigned to each trip destination. The 5% with the lowest matching scores were then dropped. The second round of matching involved manually checking and removing unreasonable automatic school assignments. After the matching procedure, the distance from the stated destinations and the matched schools turned out to be fairly reasonable. For the public elementary school trips, the median of these distances is less than 0.088 mile, meaning the potential school is not far from the reported destination of school trips. The matching result for high school trips is similar; the median distance between the reported destination and the matched public high school is 0.121 miles. 3.3.2.3 Choice set The true choice set of the traveler is unknown to us (Simma and Axhausen 2002). The only observed alternative is the chosen alternative (Swait 2001). The simplest solution is to draw a subset of the alternatives from the universal choice set for each trip and assume that the IID (identically and independently distribution) property (McFadden 1978) holds in the destination choice model (Simma and Axhausen 2002, Pozsgay and Bhat 2002). The feasible choice set for each traveler can be delineated utilizing the observed travel distance or travel time, assuming that the conceivable choice set is correlated with the observed travel distance/time (Scott and He 2012, Kwan and Hong 1998). The same rationale in choice set generation can be applied to school choice studies. For example, Burgess et al. (2009) proposed an approach of forming the feasible choice set by defining the search radius for the current year’s catchment area as the 80 th percentile of the travel distance from the previous year’s cohort and capped at 20km. A similar approach is adopted here to delineate the feasible choice set, but the search radius is based on the observed travel distance from the same year’s travel survey and set to be greater than the true travel distance because some school alternatives can be located farther than 70 the actual chosen school. By choosing a greater search area, the chance of missing feasible alternatives is smaller. From the RHTS survey, the mean travel distance of students attending K- 12 schools is 2.04 miles and 2.97 miles for elementary school students and high school students, respectively. The travel distance is highly skewed: the median (i.e., 0.72 miles at elementary and 1.47 miles at high school level) is much smaller than the mean travel distance, suggesting that most students had a short travel distance but a small portion of them traveled a long distance. To define the search radii that the majority travelers had (e.g., 85%) while allowing for a greater search area for this small portion of travelers, a cutoff is used (i.e., 85 th percentile of the travel distance). For elementary school trips, the 85 th percentile of the travel distance for all elementary school students is 3.04 miles. If a student’s travel distance is less than the 85 th percentile then his/her search radius is 3.04 miles; otherwise the search radius is the student’s travel distance multiplied by 1.1. For example, if the individual traveled 8 miles, which is greater than the 85 th percentile cutoff mark (8>3.04), then the search radius is 8.8 miles. The multiplier (i.e., 1.1), which is a somewhat arbitrary number, allows for a larger search area for the top 15% of the travelers who traveled a longer distance than others. For high school trips, the 85 th percentile is 4.58 miles. After the delineations, schools contained in each catchment area form an individually unique choice set for each student. Within each choice set, public schools and private schools are fundamentally different. First, public schools are not allowed to charge tuition. Second, public schools behave as a local monopolist and may not expend all the revenues for purposes valued by students (Manski 1992). Due to such differences, the following parts will only focus on public school trips where the trip destination is a public school. In addition, private schools are dropped from the choice set of these trips. Eliminating private school trips and private school options in the choice set has several implications. First, by removing private school trips, we can estimate 71 the district boundary effect more precisely. Because there is no district boundary imposed on private schools, students are free to choose any private school. Hence the travel distance to private schools is longer than that to public schools. Second, by removing private school options, we have a set of more standardized measures of school alternatives. Private schools have distinctively different attributes from public schools. Private schools have academic superiority due to more autonomy and power (Chubb and Moe 1990), less uncertainty of admission, smaller class sizes, and a better off student population in terms of socioeconomics (Calvo 2007). Moreover, the consideration of cost and religious instruction further sets private school choice apart from public school choice (Calvo 2007). Therefore, after eliminating private school options, the effect of test scores and school locations may not be fully captured because both academic quality and travel distance are downscaled. However, this does not mean that the estimates are necessarily biased because the tradeoff between distance and school quality in private school choice may be similar to that in public school choice. The catchment areas for students attending public schools are shown in Figures 3.1 and 3.2. The figures show that families from the central area had smaller search radii whereas families from the outskirts had greater ones. The choice set generation results are summarized in Table 3.1. Each student’s individual choice set contains a different number of school alternatives. The variation in the size of the choice set is a consequence of both individual travel constraints (e.g., mobility level, willingness to travel) and the spatial distribution of the schools. In general, the choice set at the high school level is smaller than at the elementary school level. While the majority of elementary school students have less than 50 alternatives in their choice set, the majority of high school students have less than 15 alternatives. This is because of the smaller number and larger enrollment and class size of high schools vs. elementary schools. In other 72 words, high schools tend to have a larger service area than elementary schools, resulting in a much greater distance between high schools. Figure 3.1: Search radius of elementary school travelers 73 Figure 3.2: Search radius of high school travelers Table 3.1: Summary of the size of choice sets Number of schools in each choice set Frequency Elementary schools High schools 1 to 5 145 357 6 to 10 195 169 11 to 15 155 175 16 to 20 123 13 21 to 30 253 11 31 to 50 377 5 51 to 100 65 9 101 to 500 33 8 501 to 1000 14 0 1001 to 2000 5 0 Total 1,365 students (57,265 alternatives) 747 students (7,344 alternatives) 74 3.4 Models 3.4.1 Model specification Student travelers’ school destination choice is predicted using a binary logistic model (McFadden 1974). The utility function consists of the schools’ attributes, which can be categorized as location and school characteristics, and the individual and household attributes via interaction terms. Because parents of different levels of socioeconomic status have different preferences across school characteristics (Burgess et al. 2009, Schneider et al. 1998), the coefficients of the interaction terms reflect the marginal effect of the school location and attributes for a particular group of parents. The utility of destination j for individual n in the model is specified as jn jn jn V U    3.1 ) , , ( n j j jn T S L f V  C C C j n n     , 3.2 or more specifically n j n j j j jn T S T L S L V            4 3 2 1      where: L is a vector of location variables S is a vector of school attributes T is a vector of socioeconomic and neighborhood variables of student n α is an intercept β is a vector of coefficients of the independent variables and interaction terms ε is the disturbance, which is assumed independent from each other. C n is an individually unique choice set An individual n will choose school j if and only if 75 in jn U U  n C i j   , 3.3 The dependent variable is the probability whether an individual n chooses school j: ) exp( ) exp( ) exp( ) ( jn in jn n V V V j Y P    3.4 Definitions of the dependent and independent variables are summarized in Table 3.2. The dependent variables are grouped into three categories: location (L), school attributes (S), and attributes of the decision maker (T). Interaction terms are generated between the attributes of the decision maker and three school variables: distance from home, the API score, and a dummy variable indicating if the school is located out of the home district. Detailed definitions and reasons for variable selection are explained in the following section. 76 Table 3.2: Variable definitions Variable Definition Dependent variable P n (Y=j) The probability a school alternative j is chosen by individual n Independent variable Location variables (L) Distance Distance from home to school alternatives Neighborhood school 1 if the school alternative is the neighborhood school, 0 otherwise Nearest school 1 if the school alternative is the nearest school from home, 0 otherwise Outside school district 1 if the school alternative is located outside the residential district, 0 otherwise School attributes (S) API score The API score of the school alternative Enrollment Enrollment of the school alternative Student per teacher Number of students per teacher of the school alternative Attributes of decision maker (T) School quality Weighted API score of the residential school district 1 st quartile Quality (highest) 1 if the student is from a district ranked at 1 st quartile (in quality), 0 otherwise 2 nd quartile Quality 1 if the student is from a district ranked at 2 nd quartile, 0 otherwise 3 rd quartile Quality 1 if the student is from a district ranked at 3 rd quartile, 0 otherwise 4 th quartile Quality 1 if the student is from a district ranked at 4 th quartile, 0 otherwise School density Number of schools within 10 miles from home 1 st quartile Density (highest) 1 if the student is ranked at 1 st quartile (in density), 0 otherwise 2 nd quartile Density 1 if the student is ranked at 2 nd quartile, 0 otherwise 3 rd quartile Density 1 if the student is ranked at 3 rd quartile, 0 otherwise 4 th quartile Density 1 if the student is ranked at 4 th quartile, 0 otherwise Income Less than $10k 1 if the household income is less than $10k, 0 otherwise $10k to $25k 1 if the household income is between $10k and $25k, 0 otherwise $25k to $35k 1 if the household income is between $25k and $35k, 0 otherwise $35k to $50k 1 if the household income is between $35k and $50k, 0 otherwise $50k to $75k 1 if the household income is between $50k and $75k, 0 otherwise $75k to $100k 1 if the household income is between $75k and $100k, 0 otherwise $100k to $150k 1 if the household income is between $100k and $150k, 0 otherwise Over $150k 1 if the household income is more than $150k, 0 otherwise Race White 1 if the student is White, 0 otherwise Hispanic 1 if the student is Hispanic, 0 otherwise African American 1 if the student is African American, 0 otherwise Asian/Pacific islander 1 if the student is Asian or Pacific islander, 0 otherwise Other ethnicity 1 if the student is other ethnic, 0 otherwise 77 3.4.2 Selection of variables 3.4.2.1 Location To measure location, distance from home to the school alternative is used, and it is expected to decrease the school utility. Both travelers’ origin and destination data from the RHTS travel survey and the school location data from the California Department of Education are geocoded using X, Y coordinates. Therefore, distance from the school to the family home can be measured by the point-to-point Euclidean distance. School choice also is influenced by the boundary effect; school location means more than just geographical distance. When a study area consists of more than one school district where students may transfer out of their home district, some authority constraints, such as school district boundaries, should be considered as well, which differentiates school destination choice models from other types of travel (e.g. shopping and recreational). Three dummy variables are defined to reflect the spatial constraints: whether the school is a neighborhood school, the nearest school, and outside the residential school district. Nearest school only accounts for Euclidian distance and may or may not cross the district boundary. Neighborhood school refers to the nearest school that is within the same district boundary. Outside school district indicates whether a school is located in a non- residential district. Distance and these three dummy variables are closely associated. Shown in Table 3.3, more non-neighborhood schools and out-of-district schools were chosen as the travel distance increased. More than a quarter of the chosen schools are not in the residential district for travel distances of more than 2 miles. 78 Table 3.3: Proportion of neighborhood schools, nearest schools, and out-of-district schools actually chosen Elementary School Trips High School Trips Travel distance (in mile) Neighborhood school Nearest school Out of district school Travel distance (in mile) Neighborhood school Nearest school Out of district school <0. 5 (N=531) 85.69% 87.38% 1.69% <0. 5 (N=90) 98.89% 98.89% 0% 0.5 - 1 (N=342) 40.94% 41.52% 2.92% 0.5 - 1 (N=138) 90.58% 94.20% 3.62% 1 - 1.5 (N=142) 11.97% 11.97% 11.97% 1 - 1.5 (N=152) 79.61% 81.58% 2.63% 1.5 - 2 (N=85) 5.88% 5.88% 10.59% 1.5 - 2 (N=89) 67.42% 69.66% 6.74% >2 (N=265) 3.77% 3.77% 36.98% >2 (N=278) 24.82% 24.82% 25.54% TOTAL (N=1365) 45.93% 46.74% 10.48% TOTAL (N=747) 62.12% 63.45% 11.51% The median travel distance in different school choices have sizable disparity (Figure 3.3). Three types of public school choices can be defined under the school choice policy: neighborhood school, other schools within the district, and school out of the home district. Students attending the neighborhood school incur the shortest travel distance: 0.35 mile and 1.09 mile at the elementary school and high school level, respectively. Students going to schools out of their home district undertake the longest travel distance: 3.83 mile for elementary school students and 4.53 mile for high school students. Figure 3.3: School choice and median travel distance (in mile) 0.0 1.0 2.0 3.0 4.0 5.0 Elementary School High School 0.35 1.09 1.14 2.50 3.83 4.53 Neighborhood school Other schools within district Schools out of district 79 Because the neighborhood school is the closest school within the residential district, it is expected to be more likely selected than any randomly selected schools. The nearest school, which might be located across district boundaries, is also very likely to be chosen given its proximity to home. By contrast, school alternatives outside the district are expected to have a lower probability of being chosen because seats in a non-residential district are not guaranteed and the transportation costs of leaving the residential district are high. Because most nearest schools are also the neighborhood schools, these two variables are highly correlated and thus not included in the model together. 3.4.2.2 School quality and other school attributes California established a proficiency score, known as the Academic Performance Index (API), to measure school quality for individual schools. This score measures a school’s academic performance and growth based on test scores of students who participate in the Standardized Testing and Reporting (STAR) Program and the California High School Exit Examination. API scores are calculated by the California Department of Education (CDE) and disseminated directly to schools and districts. The API scores also are posted on the CDE‘s and most schools’ web sites, making the API a readily accessible standard measure of academic performance. In addition to measuring each school’s quality, the API score is also used to measure the push effect of a student’s neighborhood. Because school quality is highly valued by parents in the choice process, schools with low performance are more likely to push parents to seek out better schools than schools ranked high in school performance. Moreover, wealthier families have greater means to live close to good schools and are likely to live in high-performing school districts. To measure the correlation between income and school district quality, and to test 80 whether families from low-performing districts are more likely to exercise the school choice option, a district quartile variable is calculated as follows. Table 3.4: Test scores for school districts Elementary School and Unified School Districts Quartile of districts # of districts # of schools Min API score Max API score 1 40 326 769 911 2 40 396 705 764 3 40 469 628 704 4 40 912 497 627 High School and Unified School Districts Quartile of districts # of districts # of schools Min API score Max API score 1 29 52 715 876 2 28 63 641 715 3 29 94 567 638 4 28 119 423 564 The districts are ranked in quartile by the weighted average API score 5 of 2001 as a proxy for their quality (Table 3.4). The best performing districts are placed in the 1 st quartile and the poorest performing district in the 4 th quartile. In each quartile there are an equal number of school districts. A large gap exists in test scores between quartiles. For the elementary school level, the API scores in the lowest quartile range from 497 to 627, compared to the range of 769 to 911 in the highest quartile. A similar gap in the test score can be found at the high school level. As appears in Table 1, the size of school districts is correlated with district performance. The number 5 Please note that not all the districts are ranked. The weighted average API scores are based on the API score of individual schools. However, the geocoded school database only contains schools from 160 out of 173 school districts for elementary schools, and 114 out of 121 school districts for high schools. For this reason, 10 elementary school trips and 3 high school trips were dropped in the final set of analysis because there is no information on their residential school district. 81 of schools in each quartile increases as the district rank decreases. While there are only 326 elementary schools in the top quartile, the school number nearly triples in the bottom quartile, reaching a total of 912 schools. This correlation between the district size and district rank is also observed at the high school level: beginning from 52 high schools in the top quartile, the number rises to a total of 119 in the bottom quartile. Parents also consider other school attributes, such as peer effect and racial composition (Calvo 2007, Weiher and Tedin 2002). However, some of these attributes, such as racial composition and parents’ education level, are not included in the model because there are strong correlations with API score, such as percentage of Whites (ρ=0.8655), percentage of Hispanics (ρ=-0.9436), percentage of English learners (ρ=-0.9060), percentage of students eligible for free or reduced price meals (ρ=-0.9477), and average education level of the parents (ρ=0.8698). Enrollment is also added to the model to measure the size of the school. A larger school would be expected to draw a greater number of students than a smaller one. In addition to enrollment, class size is also controlled for because parents prefer a smaller class to a larger class (Burgess et al. 2009, Kleitz et al. 2000). Thus, a ratio variable—students per teacher—is added to the model as well, and it is expected to decrease the utility of a school. 3.4.2.3 School density Travel distance is associated with the density and spatial distribution pattern of schools (Ewing et al. 2004). When a family is living in a high density area, such as the central city, the dense distribution of and easy access to schools shorten the distance from home to the nearest school; when a family lives in a low density area, such as suburban counties, the sparsely distributed schools result in a relatively long travel distance. To control for this information, a school density variable is generated (Table 3.5). It is defined as the number of schools within a 10 mile radius 82 from home. Because there are more intervening opportunities, schools far away from home are especially unattractive if it is located in an area with a relatively high level of school density, compared to an area with a low school density level. Using the school density variables, travelers are broken down into quartiles, from those surrounded by the highest school density (defined as quartile 1) to those surrounded by the lowest school density (defined as quartile 4). Each quartile contains roughly the same number of students. Table 3.5: Summary of school density (number of schools within 10 mile radius from home) Grade Mean Median Min Max Std Elementary School 148.9 115 1 342 110.7 High School 21.3 16 0 50 15.4 3.4.2.4 Income category With quartile measures of school density and school quality in the residential area as well as the distance variable, the relationship between income and school characteristics can be tabulated (Table 3.6). The ranking of school density and the residential district quality mirrors the education opportunity gap between the rich and the poor. In general, households in lower income categories are more likely to live in areas with lower school quality (4 th quartile of school quality) and higher school density (1 st quartile of school density). This observation echoes Alonso’s (1964) rent bidding theory extended to public education: people who have a higher willingness-to-pay and affordability for public education will bid out others and reside in good school districts. Low- income families tend to have more financial and time constraints on travel arrangements (Grieco 1995). Because of high land prices in good school districts, poor households are more likely to live in districts with low academic performance. Low-income households also tend to travel shorter distances compared to high-income groups because of the easy access to schools in their neighborhoods. A Chi-square test (for school density and quality) and ANOVA test (for the 83 distance variable) show that there is a statistically significant difference (at the 95% level) between the school characteristics and distance among different income categories. The RHTS survey also reports that low-income households have a smaller number of workers per household, lower housing ownership, lower levels of car ownership and availability, and shorter travel distance from home to school. When the school choice programs are available, several studies using survey data showed that families of low socioeconomic status and racial minorities place a stronger emphasis on school quality than high-income parents (Kleitz et al. 2000, Weiher and Tedin 2002, Schneider et al. 1998). While the demand for quality schools can be met through the transfer programs, the realization of such education opportunities may be limited due to the lower mobility level and higher fraction of distance associated with families from low-performing districts. Table 3.6: Summary of selective household mobility indicators of students attending K-12 public schools Obs. Public school quality in home district School density in residential area 1 st quartile 2 nd quartile 3 rd quartile 4 th quartile 1 st quartile 2 nd quartile 3 rd quartile 4 th quartile <10k 118 2.54% 5.08% 22.88% 69.49% 45.76% 15.25% 17.80% 21.19% 10k to 25k 376 3.46% 13.03% 24.20% 59.31% 38.83% 25.80% 17.82% 17.55% 25k to 35k 279 6.09% 14.70% 25.09% 54.12% 29.75% 25.09% 23.66% 21.51% 35k to 50k 273 7.33% 23.44% 31.87% 37.36% 21.25% 17.58% 27.47% 33.70% 50k to 75k 410 11.46% 25.37% 35.85% 27.32% 19.02% 25.85% 27.32% 27.80% 75k to 100k 230 19.57% 20% 35.65% 24.78% 12.17% 29.57% 24.35% 33.91% 100k to 150k 157 32.48% 28.03% 22.29% 17.20% 10.83% 36.94% 23.57% 28.66% >150k 95 30.53% 34.74% 9.47% 25.26% 6.32% 44.21% 29.47% 20% Total 1938 11.61% 19.97% 28.28% 40.14% 24.25% 26.16% 23.84% 25.75% Note: Respondents who refused to report household income category (n=174) were not included in this table. 84 85 3.4.2.5 Racial information Parents of different racial groups may have different preferences for school characteristics (e.g., test scores, racial composition). For example, some studies showed that high-income White, Hispanic, and Asian parents prefer high test scores and a low percentage of African-American students whereas African-American parents are less sensitive about such indicators (Calvo 2007). Other studies pointed out that minority parents may choose a school with a higher proportion of students of the same race, a sorting process along racial/ethnic lines (Henig 1990, Weiher and Tedin 2002, Glazerman 1998). This phenomenon among minorities is referred to as “own-group preference” (Glazerman 1998). This can be interpreted as, when the minority household is living in a racially mixed neighborhood, the parents may travel farther should they prefer another school with more students of the same race. This preference may lead to a higher chance of choosing a non-neighborhood school or even an out-of-district school. 3.4.3 Descriptive analysis The final sample consists of 1,172 elementary school students and 620 high school students. The number of school alternatives in the choice sets totals 49,691 at the elementary school level and 6,156 at the high school level. Descriptions of the travelers and the chosen schools are listed in Table 3.7. For the distance variable, the median travel distance is 0.65 miles and 1.46 miles for elementary school and high school students respectively. The travel distances to high schools are longer due to their lower density and larger service area. A large portion of the students chose the neighborhood school: more than 46% of elementary school students and 63% of high school students attended their neighborhood school. Because slightly more students chose their nearest school rather than neighborhood school, which is a subset of the nearest schools by definition, the variable Nearest school was used in the model. Students going out of their residential district 86 were not common, at roughly 10%. The school attributes also differ between elementary schools in that some elementary schools have higher API scores, smaller enrollments, and smaller class sizes. In terms of the school quality of the residential districts, around 30% of the students lived in the top two quartiles verses roughly 70% in the lower two quartiles. This is because the school districts are ranked in quartile, with each quartile containing the same number of districts, and the poorer performing districts usually have more schools and students than the better performing districts. By contrast, the school density is ranked in quartile based on the density of students; therefore, each quartile has almost the same number of observations. When it comes to the demographics and socioeconomic status of the travelers, Hispanics were the largest ethnic group among the sampled elementary school students (46.50%), but their enrollment dropped at the high school level (34.68%), surpassed by Whites (45.97%). For income level, approximately 41.07% of the households had an income level below $35,000 while 12.72% of the households had an annual income of more than $100,000, reflecting the large wealth gap of people living in the Los Angeles region. Because household income information is highly correlated with school density and residential district school quality as shown in the previous section, it will not be included in the model. 87 Table 3.7: Descriptive analysis: the attributes of the chosen alternatives and the decision makers K-6 th grade (N=1172) 7 th -12 th grade (N=620) For continuous variables Mean Median Std. Dev. Mean Median Std. Dev. For categorical variables Percent Percent Location variables (L) Distance (home to school) 1.7936 .6463 4.4440 2.8265 1.4623 5.1507 Neighborhood school 46.33% 63.06% Nearest school 47.01% 64.03% Outside school district 9.90% 10.81% School attributes (S) API score 666.3925 659 119.5026 612.1532 606 99.2938 Enrollment 569.4181 535 223.4913 1935.29 1855.5 708.4107 Student per teacher 7.5251 6.415 4.4757 23.7560 21.995 9.8172 Attributes of the decision makers (T) Residential school district 1 st quartile (highest) 11.60% 11.29% 2 nd quartile 19.28% 20.16% 3 rd quartile 25.60% 33.55% 4 th quartile 43.52% 35% School density 1 st quartile (highest) 25.77% 22.26% 2 nd quartile 24.83% 28.23% 3 rd quartile 24.49% 22.74% 4 th quartile 24.91% 26.77% Income Less than $10k 6.48% 5.65% $10k to $25k 22.01% 16.29% $25k to $35k 14.93% 14.68% $35k to $50k 13.40% 13.39% $50k to $75k 21.50% 21.13% $75k to $100k 10.07% 14.03% $100k to $150k 7.00% 9.52% Over $150k 4.61% 5.32% Race White 36.52% 45.97% Hispanic 46.50% 34.68% African American 6.74% 10% Asian/Pacific islander 3.33% 4.35% Other ethnicity 6.91% 5% Note: Travelers who refused to report their ethnicity and household income (193 observations at the elementary school level and 127 at the high school level) are removed from descriptive analysis and statistical modeling. 88 3.5 Results Estimations of the variables are summarized in Table 3.8. Models at both grade levels have reasonable explanatory power. The pseudo R 2 is 0.34 and 0.44, respectively. Both models have a negative intercept, implying that the chosen alternatives as one category reported in the tables is less likely to occur than the reference group (all non-chosen alternatives represent the other category), which is expected because students have more non-chosen than chosen schools in their choice set due to the research design: the choice set of each student consists of one chosen school plus all other schools in the feasible choice set delineated by the search radius. Hence, the number and occurrence of non-chosen alternatives is much greater than the chosen alternatives. For both elementary and high school trips, all location variables are highly significant at the 99% level with expected signs. Distance is a significant deterrence for travel, which is manifested by its negative sign. Compared to elementary school trips, the effect of distance on travel is smaller at the high school level: the coefficient is reduced from -.6737 to -.2060. The effect of distance is partially captured by the other two location variables: nearest school and outside the residential school district. Being the nearest school from home has a much greater chance of being selected (with estimates of 2.8660 and 2.7092). By contrast, if a school is located outside the school district, its probability of being selected will be much lower (-.1.0258 and - 1.2753). This extra location and boundary effect is similar between elementary and high school levels. Most estimates of the school characteristics variables are significant. The API score, which measures school quality, increases the utility of school alternatives. Similar to the distance variable, the effect of this test score variable shrinks at the high school level, down from .0034 to .0018. Enrollment also is statistically significant at both grade levels. For high school trips, the enrollment factor has a greater magnitude. The student per teacher variable is significant at the 89 high school level with the expected sign but has an insignificant effect at the elementary school level. Three groups of interaction terms are created by multiplying the distance, outside school district, and the API score with the decision maker’s attributes, including school quality of the residential district, school density within 10 miles from the family home, and racial information. These interaction terms reveal the heterogeneous preferences of different demographic and socioeconomic groups. Distance and test scores are used in generating the interaction terms because these are the two most important factors in conventional school choice theory. However, inter-district transfers now allow students to choose schools from another district. Whether these extra school alternatives are welcomed by different groups may give us different perspectives of new school choice policies. For the school quality of the residential district interaction terms, the 4 th quartile (poorest school quality) serves as the reference group. This factor has no difference on preference for distance, boundary effect, and the test score at the elementary school level. However, this factor becomes significant at the high school level regarding distance and boundary effect. The estimates of the distance and school quality of residence interactions are significant and positive for the 1 st and 2 nd quartile (.0728 and .2037, respectively), suggesting that those who live in better school districts are less discouraged by travel distance. This is expected because households who can afford to live in good districts have higher incomes and mobility levels, which make transportation costs relatively inexpensive. With respect to who is more willing to leave the school district, the result is consistent with my hypothesis that students from better districts are more likely to stay, whereas those from the poorest performing districts are more likely to transfer to a different district, although the effect is significant only at the high school level. The coefficients are -2.95 and -1.97, respectively, suggesting that students from the 1 st and 2 nd quartile 90 are much less likely to leave their school districts, compared to the bottom quartile. This finding confirms that students from the better districts have a higher probability of choosing a school within the district, and vice versa. The higher inter-district transfer rate for students from the bottom districts may also mirror the major criteria in inter-district transfers: whether to allow a transfer depends on the difference in school characteristics between the residential and accepting districts (Los Angeles County Office of Education 2010). Because they have the poorest indicators, the bottom districts may increase the students’ likelihood of getting an opportunity to attend schools in a non-residential district. For the school density interaction terms, the 1 st quartile (areas with densest schools) is the reference group. This factor exhibits the strongest effect among the interaction terms, especially when it interacts with distance. It is hypothesized that there is a relationship between density and travel distance. The results are as expected. Families from the densest areas (1 st quartile) considered distance as more of an obstacle than families residing in other quartiles. This trend is particularly linear at the elementary school level: the estimates decrease from .6383 to .5543 to .5041, meaning that the negative effect of distance shrinks as school density increases. This confirms that distance from home to school is especially unappealing in high density areas. Hence, students from those high density districts travel shorter distances. The lower willingness to travel also can be related to income and mobility level. The finding at the high school level is consistent with this hypothesis as well, although only the 4 th quartile (.2057) exhibits a significant difference from the 1 st quartile. For the racial information interaction terms, White students are chosen as the reference group. Most racial attributes do not have a significant effect, implying that after controlling for the residential area’s school quality and school density, different racial groups have no statistically significant different preference for distance, boundary effect, and school quality. 91 However, there are a few significant interaction terms at the high school level. For example, Asians/PI (Pacific Islanders) are less willing to travel (-.1359) and African Americans find school quality less attractive (-.0010), compared to Whites. In addition, American Africans and Asian/Pacific Islanders are more likely to leave their home district (.9442 and .17149). Although beyond the scope of this paper, it would be valuable to explore why certain ethnic groups would leave their districts and whether the finding conforms to the “own-group preference” phenomenon among minorities (Glazerman 1998). 92 Table 3.8: Estimation results for school destination choice models Elementary School High School Coef. Std. Err. Coef. Std. Err. Intercept -5.0993 *** .3040 -3.5285 *** .5101 Location Variables Distance (home to school) -.6737 *** .0838 -.2060 *** .0661 Nearest school 2.8660 *** .0847 2.7092 *** .1406 Outside school district -1.0258 *** .3530 -1.2753 *** .4692 School Characteristics API score .0034 *** .0005 .0018 ** .0008 Enrollment .0005 * .0003 .0008 *** .0003 Student per teacher .0005 .0156 -.0419 * .0216 School Quality Interaction Distance x 1 st quartile (Highest) -.0537 .0668 .0728 * .0403 Distance x 2 nd quartile -.0244 .0248 .2037 *** .0700 Distance x 3 rd quartile .0315 .0426 .0660 .0611 Outside school district x 1 st quartile (Highest) -.2883 .4329 -2.9477 *** .7892 Outside school district x 2 nd quartile -.4170 .3318 -1.9729 *** .4717 Outside school district x 3 rd quartile -.1075 .2874 -.7134 .4566 API x 1 st quartile (Highest) -.0000 .0002 .0005 .0004 API x 2 nd quartile -.0000 .0002 -.0000 .0004 API x 3 rd quartile .0000 .0002 -.0000 .0004 School Density Interaction Distance x 4 th quartile (Lowest) .6383 *** .0844 .2057 *** .0711 Distance x 3 rd quartile .5543 *** .0861 .0667 .0826 Distance x 2 nd quartile .5041 *** .0832 .0866 .0583 Outside school district x 4 th quartile (Lowest) -.3206 .4028 -.4507 .6364 Outside school district x 3 rd quartile -.0676 .3316 -.2166 .5943 Outside school district x 2 nd quartile -.2758 .3067 .7917 * .4083 API x 4 th quartile (Lowest) -.0002 .0002 .0010 ** .0004 API x 3 rd quartile -.0005 ** .0002 .0005 .0005 API x 2 nd quartile -.0009 *** .0002 -.0003 .0004 Racial Information Interaction Distance x Hispanics -.0493 .0522 .0618 .0516 Distance x African American .1037 .0725 .0986 .0676 Distance x Asian/Pacific islander .0517 .1385 -.1359 ** .0573 Distance x Other ethnicity -.0295 .0454 .0722 .2082 Outside school district x Hispanics -.1337 .2897 -.6546 .4316 Outside school district x African American -.2164 .5261 .9442 ** .4758 Outside school district x Asian/Pacific islander .1842 .5418 1.7149 *** .6379 Outside school district x Other ethnicity -.3791 .4498 -.5908 .8694 API x Hispanics .0002 .0002 -.0004 .0003 API x African American -.0003 .0003 -.0010 ** .0005 API x Asian/Pacific islander -.0001 .0004 -.0005 .0006 API x Other ethnicity .0002 .0002 -.0000 .0009 MODEL SUMMARY Log Likelihood Null model -5549.6842 -2010.8611 Full model -3656.3123 -1125.035 Pseudo R 2 0.3412 0.4405 Note: *** indicates significance at 99% level, ** indicates significance at 95% level, * indicates significance at 90% level. 93 Nonetheless, it remains somewhat puzzling that the effect of the distance and school district interaction terms involving Asians/PI at the high school level is opposite: This group is more likely to transfer out crossing their district boundary whereas they are less willing to travel. Upon a close examination, Asians/PI traveled longer distances on average than the whole sample. Their median travel distance is 1.974 miles compared to 1.462 miles for all ethnic groups and 1.626 for Whites (reference group). The negative effect of distance is due to the API score control. Asians/PI attended schools of higher test scores than average. The median API score of this group is 715 compared to 606 for the population and 653 for Whites. Therefore, Asians/PI did travel farther than both the population and the reference group, but primarily for the sake of school quality. When the school is of an average quality, this group will be discouraged by distance more than the other groups. Therefore, their lower willingness to travel (after controlling for test scores) does not conflict with the fact that this group is more likely to cross district boundaries. While the sample only consists of about 3.33% of Asians/PI, Asians/PI accounted for 13.04% of those who transferred out of their residential district, suggesting that this group of families is better in exercising the inter-district transfer option. A further investigation on the location of the homes of 11 Asians/PI students from eight households who transferred out 6 shows that these homes are all close to the district boundary. Whether this group of families is more informed of the school choice policy or whether they chose their residential location more strategically deserves further investigation. Nonetheless, given the small number of Asians/PI in the sample and the number of those who left their residential district, this racial group may not be a representative sample. Therefore, the outcomes here should be interpreted with discretion. 6 This number includes one family that did not report household income category. This family is not included in the model. 94 With the estimates from destination choice modeling, a post-estimation prediction is conducted. While the pseudo R 2 provides the explanatory power of the model, prediction outcomes indicate the prediction power, even though these two indicators are often correlated. For the 1,172 elementary school trips, 551 of the predicted alternatives are the actual chosen alternatives, which is equivalent to a correct prediction rate of 47% (551/1172). For the 662 high school trips, 416 of the predictions turn out to be true destination choices, equivalent to a correction prediction rate of 67% (416/620). Because the model for high school trips has a higher explanatory power, it has better prediction power than the model for elementary school trips as expected. 3.6 Conclusion School choice policy allows students to attend a school other than their neighborhood school. The interplay between conventional school assignments based on home location and the increasingly popular school open enrollment policies, which grant students the right to intra-district and inter- district transfers, has created a more diverse choice set for parents, including neighborhood schools, non-neighborhood schools, and out-of-district schools. This paper examines how parents choose schools under the open enrollment program while gauging the fraction of distance and boundary effect as well as the attraction of school quality. Drawing from travel diaries from the Los Angeles region, where school choice policy has been implemented, this paper uses an activity-based approach to track where students go during their school trips and to examine how much the spatial location and academic quality of a school can affect the destination choice. Both the school alternative attributes and the travelers’ attributes were included in the model to test for their influence on the probability a school destination will be chosen. The two main categories of variables, school location and school attributes, are both highly significant. 95 Distance and test scores, as expected, have a large elasticity, suggesting their influential impact on probability predictions. This is consistent with the education literature, which suggests that distance and test scores are the two most frequently referenced indicators to gauge the attractiveness of a school. In addition, interaction terms are used to examine whether there are heterogeneous preferences for location and school characteristics, accounting for the differences in residential area’s school quality and school density and the household’s race. It is shown that different demographic and socioeconomic groups have heterogeneous decision making preferences in choosing a school, especially in terms of their preferences for distance. There are two noticeable linear trends. First, families from better school districts are less likely to leave their district. Those living in the top quartile have a lower demand for travel because they can afford the premiums for proximity to good schools and ensured admission. In contrast, students in the poorest districts have a higher probability of leaving the residential district by exercising the inter-district transfer option. This finding supports an earlier hypothesis that the poorest performing districts are associated with a greater push effect. Second, families from dense school areas consider distance as a greater impediment whereas those living in areas with a smaller number of schools (2 nd through 4 th quartile) are more willing to travel. This is also consistent with our expectation because high school density means a shorter distance from home to school. Such easy access to schools makes long distance travel very unappealing. Besides distance, boundary effect is another obstacle for long distance travel. Even under the school choice policy, traditional school assignment remains a general practice with a substantial portion of the student body (46% at the elementary and 63% at the high school level) attending neighborhood schools. Being located outside the residential district has a significantly negative impact. Even though inter-district transfers have been made possible, the majority of the students, approximately 90%, still opt for schools in their residential districts. The smaller 96 proportion of students enrolled in a non-resident district school implies the constraints and difficulties of large-scale inter-district transfers. Intra-district transfers, compared to inter-district transfers, appear more common and easier to adopt. The results are not surprising given the many challenges of crossing district boundaries (Dillon 2008). For example, the implementation of open enrollment programs may not be effective due to the lack of proper transportation assistance and busing services (Ryan and Heise 2002, He 2011). While school choice policy is appealing in that it allows students to attend a better school according to their own individual pursuits, there are still various possible factors (i.e., class room capacity, application process time, and transportation cost) that decrease the attractiveness of non-residential districts requiring further investigation. That being said, school choice policy can have an influential impact on long distance travel and active commuting, nevertheless. As shown in Table 3, for those who traveled more than 2 miles in their journeys to school, a substantial number of them attended out-of-district schools (i.e., 37% of the elementary school trips and 26% of the high school trips). This finding echoes previous studies that examined the effect of school choice policy on travel mode choices (Wilson et al. 2010, Yang et al. 2012). If school choice policy continues to gain popularity and these open enrollment programs are implemented more effectively, we may expect more students to leave their home district, embarking on a longer trip that is more likely to be undertaken by automobile or by bus should an adequate busing service exist. This paper is limited in several aspects. First, it excludes all private school students. The assumption that children will choose between either a set of private or public schools exclusively may not hold in practice. Second, it excluded all private schools in the choice set. 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The Effect of Intra-Household Scheduling and Spatial Coordination 4.1 Introduction In the United States, the share of children age 6 to 12 who travel to school by private vehicle has increased from 15% in 1969 to 50% in 2001. An outcome of increased car dependency is that children are missing an important part of physical exercise outside their classrooms (Tudor-Locke et al. 2001). Much research on school transportation has been conducted to identify what factors influence children’s travel-to-school mode choice and how to incorporate the information into urban design and transportation engineering (DiGuiseppi et al. 1998, Ewing et al. 2004, McMillan 2005, McMillan 2007, McDonald 2008a, Müller et al. 2008, Black et al. 2001, Schlossberg et al. 2006, Babey et al. 2009, Zhu and Lee 2008, Davison et al. 2008). A child’s mode to school is influenced by the parent(s). As part of general parental responsibilities, the parent decides whether the child is escorted to school or travels by himself/herself. Thus an increasing share of auto trips may reflect parental choices and constraints. For example, women’s increased labor force participation can be a constraint as important as travel distance. Although a child’s mode choice depends on parental choice, the decisions of escort and travel mode are usually modeled as separate decisions with most studies focused on mode choice (McMillan 2007, McDonald 2008a, Wilson et al. 2010). In fact, the child’s mode and whether the child is escorted by a parent (or other caretaker) are related. For example, children who are escorted to school are most likely to be dropped off or picked up by car, whereas those who travel independently are more likely to use modes such as walking, biking, and bus. 103 To study the escort-mode joint decision, it is important to consider intra-household bundling constraints. Intra-household bundling constraints can be defined as the scheduling and spatial constraints that determine whether a household member is able to join another member during an activity. Applying this concept to school trips, whether a parent can escort their children to school may depend on the parent’s scheduling and spatial constraints, e.g. work schedule and job location. The effects of intra-household bundling have only recently been addressed: parental employment and flexibility of work hours are significant factors in escort and/or mode choice of children’s school trips (McDonals, 2008; Vovsha et al. 2004, Vovsha and Petersen 2005, Yarlagadda and Srinivasan 2008). Spatial constraints, which may also affect the joint trip realization, have not been accounted for. The child may attend a non-neighborhood school, increasing trip distance and making walk or bike trips less feasible. Attendance at non- neighborhood schools is increasingly likely due to open enrollment policies. In some cases, students may be able to transfer to districts where their parents work. Therefore, although the student attends a non-neighborhood school that is farther from home than a neighborhood school, it can be closer to the parent’s work location, which in turn facilitates parental pickup and drop- off duties. To the author’s knowledge, little of the school-work spatial relationship has been studied. This paper will complement previous studies by including the spatial (dis)coordination and time (de)synchronization between parents and children in the model. The importance of intra-household spatial and temporal coordination on the escort-mode choice may vary across different household structures because of different household structures and unequal chauffeuring responsibility. For this reason, five types of households are defined in this study, including two types of two-parent households (i.e., dual-earner, non dual-earner), two types of single-parent households (i.e., father-headed, mother-headed), and no-parent households (i.e., other-headed). The main focus group of this research is the dual-earner households, because 104 only for this household structure that the father’s and mother’s employment status and job locations can be identified at the same time, which enables their respective effect on escort-choice decision to be estimated. In the survey data used in this study—2001 SCAG (Southern California Association of Governments) Post Census Regional Household Travel Survey (RHTS)—dual earner households accounted for roughly 73% of the households that participated in the school trips. This research presents a first attempt in bringing both scheduling and spatial variables that are derived from the parent’s work arrangement and workplace to model escort-mode decisions of school trips. The outcomes in this paper demonstrate that the parent’s, especially the mother’s increasing work hours and distant job location could result in an increased likelihood of several alternative escort-mode choices. Mothers who work longer hours and farther away from home are less likely to escort their children in car. These trips have been substituted by alternative escort choices such as escorted by fathers and by siblings, or alternative mode choices such as active commuting and busing. Moreover, the estimates of the spatial coordination variables suggest that, when the parents would like to escort the child to school, the child may attend a school closer to his/her parent’s workplace in order to facilitate the joint-trip realization. This decision may result in a longer travel distance and a different mode choice than those who travel independently. 4.2 Theoretical Framework and Empirics 4.2.1 Theoretical framework of time geography This paper adopts a time geography framework (Hägerstrand 1970), which centers around the spatial and temporal constraints on the movement of individuals. The advantage of this framework lies in its ability to treat both individuals and society as a whole and its focus on “the 105 various types of constraints and finitude which wall-in the action alternatives of individuals” (Pred 1977, pp. 210). According to this theory, the constraints can be categorized into three types: individual, bundling, and societal constraints. Individual constraints refer to biological, physiological necessities; bundling constraints refer to when, where, and how long must an individual join others; and societal constraints refer to accessibility to specific domains at specific times determined by rules, laws, economic barriers (Hägerstrand 1970; Pred 1977). Although the joint school trips involve all three types of constraints, its realization depends heavily on the bundling and societal constraints. Bundling constraints emphasize both temporal synchronization and spatial coordination between the parent and the student whereas societal constraints address the institutional cooperation. It is possible that societal changes such as the provision of childcare or having flexible start time at school can relax the time and space constraints of the parents. However, institutions are usually more resistant to change as it is a collective effort of the interconnected social systems. For this reason, this study will focus on bundling constraints such as parental work arrangement and workplace location, which are likely to affect the space and time restrictions more easily within the household. 4.2.2 Empirics of temporal synchronization and spatial coordination Previous studies on household interactions have focused mainly on household heads until recently. Vovsha and Petersen (2005) examined household interactions between adults and children regarding their joint trip decision makings. Using data from the Atlanta region, they combined both to and from school trips and defined three escorting decisions (i.e., ridesharing with a household member who is on the way for a mandatory activity, pure escorting by a household member who has no mandatory activity on the tour, and no escort) each way. The estimation results showed that part-time workers and non-workers were significantly more likely to escort 106 their children but for inbound trips only. The authors suggested that their model would be enhanced by explicitly including an additional variable—flexible work hours. One drawback of Vovsha and Petersen’s (2005) model is that they only accounted for auto trips and ignored other transportation mode choices, especially for the active commuting modes. With a focus on walking and biking mode choice, McDonald (2008a) tested whether parent’s work schedule can affect children’s mode choice to school. With a national sample in the United States, McDonald’s work revealed that the mother’s work status and departure time increased the likelihood that elementary and middle schoolers’ active commuting, but the association was not found in the father’s work status. It was found that mothers who traveled to work in the morning were associated with a 7.7% decrease in children’s walking or biking to school. In contrast, fathers who traveled to work in the morning were found to increase children’s non-motorized travel by 7%. While the findings are interesting, the decision is limited at the mode choice level and does not link mode choice with escort choice. Yarlagadda and Srinivasan (2008) used an escort-mode choice model to study the effect of household interactions. For some modes (i.e., bike and drive, school bus, and transit), the escorting decisions are not differentiated. Only walking and being a passenger were split by the escorting arrangement (i.e., walked alone, walked by mother, driven by mother, driven by father, and driven by other). They found that the father and mother’s employment status and work schedule had a significant impact on children’s private vehicle use. Working mothers were more likely to drop off the children, whereas working fathers were less likely to drop off their children. The association between parent’s work commitment and children being chauffeured were not found in pick up trips, suggesting less temporal overlaps between work-school end times than the overlaps for start times. 107 One caveat of the aforementioned escort and/or mode choice studies (Vovsha and Petersen 2005, McDonald 2008a, Yarlagadda and Srinivasan 2008) is that, despite their attempts to include parents’ work schedule in school trips, the focus still remained on time synchronization whereas spatial coordination among household members (i.e. the distance from parent’s work place to school) has largely been missing. We know that scheduling and joint trip decisions are influenced by factors along both the time and space dimension (Hägerstrand 1970). The distance from the parental work place to the school is expected to decrease parents’ involvement in school trips; hence, this spatial variable will likely affect the escort and mode choice. This paper will fill this gap by including both space and time constraints in the escort-mode choice models. 4.3 Methodology 4.3.1 Study area and data In this study, the trip data came from the 2001 SCAG (Southern California Association of Governments) Post Census Regional Household Travel Survey (RHTS), covering six counties in the region: Los Angeles, Orange, Riverside, San Bernardino, Ventura, and Imperial. Because it is a rural county, Imperial County was excluded from further analysis, leaving 16,024 households in the sample of the five-county Los Angeles Region. My sample of school trips is selected based on age (5-18) and the trip purpose indicated in the survey. A trip is selected if and only if the primary or secondary trip purpose is going to school (attending classes) and the age of the traveler is 5-18, a normal age for K-12 schoolers. Statistical analysis of this travel survey shows that students in the Southern California Region had high car dependency and low usage of alternative modes. Among this age group of travelers, more than 60% travel to school by private vehicle, roughly 24% on foot or by bicycle, and slightly more than 11% by school bus; few students travel by transit bus or by subway 108 (Figure 4.1). Because trips undertaken by rail and express bus have a very small share by students in the region (3 trips accounting for 0.09%), they are removed from further analysis rather than combined with bus trips (to become transit trips). The rest of the transportation mode choices are combined into four: walking and biking (active commuting modes or non-motorized modes), bus (school bus and local bus), being a passenger, as well as driving. Figure 4.1: Mode choice summary (N=3,172) Different types of households view and share the escort responsibility differently. Therefore, household structure is expected to play an important role in the escort decision. The focus group in this paper is two-parent households, which account for 73.12% of the households. There are also a substantial proportion of the households that are single-earner households: mother-headed households account for over 20.55% and father-headed households take up 5.64%. Table 4.1 shows that, in general, slightly over half of the trips are escorted by parents: mothers share roughly 40% of the escort responsibility and fathers share a much smaller fraction of the escorts at 12%. Trips of students from single-parent households exhibit significantly different patterns. For example, students from these families are more independent on their journeys to 21.78% 2.24% 3.18% 60.44% 1.10% 0.06% 11.19% 0% 10% 20% 30% 40% 50% 60% 70% 109 school. The share of their independent trips is 2%-8% higher than general households. Students from father-headed households are nearly three times more likely to be escorted by the father (35.47% vs. 13.08%), almost twice more likely to travel with their siblings (28.49% vs. 14.78%), and over seven times more likely to be escorted by other household members (6.40% vs. 0.21%). By contrast, students who live with a single mother have escort patterns similar to the general households except that more trips are undertaken independently (30.63% vs. 20.49%). Although it is known that single parents need to balance both childcare and work and they may be more likely to receive help from their family to share some childcare responsibilities, the statistics here show that single mothers do not receive as much escort assistance from other household members as single fathers do (1.94% vs. 6.40%). Lastly, notwithstanding the small sample sizes of students from non parent-headed households, they exhibit very different travel patterns as well compared to traditional household types. Table 4.1: Escort decision by household structure Escort Decision All Households By Household Structure Travel companion Two parent Father headed Mother headed Child or other household member headed Parent(s) Father & Mother 1.61% 2.16% N/A N/A N/A Father 11.68% 13.08% 35.47% 0% 0% Mother 40.64% 43.10% 0% 43.76% 0% Others Sibling(s) 15.94% 14.78% 28.49% 16.53% 27.78% Other household member(s) 0.88% 0.21% 6.40% 1.94% 0% Non-household member(s) 6.37% 6.18% 4.65% 7.13% 22.22% Independent Self 22.88% 20.49% 25% 30.63% 50% Total number of trips 3169 2362 172 617 18 Percentage 100% 74.53% 5.43% 19.47% 0.57% 110 4.3.2 Defining escort-mode (EM) choices After linking transportation mode and removing trips with unknown travel companions and travel modes, the preliminary data set of households is reduced to 3,169 trips. Table 4.2 shows that walking is more frequently seen during trips undertaken alone or accompanied by siblings. When trips are escorted by parents, they are predominantly undertaken by car. Similar car dependence level is observed when trips are escorted or accompanied by other household members or non- household members. An interesting difference is found again between trips escorted by fathers and by mothers. It appears that women have continued their traditional role in childcare; the number of trips escorted by mothers is over three times as many as trips escorted by fathers. In addition, when the father escorts school trips, over 95% of the students are passengers and only 3% of them walk; whereas when the trips are escorted by mothers, more students walk (11.96%). Table 4.2: Escort-mode decision analysis (row percentage in brackets) Escort Type Relationship Travel companion N Walk Bike Drive Passenger Local/Express bus School bus Independent Self 725 (100) 333 (45.93) 52 (7.17) 74 (10.21) 28 (3.86) 238 (32.83) Dependent With household member Escorted by parent(s) Father & Mother 51 (100) 4 (7.84) 47 (92.16) Father 370 (100) 11 (2.97) 2 (0.54) 1 (0.27) 356 (96.22) Mother 1,288 (100) 154 (11.96) 3 (0.23) 2 (0.16) 1,124 (87.27) 4 (0.31) 1 (0.08) Not escorted by parent Sibling(s) 505 (100) 183 (36.24) 14 (2.77) 16 (3.17) 176 (34.85) 2 (0.40) 114 (22.57) Other household member(s) 28 (100) 6 (21.43) 21 (75.00) 1 (3.57) No household member Non- household member(s) 202 (100) 8 (3.96) 193 (95.54) 1 (0.50) Total 3,169 (100) 691 (21.80) 71 (2.24) 101 (3.19) 1,917 (60.47) 35 (1.10) 355 (11.20) Note: The dominant transportation mode for each escort type is underlined. 111 112 Suppose for each transportation mode we have five escort decisions: travel alone, escorted by mom, escorted by dad, accompanied by siblings, escorted/accompanied by others. Meanwhile suppose we have five transportation modes (i.e., walking, biking, bus, driving, being driven), then this exhaustive set of escort-mode choices would contain a total of 25 (5 x 5 = 25) alternatives. It would be difficult to estimate for such a large of choice set with the given dataset because many alternatives account for a very low percentage of the total trips. To avoid the potential collinearity problem that may be introduced by a small number of observations for certain alternatives, it is necessary to redefine/reduce the alternatives. For trips chauffeured by both fathers and mothers, given the traditional household relationship where men are more often the decision makers than women, the father is more likely to be the decision maker during these trips. Hence, for trips when both parents are present, these trips are considered similar to trips escorted by father and thus grouped together (EM1). Trips driven by the mother is the most frequent escort-mode alternative among the seven choices; hence it is chosen as the reference group (EM2). Trips chauffeured by others make up a significant proportion of the total trips and therefore are categorized as a separate choice (EM3). Walking or biking trips are only observed in three escort choices: either independent travel or with siblings or parents. In other words, active commuting is rarely accompanied by other household members or non-household members. Furthermore, walking or biking trips escorted by parents are infrequent. To ensure that the model converges in the estimation, walking/biking trips escorted by parents are combined with walking/biking trips escorted by siblings. Therefore, there are two alternatives for active commuting trips, either with a companion (EM4) or independently (EM5). Lastly, driving and busing trips are conducted predominantly alone or with minimal participation of parents. Therefore, under the categories of driving (EM6) and busing (EM7) there are no escorting decision differentiations. 113 Table 4.3 lists the seven escort-mode alternatives to be modeled for all general households and dual-earner households. Driven by mother (EM2) is the dominant escort-mode choice for all households (35.47%). It also dominates the escort-mode choice for two-parent households (37.47%) and mother –headed households (38.74%). In fact, students from two-parent families have shares of each escort-mode alternative similar to the shares observed in mother- headed households (except for the higher share of bus trips), suggesting mothers take up the main escort responsibility. By contrast, students from father-headed households are much more likely to be driven by the father and others. In households without parents, students are significantly more likely to be chauffeured by other household members, drive, or go to school by bus. This result is not unexpected; when the parent is not present in a household, the involvement of other caretakers or the independency of the student during school trips increases as a response. However, given the small number of observations in other-headed households, these trips will be removed from further analysis. Table 4.3: Escort-mode choice alternatives, by household type Mode Escort Party Escort-Mode Decision Choice All Households Two-parent Households Mother- headed Households Father-headed Households Other-headed Households Obs. Col. Pct Obs. Col. Pct Obs. Col. Pct Obs. Col. Pct Obs. Col. Pct Passenger Father & mother, or father only Driven by both parents or by fathers only EM1 403 12.72% 344 14.56% 0 0.00% 59 34.30% 0 0.00% Mother Driven by mother only EM2 1,124 35.47% 885 37.47% 239 38.74% 0 0.00% 0 0.00% Siblings, other household or non- household members Driven by others EM3 390 12.31% 246 10.41% 87 14.10% 48 27.91% 9 50.00% Walk or bike Parent, siblings, other household or non- household members Active commuting with a companion EM4 377 11.90% 294 12.45% 66 10.70% 17 9.88% 0 0.00% Self Active commuting independently EM5 385 12.15% 265 11.22% 96 15.56% 22 12.79% 2 11.11% Drive Any type Drive EM6 101 3.19% 72 3.05% 20 3.24% 6 3.49% 3 16.67% School bus or local bus Any type Bus EM7 389 12.28% 256 10.84% 109 17.67% 20 11.63% 4 22.22% Total 3,169 100% 2,362 100% 617 100% 172 100% 18 100% Note: The dominant escort mode for each household type is underlined. 114 115 4.4 Models Because there is no theoretically clear hierarchy of the escort and mode choice decision, both decisions are assumed simultaneous and then they are considered a joint choice decision (Yarlagadda and Srinivasan 2008). The escort-mode choice is estimated using the multinomial logit model (MNL). The multinomial logit regression fits the model by using the method of maximum likelihood estimation. Coefficient estimates on the probability of each of the outcomes compared to the reference group are reported. The utility accounts for factors that influence not only mode choice but also escorting decision. The utility function used in this analysis is the sum of the utility of individual n choosing option i to school: jn jn jn V U    4.1 n j j jn X V     C j   4.2 D E R H S X 5 4 3 2 1            4.3 where α is the alternative specific constant; β is the vector of coefficients for the utilities; ε is the disturbance term for individual n; S is student’s attributes (i.e., age, gender, ethnicity); H is household variables (i.e., car ownership, income); R is residential built environment variables (i.e., population density, median house value); E is parents’ employment status (i.e., work status, flexibility of work hours,); and D is distance variables (i.e., distance from home to school, distance from school to the parents work place) 116 An individual will choose j if and only if  U jn U ln  j,l C 4.4 The probability that an individual chooses (i, j) is:    C q p n pq n ij n V V j i P ) , ( ) exp( ) exp( ) , ( 4.5 It is assumed that the error terms are irrelevant independent distributed (IID) (McFadden, 1978). Although the model can be modified to allow for correlations between the error terms by using mixed-logit model, a previous study showed that the mixed-logit structure did not outperform the MNL structure (Yarlagadda and Srinivasan 2008). Hence, the IID property of the disturbance will be assumed in this analysis. As defined in the utility function, the explanatory variables are individual specific. The popularity of the alternatives is reflected by the constant α and the coefficient β. The reasons why there are no alternative attributes in the utility function are twofold. First, alternative attributes are not directly measured in the travel survey (i.e., travel cost); hence, any assumptions and the measures generated thereby can introduce errors in variables. The constant term α is in fact a function of the unmeasured alternative variables Z, which can be expressed as: j j Z    Therefore, α captures the sum information of the alternative attributes. Second, the focus of this research is on how attributes of the individual n (i.e., work arrangements, distance from the school) may affect their choice, rather than the attributes of the alternatives. As a matter of fact, the alternative attributes are often not included in escort and/or mode choice studies in school transportation (Yarlagadda and Srinivasan 2008, McMillan 2007, McDonald 2008a). 117 Also, it should be noted that, the escort-mode choice is a short-term choice conditional upon previous long-term choices such as home, work, and school location. These prior decisions and the resulting relatively fixed location of home, work, and school is indeed the reason why spatial coordination of parents and children needs to be included in the escort-mode choice decision. Selection of Variables The main contribution of this research is to consider both parent’s time and space constraints related to children’s school trip. These constraints are reflected in the parents’ employment and distance variables, also defined as the temporal and spatial intra-household coordination, respectively. Other factors that influence the escort and mode choice decision are also included in the model. Overall, the explanatory variables entered the model can be grouped into five categories: student’s individual attributes (S), household characteristics (H), neighborhood build environment (R), parents’ employment status (E) and distance variables (D) (Equation 3). Definitions of these variables are listed in Table 4.4. 118 Table 4.4: Definition of variables Intra- household Coordination Category Variable Definition/Value N/A Student traveler’s personal attributes (S) Age Age of the student Female 1 if the student is female, 0 otherwise Household attributes (H) Number of siblings Number of siblings of the student Total vehicle Total number of vehicle in the household Household income Low income (less than $35,000); middle income ($35,000-$75,000); high income (over $75,000) Ethnicity White/Not Hispanic; Hispanic; African American; Asian/Pacific Islander; Other Residential neighborhood built environment (R) Population density Population density per square mile of the census tract Median house value ($) Median house value of the census tract Temporal Parent employment status and work arrangement (E) Father employment status Full time; part time; unemployed Father’s work hours Total number of hours worked per week at main job (answered if employed) Father with Flexitime Work hours not fixed (answered if employed) Mother employment status Full time; part time; unemployed (answered if employed) Mother’s work hours Total number of hours worked per week at main job (answered if employed) Mother with Flexitime Work hours not fixed Spatial Distance derived from the location information of home, school, and the parent’s workplace (D) Home-School Distance from home to school Home-Father’s job Distance from home to father’s workplace Home-Mother’s job Distance from home to mother’s workplace School-Father’s job Distance from school to father’s workplace School-Mother’s job Distance from school to mother’s workplace 119 The two most interesting explanatory factors in this study is parent employment status and work arrangement (Vovsha and Peterson 2005, Yarlagadda and Srinivasan 2008, McDonald 2008a) and the proximity of the parent’s workplace to school. These factors are proxy for intra- household temporal and spatial coordination. The total number of work hours is expected to lower the probability of escorted trips by the parent, while the option of flexible hours may counteract the negative impact of long work hours. Likewise, the distance between work place and school is an impedance to joint trip. Although the distance between home and school has been shown to be influential in mode choice decisions, the distance involving the workplace is rarely considered. It should be noted that childcare is traditionally considered the mother’s responsibility in a household. Thus, even though both fathers’ and mothers’ work status and location are estimated, the results of the mother may be more intuitive since the mother is usually the caretaker and her work-related variable is expected to have a more direct impact on the escort- mode decisions. The descriptive summary of the explanatory variables is shown in Table 4.5. The control variables are selected for the following reasons. Children’s independent travel is associated with their demographic and the family’s socioeconomic status. Age is a critical factor as younger children are more likely to be escorted to school (Vovsha and Peterson 2005, Yarlagadda and Srinivasan 2008), which is probably due to personal and traffic safety concerns. Additionally, older students have a stronger desire for and a higher chance of being granted the freedom to travel independently. The age effect can be prevalent across all transportation modes such as walking, biking, driving, and take the bus (Yarlagadda and Srinivasan 2008). As for the gender variable, it can affect travel independence as well (Vovsha and Peterson 2005, Yarlagadda and Srinivasan 2008). Parents are likely to be more concerned about personal safety for female than male children. Thus female students are less often allowed to travel outside the parent’s guardianship, not to mention travel alone. 120 The reasons for selecting household characteristics (i.e., the number of siblings, car availability, household income, and ethnicity) are as follows. Children with siblings are usually more likely to travel and conduct activities with their siblings, including going to school. It is also likely that having more siblings will increase children’s active commuting (McDonald 2008a). The number of private vehicles is likely to reduce the propensity of using alternative transportation modes (McMillan 2005). Both income (Vovsha and Peterson 2005) and ethnicity (Yarlagadda and Srinivasan 2008) categories are shown to affect escort-mode choices. In terms of mode choice decisions, high income households have higher mobility and thus can travel farther; hence, they are expected to have a higher percentage of auto trips and lower percentage of non- motorized trips. In other words, high income groups (i.e., over $75,000, accounting for 28% in the final sample) are expected to chauffeur or drive alone more often whereas low income group (i.e., below $35,000, accounting for 37% in the final sample) are more likely to walk or bike or take bus (He 2011). In terms of ethnicity, a higher rate of Hispanic students’ active commuting has been observed nationwide (McDonald 2008a). Given the large number of Hispanics in the Southern California region, it will not be surprising to observe a distinctively different travel behavior pattern when compared to Whites. In fact, it has been documented that Hispanics are more likely to take bus or commute on foot or bike to school (He 2011). As another control variable, built environment is a component in which urban planners have a keen interest. The neighborhood level built environment is indicated by population density and the median house value of the census tract. There has been a number of empirical studies have shown the positive effects of residential density on active commuting (McDonald 2008a, He 2011). A higher population density is likely to be associated with more activity opportunities and street mutual monitoring, thus creating more livable and safer neighborhoods, which may facilitate children’s independent travel. The relationship between density and children’s active 121 commuting, however, is still under debate and requires further examination. The variable of median house values is used to proximate various neighborhood amenities. Table 4.5: Descriptive statistics, by household structures All households (N=3151) Two-parent households Mother-headed households (N= 617) Father-headed households (N=172) Dual-earner households (N= 1320) Non Dual-earner households (N= 1042) Continuous variable Mean Std Mean Std Mean Std Mean Std Mean Std Discrete variable Percent Percent Percent Percent Percent Demographics Age 10.700 3.597 10.948 3.603 10.252 3.578 10.781 3.581 11.209 3.471 Female 46.68% 45.63% 47.22% 48.20% 45.93% Household Structure Number of siblings 1.471 1.113 1.341 .960 1.722 1.158 1.418 1.263 1.140 1.078 Car Availability Total vehicle 1.974 1.016 2.336 .892 1.900 .974 1.368 1.011 1.820 1.007 Income Category Low income (<35k) 36.81% 18.20% 46.88% 60.83% 34.39% Middle income (35k- 75k) 35.57% 41.99% 30.47% 27.90% 43.95% High income (>=75k) 27.62% 39.81% 22.65% 11.27% 21.65% Ethnicity White/Not Hispanic 45.42% 55.49% 40.00% 32.04% 42.42% Hispanic 39.34% 29.91% 49.37% 43.50% 36.36% African American 6.89% 4.79% 3.51% 17.48% 12.12% Asian/Pacific Islander 3.36% 4.63% 2.34% 2.52% 2.27% Other 4.99% 5.18% 4.78% 4.47% 6.82% Neighborhood BE Population density 8159.273 8387.814 7213.962 7453.887 8364.926 9083.438 9995.221 9115.964 7582.175 6793.919 Median house value ($) 193857.5 119298.8 206543.9 121120.8 192391.3 124572.6 171261.1 103770.5 186436.6 112241.5 Parents Employment Father worked FT 89.84% 96.23% 83.09% -- 81.05% Father worked PT 3.67% 3.77% 3.30% -- 5.50% Father unemployed 6.49% 0% 13.61% -- 13.45% Father’s work hours a 44.93 11.049 45.158 11.063 44.796 10.965 -- 43.336 11.509 Father with Flexitime b 40.49% 41.89% 47.04% -- 35.14% 122 Table 4.5 (Continued) All households (N=3151) Two-parent households Mother-headed households (N= 617) Father-headed households (N=172) Dual-earner households (N= 1320) Non Dual-earner households (N= 1042) Continuous variable Mean Std Mean Std Mean Std Mean Std Mean Std Discrete variable Percent Percent Percent Percent Percent Mother worked FT 47.02% 73.79% 7.83% 55.74% -- Mother worked PT 14.66% 26.21% 2.19% 10.45% -- Mother unemployed 38.32% 0% 89.98% 34.21% -- Mother’s work hours a 35.823 13.341 35.175 13.783 36.430 11.452 38.046 11.883 -- Mother with Flexitime b 36.16% 36.36% 63.64% 33.01% 36.32% -- Distance (mile) Home-School 2.663 7.507 2.900 6.900 2.644 9.947 2.185 3.671 2.700 4.156 Home-Father’s job 13.081 19.927 13.316 17.781 13.112 23.391 -- -- 10.799 15.965 Home-Mother’s job 7.849 10.490 7.677 9.809 9.465 14.439 8.010 11.432 -- -- School-Father’s job 13.586 20.404 13.675 18.183 13.867 24.046 -- -- 11.067 15.252 School-Mother’s job 8.010 10.667 7.754 9.976 9.922 14.399 8.357 11.656 -- -- Note: a. Work hours is available for employed father or mother only. b. Percent of father or mother with Flexitime is available for employed father or mother only. 123 124 4.5 Results Seven escort-mode choices (defined earlier in Table 4.3) form the choice set. Mother’s escorted trip by car is chosen as the reference choice due to its highest frequency in the observations. As the main variables in this research, the variables that measure the intra-household temporal synchronization and spatial coordination have a significant impact on the escort-mode decisions. It should be noted that some employment and location information (i.e., work hours, access to flexible work hours, workplace location) is only available for employed parents. Therefore, only dual-earner households have adequate information to estimate the full model, in which the hypothesized relationship of intra-household temporal and spatial coordination can be fully tested and presented. Employment status is dropped in the full model because there are no unemployed parents and inadequate observations of part-time fathers in this subset of sample. However, the inclusion of the total number of work hours can to some extent account for the parent’s employment status since full-time workers normally work longer hours than part-time workers. The estimation results are summarized in Table 4.6. With respect to temporal variables, parents exhibit time wise synchronization in their escort-mode choice decisions. Both work hours and the option of flexible time affect considerably on the probability of a student’s escort-mode choice, compared to the referenced choice (i.e., chauffeured by the mother). The results confirm the temporal effects: working longer work hours reduces the parent’s chauffeuring activities whereas working with flexible work schedules allows a better childcare as reflected through an increase in the chauffeuring trips. The observations are twofold. First, when the mother works with flexible hours, the student has a lower probability of being chauffeured by others; when the father works with this option, the student is more likely to be chauffeured by the father. This finding suggests that the flexible hour program improves the parent’s childcare option. Second, the mother’s longer work hours increase several alternative 125 mode choices: children are more likely to commute actively or take the bus. This outcome suggests the mother’s escort responsibility is shifted to other household members or the children themselves when their participation in the labor market increases. This shifting is associated with the decrease in the child’s car dependence. The spatial dimension of the intra-household coordination is reflected through estimates of the distance variables. The distance from home to school, as previous studies have shown (Waygood and Kitamura 2009, McDonald 2008b, He 2011), considerably reduces the likelihood of walking or biking trips over escorted trips. The distance between school and parent’s work place, has highly significant effects on escort-mode choice decisions as well. The farther away the parent works from school, the less likely it is that they will drive their children to school. In addition, when the mother works farther from and/or the father works closer to the school, the children are more likely to be chauffeured by the father than by the mother, indicating an intra- household sharing of childcare responsibility. Moreover, when the distance between mother’s work place and school increases, children are more likely to walk to school alone. These findings along the spatial axis suggest that the parent-child joint trip can be made easier if the child attend a school closer to the parent’s workplace. This decision may facilitate the escorting trip and childcare outside school hours but at the same time may cause a longer travel distance for the child should he/she forgoes the neighborhood school. Among the explanatory variables, demographic variables have strong effects across all the three household types. Age in general has a positive effect on the likelihood of most alternatives. Older students have a higher probability of being chauffeured by others, commuting actively alone, driving, and taking the bus. This variable estimate reflects that, as the children get older, they gain more independence from their parents. In addition, the age variable has an economically large effect on student’s driving, reflected by its large coefficient. When it comes to 126 gender, this variable has a relatively weak effect, although previous findings suggested that female students tend to be less likely to conduct their journeys on foot or by bicycle than males (Black et al. 2001, He 2011, Sirard and Slater 2008, Timperio et al. 2004). Regarding the household structure variables, the number of siblings increases the joint trips with parents and reduces independent trips. The effect is especially strong in non-motorized trips: students with more siblings are more likely to walk or to bike to school with the parent/siblings and less likely to commute actively alone. This result is in alignment with a previous study (McDonald 2008a), which shows that having siblings is associated with a higher likelihood of non-motorized travel for high school students. Because many siblings attend the same school, the sibling(s) are likely to be the travel companion(s), reducing the perceived duration and safety concerns associated with walking and biking trips. Car availability is often considered to be influential on mode choice (McMillan 2005, He 2011). The outcomes here show that the number of vehicles reduces active commute regardless whether the trips are undertaken with a companion or alone. Vehicle availability also contributes to a student’s driving because easy access to cars can considerably reduce the relative attractiveness of alternative modes. Income has a strong impact on alternative transportation mode choices. Students from low income households have a greater tendency to take the bus and/or to walk or bike. Ethnicity effect is found to be insignificant, although an earlier study suggested that students from the ethnic minority groups have a higher probability of taking the bus or commuting actively than Whites (He 2011). The last control variables are the neighborhood built environment variables. Population density is shown to have a positive effect on a student’s commute on foot or by bike. The result echoes previous tests with respect to the effect of density on active commuting (McDonald 2008a, He 2011). A higher density is likely to be associated with shorter trip distances and hence a lower 127 likelihood of driving or taking the bus. The median house value is used to proximate neighborhood amenities. It is expected that families from wealthy neighborhoods may have a high car ownership and thus an infrequent use of public transit. However, this variable has an insignificant impact in most models. Table 4.6: Estimation results for dual-earner households (Reference group: driven by mother, EM2) Mode Choice Passenger Walk or Bike Drive Bus Escort Choice Both or Father (EM1) Others (EM3) Parents or Siblings (EM4) Alone (EM5) Any (EM6) Any (EM7) Coef Std err Coef Std err Coef Std err Coef Std err Coef Std err Coef Std err Constant -.726 .764 -4.971 *** .872 -1.653 1.155 -4.400 *** .948 -43.318 *** 7.465 -4.265 *** .973 Demographics Age .012 .032 .162 *** .036 -.018 .050 .245 *** .039 2.261 *** .402 .188 *** .039 Female .002 .205 .147 .229 -.385 .294 -.220 .247 .864 .534 -.132 .250 Household Structure Number of siblings -.196 .120 -.037 .128 .617 *** .165 -.336 ** .144 -.403 .312 .100 .141 Car Availability Total vehicle -.111 .133 .224 .138 -.927 *** .245 -.282 * .169 1.094 *** .298 -.185 .164 Income Category Low income .187 .366 1.257 *** .388 1.038 ** .515 1.484 *** .427 .586 1.429 1.689 *** .422 Middle income -.061 .238 -.078 .277 .795 ** .399 .646 ** .299 .090 .579 .682 ** .314 Ethnicity Hispanic .130 .273 .144 .309 .141 .375 -.361 .340 .236 .735 .243 .323 Non White nor Hispanic -.296 .315 -.364 .363 -.313 .459 .016 .335 -.430 1.003 .098 .382 Neighborhood BE Population density .008 .017 -.002 .021 .025 .020 .039 ** .017 -.046 .062 -.048 ** .024 Median house value .000 .001 .002 ** .001 .002 .002 .000 .001 .000 .002 -.000 .001 Parents Employment Father’s work hours -.010 .008 .011 .009 -.013 .012 .005 .009 .042 * .025 -.010 .011 Father with Flexitime .362 * .210 -.372 .247 .250 .295 -.314 .262 -1.061 * .603 -.108 .259 Mother’s work hours .009 .007 .006 .009 .027 *** .008 .022 *** .008 .029 .019 .024 *** .008 Mother with Flexitime .006 .212 -.731 *** .261 -.089 .313 -.117 .261 -.257 .552 .326 .258 Distance Home-School -.050 * .030 -.011 .021 -.577 *** .163 -.211 *** .071 -.091 .103 .041 ** .020 School-Father’s job -.026 *** .010 .009 .006 .014 ** .006 -.023 ** .012 .011 .012 -.007 .009 School-Mother’s job .052 *** .013 .050 *** .013 .019 .020 .068 *** .015 .032 .036 .028 * .015 Summary Statistics N=933 Log likelihood Pseudo R 2 0.1881 Null model -1590.3718 LR Chi 2 598.42 Full model -1291.1617 p 0.0000 Note: *** indicates significance at 99% level, ** indicates significance at 95% level, * indicates significance at 90% level. 128 129 4.6 Conclusion Compared to the studies on adults’ activity-travel patterns, “the activity-travel field is in its infancy in its understanding of children-adult activity-travel and decision-making interactions” (Paleti et al. 2011, p. 277). That said, more empirics are needed for a better understanding of the parents-children joint trip. School trips of K-12 students perhaps are the most representative joint trips between parents and children since they are mandatory trips where the majority of them (e.g., over 50 percent as shown in Table 4.2) are escorted by the parent. The research on joint-trip decision accounting for temporal and spatial coordination is especially needed because women’s increasing participation in the work force may cause scheduling constraints for escorted trips and consequentially lead to changes in children’s travel mode. In this paper, joint escort-mode choice of journeys to school is modeled for K-12 students in the Los Angeles region. This paper reveals a strong effect of parental, especially women’s work arrangements and location on children’s travel behavior. The main interesting variables fall into two categories: the parent employment status and the job location in relation to the school location. The results show that the parent’s longer work hours increase the likelihood of the alternative modes such as active commuting, driving, and busing. It also implies that the effect of work hours on escort-mode choice may be offset by the option of flexible work hours, which reduces the probability that a trip is escorted by others. In addition, the closer is the mother’s workplace relative to the school, the more likely that the mother will chauffeur their students to school. As this distance measure goes up, the school trip is more likely to be escorted by the father or others, and more likely to be undertaken by active commuting, or by bus. To make the parental escorting trip possible and childcare before/after school hours more manageable, a short distance between the parent’s workplace and the school is important, especially in dual-earner household. When the parent chooses a school closer to 130 his/her workplace instead of the neighborhood school, the child’s travel distance is likely to increase and the child is more likely to be escorted in car. Since most escorting trips are carried out by the mother, the distance between the mother’s workplace and the school influences more on the escort decision than the father’s. This situation would be very different if the mother is a (full-time) housewife. Because the housewife stays at home, she would prefer the child to attend the neighborhood school so that the distance between the mother and the child can be minimized. Such a short distance from home to school would facilitate the non-motorized travel modes. However, women’s increasing participation in the labor market makes their role as the housewife less relevant. The results of this research are also useful for us to understand the working mother’s dual responsibilities. Traditionally mothers undertake more childcare responsibilities and undertake more chauffeuring trips than men. Nowadays working mothers devote more time to their career. Their longer work hours and farther work location away from home and/or school would inevitably change the child’s means of travel to school. This dual role in the labor market and in the family may cause considerable amount of stress for working mothers (Staines and Pleck 1983) because childcare responsibility in a household is still primarily remained on the mother’s shoulder (Peterson and Gerson 1992, Ozer 1995, Scarr 1996). From within the household, the contribution from the father over the years is increasing (Peterson and Gerson 1992), and the help from the spouse for childcare has been a robust predictor of the mother’s psychological well- being and distress (Ozer 1995). From the society’s perspective, certain labor policies and programs have been created to address this issue. For example, in Nordic countries, family- friendly government policies grant mothers paid maternity and parental leaves, child allowances and part-time work (Scarr 1998). However, these types of policies have their own disadvantages as it may cause women’s loss of experience and discontinuity in the labor force (Cherlin 1992). In 131 comparison, there are more working women in the United States. The continuous work experience in most cases is a condition to “career advancement, higher incomes, retirement benefits, and other markers of gender equality” (Scarr 1998, p. 100). More importantly, women’s labor force participation can lead to “higher family income, greater personal satisfaction, and more social support” (Scarr 1998, p. 100). Conflict and stress can arise when women need to carry dual responsibility. To address this issue, government and private employers can create more family friendly policies and programs to improvement the family-work balance and help reduce workers’ stress induced by fixed work hours and job location. Since the option of flexible time and proximity of the mother’s workplace to school increases the likelihood of mother-children joint school trips, programs (e.g., Flexitime, school choice policy) that can relax the mother’s temporal and spatial constraints may improve the mother’s childcare option. The outcomes of this paper help us better understand children’s travel behavior in journeys to school. School trips escorted by the mother (or the father) do not necessarily lead to a better active commuting outcome; rather, these trips are likely to be motorized trips. This change stems from the changing societal roles of women, leading to fewer full-time mothers who would devote their time to walk or bike to school with their children. Therefore, children’s journeys to schools are frequently embedded in commute trips, which are likely to be undertaken by car. 132 Chapter 4 References Angel R.D., Caudle W.L., Noonan R., and Whinston A. 1972, Computer-assisted school bus scheduling. Management Science, 18, B279-B288. Babey S.H., Hastert T.A., Huang W., and Brown E.R. 2009, Sociodemographic, family, and environmental factors associated with active commuting to school among US adolescents. Journal of Public Health Policy, 30, 203-220. Black C., Collins A., and Snell M. 2001, Encouraging walking: The case of journey-to-school trips in compact urban areas. Urban Studies, 38, 1121-1141. 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Yarlagadda A.K. and Srinivasan S. 2008, Modeling children’s school travel mode and parental escort decisions. Transportation, 35, 201-218. Zhu X. and Lee C. 2008, Walkability and safety around elementary schools: Economic and ethnic disparities. American Journal of Preventive Medicine, 34, 282-290. 135 CHAPTER 5 CONCLUSION Using the urban economics and travel behavior theories and modeling methods, this dissertation explains why children travel longer distances and walk or bike to school less than they did 30-40 years ago. The purpose of this research is to show that the heterogeneity in people’s travel outcomes stems from multiple constraints. By using land price and travel diary data relevant to school trip activity, this research demonstrates that to understand people’s mobility, a comprehensive study of the built environment, institutional policies, as well as intra-household constraints is often required. Each of these constraints is emphasized in one of the three essays. The first essay illustrates the co-location of high (or low) quality schools and high (or low) income neighborhoods and proves that proximity to a good school increases housing prices significantly. Because public education premiums are high, homeowners from rich neighborhoods/good performing districts would most likely resist any policy that might affect the status quo. Meanwhile, school choice policy allows children from poor neighborhoods/low performing districts to leave their home district, a situation of which would likely weaken the homeowners’ association with their neighborhood and hence reduce incentives for promoting school improvements in their own neighborhood schools. The school choice policy to some extent has relaxed the conventional school assignment mechanism by providing parents with more choice. This study shows that, in the Los Angeles region, roughly 40-50% of the students do not attend the neighborhood schools and approximately 10% of the students exercise the inter-district transfer options. This institutional change is a response to the spatial disparity of school quality in many regions in the United States. Despite school choice policies, and in California, despite the equalization of state funding across school districts, which was a major purpose of shifting school funding to the state level, there are 136 still disparities in school quality and in land values. The high premiums homebuyers have paid for school quality and their efforts in maintaining the status quo suggest that school choice policy may encounter a certain degree of local political resistance, especially when the benefits and entitlements of the local residents are affected (i.e., the loss of their guaranteed admission to the neighborhood school and depreciated property values). Notwithstanding the obstacles to a large scale implementation of school choice policy, we have witnessed a steady growth of the school choice programs in the United States (Bierlein et al. 1993). Nowadays, most states offer mandatory or voluntary intra- and/or inter-district transfers (Heritage Foundation 2012). Given more school choices, as parents are more aware of these options, people’s travel behavior expects to diverge. The second essay shows that people incur school trips of different distances due to their heterogeneous preferences for schools. Some parents choose the neighborhood school for proximity whereas others choose a school farther away from home for better quality. When parents opt out of the neighborhood school, they travel differently. Statistics show that parents who travel long distances are associated with non-neighborhood schools; they are more likely to exercise the intra- and inter-district transfer option than those who travel short distances. The results from this essay demonstrate that, given alternative school choices, parents are willing to incur longer travel distances for better public education. The school choice policy is well intended for the low income households and is being utilized. However, most of the transfers are intra-district and only 10 percent are inter-district. The small number of inter-district transfers reflects the limitations of current policy. The first constraint comes from the seat capacity of receiving districts. Given the competitiveness of obtaining an entry ticket to a quality school, the number of extra seats for out-of-district students is limited. The second constraint results from the lack of transportation assistance. Although 137 students of low social-economic status are conceivably the most in need of inter-district transfers, they also often have low car ownership. The exercise of such an option would be very difficult for those without proper transportation means. The demand for more school choice is to some extent a school accessibility issue. If we could improve the quality of the neighborhood schools, especially those in low performing districts, more parents would choose the neighborhood school and fewer of them would choose better quality schools at distance, resulting in a shorter travel distance that would favor active commuting over motorized travel. School quality improvement may be a long term effort and it might be unrealistic to equalize school quality. Thus, in the short run, the school choice policy is necessary in that it allows children more opportunity to attend a quality school. The third essay confirms that changes in children’s travel behaviors of school trips are likely rooted in intra-household bundling constraints. Within each household, a joint trip to school can only be made possible with pre-scheduled coordination among the household members. Since escort choice and mode choice are interrelated, whether the child is escorted to school by his/her parents largely determines the transportation mode choice. Most escorted children are driven to school by car. By contrast, when the child travels with siblings or independently, walking becomes the most common choice. For independent trips, 45.93% walked whilst 10.21% drove. For sibling accompanied trips, 36.24% walked, 34.85% were driven by car, and 3.17% drove. This finding implies that in order to promote active commuting, other efforts should be made to encourage independent travel or peer-accompanied travel. A more important finding from this essay is that there is a strong effect of parental, especially women’s, work arrangements and location on children’s escort-mode choice. On the temporal axis, the parent’s longer work hours will increase the likelihood that an alternative mode (i.e., active commuting, driving, and busing) be chosen. Nonetheless, the option of flexible work 138 hours increases the probably of parental escort. On the spatial axis, the closer the mother’s workplace is relative to the school, the more likely that the mother will chauffeur her child. These findings suggest that to make the parental escorting trips possible and childcare before/after school hours more manageable, a short distance between the parent’s workplace and the school is important. When the parent chooses a school closer to his/her workplace instead of the neighborhood school, the child’s travel distance is likely to increase, and the child is more likely to be escorted in car and hence less likely to walk or bike to school. In all, these three essays contribute to the school transportation literature. This research was initiated to address the increasing reliance on automobiles in children’s journeys to school. The increasing travel distance and car use in school trips call for further examination of travelers’ underlying motives. As first mentioned in the introduction, there are at least four reasons to explain children’s increasing reliance on automobile. While the literature has primarily looked into the safety concerns and the changes in land use and density resulting from suburbanization and decentralization of activities (Yeung et al. 2008, Ewing et al. 2004), few of them have examined the role of school choice policies and women’s increasing participation in the labor force (Wilson et al. 2010, McDonald 2008a). The empirics from this study show that school quality, school choice policy, and intra- household dynamics play important roles. The first and second essays link the spatial distribution of school quality and the school choice policy with traveler’s destination choice. The outcomes imply that people make rational school choice decisions. Given the high premiums of public education, not every household with children can afford to live close to the quality school. When there is an option for these households to trade between traveling and education, some households are willing and able to obtain better school quality at certain amount of transportation costs. The third essay considers the factors of parental scheduling and work location. The results of this 139 essay show that both the temporal and spatial constraints of the parents affect the child’s means of travel to school. Since a short distance between the mother’s work place and the child’s school facilitate escort trips, a child’s trip would be arranged to be close to the mother’s workplace for easier drop-off and pick-up, which will likely lead to a longer travel distance of the child and hence lower rate of active commuting. Beyond the implications for school transportation, this research has several implications for urban planning. Similar to the phenomenon of “job-housing spatial mismatch” (Holzer 1991, Ihlanfeldt and Sjoquist 1998), we have witnessed a “school-housing spatial mismatch”. As much as we understand that the job-housing mismatch is the root of the long distance commute (Cervero 1989, Giuliano and Small 1993), we should not be surprised at people’s travel patterns of school trips. California, along with many other states, has been striving to bring better education to marginalized families. Nonetheless, quality schools are still not accessible to everyone. The education premiums of land prices, as estimated here, are still high in well performing districts. The school choice policy, as one of the main education reforms in a long- term endeavor, aims for equal and accessible public education. The choice offered by this policy, however, does not come free. Conditional on the seat capacity, whether the family is willing and able to travel long distances determines the execution of the intra- and inter-district transfer options. Since people have heterogeneous preferences for school quality, those who place high value on education yet are unable to live in good districts may have a higher willingness to travel. When they opt out their neighborhood schools, their school trips would be considered an “excess commute” (Giuliano and Small 1993) to school. The phenomenon of “excess commute”, which is widely discussed in transportation literature, can be applied to trips of other purposes as well such as shopping and schooling. The making of these trips is conditional upon the traveler’s prior choice selection such as residential 140 location, shopping, and school choice, in which he/she is searching for cheaper land prices, a bigger selection of grocery goods, or a better public school, respectively. While such travel may be considered “excess” in the context of traveling, it may be not in the larger context where all the factors in the traveler’s utility function are accounted for. In the case of journeys to school, despite the fact that short travel distance plays an encouraging role in active commuting, some people may nevertheless need to travel long distances in order to attend a better school and achieve something of a higher priority such as a better human capital builtup and better employment outcomes in the long run. Children’s travel behavior can be better clarified as more research is carried out. Travel to school should not only be considered as a derived demand for personal development in the long run, but also a decision under heavy influence of the parents because they are the ones who decide where the children go and how they get there. From a planner’s perspective, walking and biking may be the best mode choice for going to school as it allows more physical exercise than other mode choices. However, as more women have participated in the labor force since the 1970s, particularly among women with children (Bureau of Labor Statistics 2009), few mothers dedicate their time and energy to walk their children to school. Rather, school trips are more likely to be imbedded in commute trips. It seems active commuting is less important than convenient childcare, which would be made easier should the child attend a school close to the mother’s (or the father’s) work place. This intra-household activity arrangement and parental influence on the child’s travel behavior deserves further investigation. Findings from this dissertation are by no means meant to downplay current efforts in promoting active commuting to school. Improvements in neighborhood safety and path walkability are important (Zhu and Lee 2008). For example, programs such as Safe Routes to School have shown positive outcomes (Boarnet et al. 2005). Rather, this study emphasizes that 141 such programs may be less effective for long distance school trips. Once we understand people’s different preferences and their diverse motives of traveling, we may need to design programs that facilitate long trips that are necessary, instead of focusing on how to shorten school trips so that children are more likely to walk or bike. For example, busing service in California could be better coordinated, especially for inter-district trips, as some families are unable to exercise the school choice option due to their low mobility level. In the near future, extended research should be conducted with more recent data from the region’s household travel survey and school quality. 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Abstract (if available)

Abstract Trips to school are increasingly undertaken in automobiles. While much research has been conducted regarding the neighborhood built environment and safe routes to school, very little has looked at school policies and intra-household dynamics. These factors can indeed influence children’s travel behavior in journeys to school. First, school quality is capitalized in residential house prices. Low income households often live in low-performing districts. Open enrollment allows students to transfer out of their neighborhood schools when seats are available. When these options are exercised, children living in low-performing districts may travel longer distances in order to attend good quality schools, compared to children living in high-performing districts. Secondly, at the household level, women have increased their participation in the labor market while remaining the primary caretaker of children. Their workplace location may affect their children’s escort and mode choice decision as well. Thus far, our understanding of children’s increased travel distance and reliance on automobile has largely been disconnected from the context of school choice and intra-household constraints. This dissertation links journeys to school with these institutional and household factors. ❧ In my dissertation, I examine the school quality capitalization effect in land values using hedonic pricing models, and I explain children’s travel behavior by looking at school choice and intra-household scheduling constraints using activity-based transportation models. By considering the spatial relationship between home, school, and workplace in the Los Angeles region, I answer the following questions: 1) How much do parents pay for school quality? 2) Are parents willing to incur longer trips for better school quality? and 3) Do parental work arrangements and location affect a child’s journey to school? These answers will help us understand why distance to school and car use have increased in recent decades and how school choice is connected to active commuting.

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Asset Metadata

Creator He, Sylvia Ying (author)

Core Title Children’s travel behavior in journeys to school

School School of Policy, Planning and Development

Degree Doctor of Philosophy

Degree Program Policy, Planning, and Development

Publication Date 08/03/2012

Defense Date 05/18/2012

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

Tag active commuting,Children,intra-household dynamics,OAI-PMH Harvest,school quality,school trips,travel behavior

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Giuliano, Genevieve (committee chair), Redfearn, Christian (committee member), Richardson, Harry W. (committee member), Ridder, Geert (committee member)

Creator Email sylviahe@mcmaster.ca,sylviahe@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-85127

Unique identifier UC11288288

Identifier usctheses-c3-85127 (legacy record id)

Legacy Identifier etd-HeSylviaYi-1126.pdf

Dmrecord 85127

Document Type Dissertation

Rights He, Sylvia Ying

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