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University of Southern California Dissertations and Theses
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Three essays in education and urban economics
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Three essays in education and urban economics
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THREE ESSAYS IN EDUCATION AND URBAN ECONOMICS by Seungwoo Chin 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 (ECONOMICS) August 2018 Copyright 2018 Seungwoo Chin For my family and friends ii Acknowledgments First of all, I would like to thanks Professor Matthew E. Kahn. He taught me the way to set up economic problems, how to approach them, and efficient ways to convey the ideas. All works in this dissertation could not have been improved without his influence. He always calls me a friend and helps me to stand up again whenever I face personal challenges. I will never forget the kind heart. Professor Roger Moon also greatly influenced my work. He helped me to open the door to the machine learning approaches, and patiently offered a guideline to research and private matters. Especially, it is an unforgotten memory for me to work on the machine learning project together with him and Professor Matthew E. Kahn. Professor John A. Strauss I would like to thank as well. He helped me to build up applied microeconomics foundation through classes, seminars and many meetings. He inspired me not only as a researcher and but also as a teacher. As a teaching assistant of his class for two semesters, I learned how responsible and dedicated a teacher is supposed to be. Second, I would like to thank my colleagues at USC. Particularly, I would like to express deep gratitude to Tushar Bharati and Dawoon Jung, my coauthors. Without their help, I could not have started economic research. They taught me to how to use economic models to real problems from the basic, and our discussions always were constructive and delightful. I also thank Jeonghwan Yun and Eunjee iii Kwon as another coauthor. For research assistance and friend, I would like to thank Hada Han, Aristidou Andreas, Jisu Cao, Haeyeun Park and Chris Yoo. Last but most importantly, I would like to thank my beloved wife, Sunyoung Park. She has always been supporting what I want to do. She was willing to move to the United States for me, although it kept her from pursuing her own career. SheandIhaveexperiencedsomanythingstogetherlastfiveyearsattheUniversity of Southern California. Facing all the events regardless of whether they are good or bad, she has always been positive and made our family move forward. And of course, I would like to dedicate this dissertation to my parents. They always respect my decision up until now, and their trust raises me up. iv Contents Acknowledgments iii List of Tables viii List of Figures x Abstract xii 1 Introduction 1 2 The Effects of Schoolwide Tracking on Low and High Skill Stu- dents: Evidence from South Korea 4 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 A Student’s Optimal Effort as a Function of Peer Effects . . . . . . 8 2.3 South Korea’s Education Policy Dynamics . . . . . . . . . . . . . . 15 2.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.1 Graduates Occupational Mobility Survey . . . . . . . . . . . 19 2.4.2 College Scholastic Ability Test . . . . . . . . . . . . . . . . . 21 2.5 The Empirical Approach . . . . . . . . . . . . . . . . . . . . . . . . 22 2.5.1 Does Ability-Mixing Affect College Enrollment? . . . . . . . 23 2.5.2 Does Ability-Mixing Affect A Student’s Test Score? . . . . . 25 2.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.6.1 Pre-Trend Analysis . . . . . . . . . . . . . . . . . . . . . . . 26 2.6.2 College Enrollment and TOEIC: GOMS . . . . . . . . . . . 28 2.6.3 College Entrance Test Score: CSAT . . . . . . . . . . . . . . 29 2.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.7.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.7.2 Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . 32 2.7.3 Hours of Studying . . . . . . . . . . . . . . . . . . . . . . . . 34 2.7.4 Teacher-PupilInteraction,Teacher’sCharacteristicsandClass Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.7.5 Direct Peer Effects on Possible Mechanisms . . . . . . . . . 36 2.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 v 3 EstimatingtheGainsfromNewRailTransitInvestment: AMachine Learning Tree Approach 61 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.2 Seoul’s New Subway Construction and Project Financing . . . . . . 64 3.2.1 The Demand for Housing Close to Transit . . . . . . . . . . 65 3.2.2 The Supply of Housing Close to the New Transit Stations . 66 3.3 The Empirical Approach . . . . . . . . . . . . . . . . . . . . . . . . 68 3.3.1 The OLS Model . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.3.2 The Machine Learning Approach . . . . . . . . . . . . . . . 69 3.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.4.1 Apartment Data . . . . . . . . . . . . . . . . . . . . . . . . 71 3.4.2 Geographic Information Data . . . . . . . . . . . . . . . . . 72 3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.5.1 The Pre-Treatment Trend . . . . . . . . . . . . . . . . . . . 73 3.5.2 OLS Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.5.3 The Machine Learning Results . . . . . . . . . . . . . . . . . 75 3.5.4 Developer Responses to the Shifting Real Estate Price Gra- dient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.5.5 Testing Two Explanations for the Price Appreciation Effects 79 3.5.6 Estimating the Value of Time . . . . . . . . . . . . . . . . . 80 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4 Is 1+1 more than 2? Joint evaluation of two public programs in Tanzania 99 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 4.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.2.1 Iodine Supplementation Program (ISP) . . . . . . . . . . . . 102 4.2.2 Primary Education Development Program (PEDP) . . . . . 105 4.2.3 Interaction of ISP and PEDP and the Question of Dynamic Complementarity . . . . . . . . . . . . . . . . . . . . . . . . 106 4.3 Data and Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . 107 4.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.3.2 Iodine Exposure . . . . . . . . . . . . . . . . . . . . . . . . . 110 4.3.3 Empirical Specification . . . . . . . . . . . . . . . . . . . . . 111 4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.4.1 School Grade Attainment and Primary School Starting Age 115 4.4.2 Delay in Starting Primary School . . . . . . . . . . . . . . . 118 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5 Conclusions 136 Reference 138 vi A Supplementary Material for Chapter 2 148 A.1 Proof of Lemma 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 A.2 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . . 149 A.3 Test for Tiebout Migration . . . . . . . . . . . . . . . . . . . . . . . 151 A.4 Appendix A.4 Growing number of colleges and college students . . . 153 A.5 Tracking Effects on Private Tutoring . . . . . . . . . . . . . . . . . 154 A.6 Summary Statistics for KEEP . . . . . . . . . . . . . . . . . . . . . 155 B Supplementary Material for Chapter 3 156 B.1 The Machine Learning Algorism . . . . . . . . . . . . . . . . . . . . 156 B.2 LINE9 Effects on Rent . . . . . . . . . . . . . . . . . . . . . . . . . 161 B.3 Conditional Average Treatment Effects . . . . . . . . . . . . . . . . 163 B.4 The Regression Tree Result . . . . . . . . . . . . . . . . . . . . . . 168 C Supplementary Material for Chapter 4 169 C.1 The ISP treatment definition . . . . . . . . . . . . . . . . . . . . . . 169 C.2 Alternative Definitions of ISP Exposure . . . . . . . . . . . . . . . . 171 vii List of Tables 2.1 Summary Statistics: GOMS . . . . . . . . . . . . . . . . . . . . . . 43 2.2 Summary Statistics: CSAT . . . . . . . . . . . . . . . . . . . . . . 44 2.3 Mixing Effects of Mixing on College Enrollments: GOMS . . . . . 51 2.4 Mixing Effects of Mixing on TOEIC Scores: GOMS . . . . . . . . . 52 2.5 Mixing Effects on College Enrollment Test Total Scores: CSAT . . 53 2.6 Mixing Effects on College Enrollment Test Subject Scores: CSAT . 54 2.7 Tracking Effects on Study Hours . . . . . . . . . . . . . . . . . . . 56 2.8 The Low Types Overestimate Themselves Under Tracking . . . . . 56 2.9 Tracking Effects on Teacher-Pupil Interaction . . . . . . . . . . . . 57 2.10 Tracking Effects on Teacher’s Quality and Class Atmosphere . . . . 58 2.11 Direct Peer Effects on Possible Mechanism . . . . . . . . . . . . . . 59 3.1 Travel Time to Major Destination in Seoul . . . . . . . . . . . . . 86 3.2 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.3 OLS Estimates of the Value of Rail Access . . . . . . . . . . . . . . 91 3.4 Apartment Characteristics in Each CATE Group . . . . . . . . . . 93 3.5 New Apartment Yields High CATE . . . . . . . . . . . . . . . . . 95 3.6 Rail Transit Capitalization: The Role of Travel Time Savings and the Local Consumer City . . . . . . . . . . . . . . . . . . . . . . . 96 3.7 Estimates of the Value of Time . . . . . . . . . . . . . . . . . . . . 98 viii 4.1 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 4.2 Impact of Iodine Supplementation Program on completed years of schooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 4.3 Impact of ISP and PEDP on completed years of schooling . . . . . 132 4.4 Impact of ISP and PEDP on primary school starting age . . . . . . 133 4.5 Conversion of an additional year into additional years of schooling . 133 4.6 Impact of ISP on height of the child (Height-for-age) . . . . . . . . 134 4.7 Within household impacts of ISP . . . . . . . . . . . . . . . . . . . 134 4.8 Impact of ISP and PEDP on hours worked . . . . . . . . . . . . . . 135 A.1 Evidence that High School Enrollment Is Not Affected By Treat- ment, GOMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 A.2 Tracking effects on Private Tutoring . . . . . . . . . . . . . . . . . . 154 A.3 Summary Statistics: KEEP . . . . . . . . . . . . . . . . . . . . . . 155 B.1 Impacts of LINE9 on Rent . . . . . . . . . . . . . . . . . . . . . . 162 C.1 ISP Coverage Variation (from Field et al. (2009)) . . . . . . . . . . 169 C.2 Probability of Protection . . . . . . . . . . . . . . . . . . . . . . . . 171 C.3 Robustness of ISP Exposure Definition . . . . . . . . . . . . . . . . 172 ix List of Figures 2.1 Enrollments in Seoul National University (SNU) . . . . . . . . . . 39 2.2 Research Design: Two Cases . . . . . . . . . . . . . . . . . . . . . 40 2.3 Treated and Controls Region . . . . . . . . . . . . . . . . . . . . . 41 2.4 Evidence on Equalization Policy: Variance of the Number of Top Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.5 Kernel Distribution of Test Score: Whole Sample . . . . . . . . . . 45 2.6 Kernel Distribution of Test Score: Treatment Group . . . . . . . . 46 2.7 Pre-Trend Analysis: Lowess Graph, GOMS . . . . . . . . . . . . . 47 2.8 Pre-Trend Analysis: Regression Analysis, GOMS . . . . . . . . . . 48 2.9 Pre-Trend Analysis: Lowess Graph, CSAT . . . . . . . . . . . . . . 49 2.10 Pre-Trend Analysis: Regression Analysis, CSAT . . . . . . . . . . . 50 2.11 Relationship Between Student’s Own Rank and Peers’ Rank . . . . 55 2.12 The Total CSAT Score and The Hourly Wage 10 Years Later . . . . 60 3.1 Map of Seoul . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.2 LINE9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.3 The Pre-Treatment Trend: 1km vs 2km (Lowess Graph) . . . . . . 88 3.4 The Pre-Treatment Trend: 0.5km vs 2km (Lowess Graph) . . . . . 89 3.5 Treatment Effect Estimates Over Time . . . . . . . . . . . . . . . . 90 3.6 The CATE Distribution . . . . . . . . . . . . . . . . . . . . . . . . 92 x 3.7 The Empirical Distribution of New Construction as a Function of the CATE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.8 Long Difference Result . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.1 Iodine Supplementation Program in Tanzania (from Field et al. (2009)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 4.2 Trends in years of education and primary school strating age before treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 4.3 Trend in completion of appropriate grade for age before treatments 129 4.4 Trend in height before treatments . . . . . . . . . . . . . . . . . . . 130 A.1 Evidence that Refutes Tiebout Migration, CSAT . . . . . . . . . . . 152 A.2 Growing number of colleges and college students . . . . . . . . . . . 153 xi Abstract This dissertation deals with two education programs and an urban development plan. Chapter 2 evaluates the education policy change from tracking to mixing system in secondary education in South Korea. In chapter 3, with the supervised machine learning approach, heterogeneity in apartment price premium caused by the new subway transit stations in Seoul are estimated. Chapter 4 explores the dynamics of human capital development, using two programs in Tanzania: Iodine Supplementation Program (ISP) and Primary Education Development Program (PEDP). The key thing that puts three essays into together is that all explic- itly study heterogeneity in treatment effects. Especially, chapter 3 takes advan- tages of supervised machine learning approach based on a regression tree in order to understand multi-dimensional heterogeneity in subway stations’ capitalization effects. Three essays imply that public programs often vary across stakeholders and policymakers should take into account differential treatment effects. xii Chapter 1 Introduction It is important to evaluate social policies in an effort to increase policy effective- ness in the future. Policymakers can draw comprehensive lessons from the past through rigorous program evaluations that use well-designed econometric tools. This dissertation deals with two education programs and a subway expansion plan. Chapter 2 investigates schoolwide tracking effects in secondary education in South Korea. Ability tracking in secondary school is prevalent all over the world. Under this allocation of students to classrooms, a positive assortment process takes place such that gifted students study with other gifted students. This sorting process creates more homogenous classrooms with “high quality peer classrooms” and “low quality peer classrooms” relative to what would be the allocation under random assignment. Despite a wide use of schoolwide tracking, evidence on it’s causaleffectsisrare. ThisexaminestheconsequencesofSouthKorea’sequalization policy. Under the new policy, students were assigned to high schools without using information on the student?s prior achievement. This policy was adopted by some regions within South Korea but not in others. This spatial variation permits a difference-in-difference research design. In one study, the transition to mixing system caused a reduction in the number of students who were admitted to top- ranked colleges. In the other study, students in the treated regions converged 1 to the mean, and the variance in college entrance test score declined. Tracking benefitshighperformingstudentswhostudymoreandgrinfromasuperiorlearning environment. In addition, how students and teachers respond to their student mix is examined. Chapter 3 deals with casual effects of subway transit station on apartments’ price, using supervised machine learning technique. Urban rail transit investments are expensive and irreversible. Since people differ with respect to their demand for trips, their value of time, and the types of real estate they live in, such projects are likely to offer heterogeneous benefits to residents of a city. With the opening of a major new subway in Seoul as a treatment for apartments close to the new rail stations, a machine learning (ML) approach based on a single regression tree is used. This ML approach yields new estimates of these heterogeneous effects. While a majority of the “treated" apartment types appreciate in value, other types decline in value. We cross-validate our estimates by studying what types of new housing units developers build in the treated areas close to the new train lines. Chapter 4 evaluates the joint effect of two public programs from Tanzania, the Iodine Supplementation Program (ISP) and the Primary Education Development Program (PEDP) on the schooling outcomes for the exposed cohorts. Parental investment in child human capital formation is associated with whether or not the child benefited from the iodine supplementation program in an important manner. Parents tend to compensate ISP untreated children, most likely in response to differences in cognition created by the ISP treatment, by sending these children to school earlier than those treated by ISP. While free primary education provision under PEDP benefited both ISP treated and untreated children by reducing the age at which these children started primary school, the impact was much higher for ISP untreated children. Free primary education provision decreased the cost of 2 investment and, hence, increased the amount of compensatory investment by par- ents. Investments in human capital for the children in our sample seem to exhibit dynamic complementarity (Cunha and Heckman(2007)). For each additional year spent at school, ISP treated children convert them into higher years of completed schooling than those not treated by ISP. 3 Chapter 2 The Effects of Schoolwide Tracking on Low and High Skill Students: Evidence from South Korea 2.1 Introduction The assignment of students to classrooms plays a key role in a young person’s human capital development. In some settings, students are randomly assigned to classrooms while in other settings students are tracked such that high abil- ity students are in the same classroom with only other high ability students and low ability students are in the same classroom with only low ability students. 1 For nations that adopt a nationwide random assignment approach or a tracking approach, the nation’s stock of overall human capital will be determined by the consequences of such a policy. 2 Given the central role that human capital has played in theories of economic growth, it is essential to have a better understand- ing of the role that a nation’s schooling policy plays in helping young people across 1 Tracking is often defined as assigning students to a different class (or school) according to their prior achievement (e.g. Slavin (1987)). 2 Austria, Germany, Hungary, Singapore, and the Slovak Republic track students to secondary school based on their performance. By contrast, Canada, Japan, Norway, Sweden, South Korea, the UK, and the US keep lower secondary education mixing (Hanushek et al. (2006), Brunello and Checchi (2007)) 4 the ability distribution to acquire skills. 3 Given the importance of tracking in skill formation, there is surprisingly little direct evidence of the effects of across-school tracking (or a macro policy of tracking) versus research on within-school tracking. Using regression discontinuity designs (Pop-Eleches and Urquiola (2013), Card and Giuliano (2016), Dustmann et al. (2017)) or randomized experiments (Duflo et al. (2011), Carrell et al. (2013), Booij et al. (2017)) have shown that within- school tracking effects are non-linear and heterogeneous. Within-school tracking research has focused on peer effects 4 to the extent that they explore how students’ academicperformancewouldbeimproved(orworsened)iftheymovedtoadifferent peer group within school (e.g. reallocation from a non-honors group to an honors group). However, research investigating the causal effects of a nation’s tracking systemhasbeenhamperedbytherelativelysmallnumberofbothfieldexperiments and natural experiments. Hanushek et al. (2006) conduct across-country compari- son in students’ performance between tracked and non-tracked system in primary and secondary education. 5 Guyon et al. (2012) document that the expansion of the elitetrackincreasedaverageacademicoutcome, whereasPiopiunik(2014)findthat the decrease in age at which ability tracking begins increased a share of students who lag far behind. 3 Tracking effects on students’ academic achievement are not fully understood in the literature, although many older studies hinge on observational design, not rigorous causal analysis. (Betts and Shkolnik (2000), Betts et al. (2011)) 4 For a detailed recent review of peer effect literature, see Sacerdote (2014) 5 This has been challenged by Waldinger et al. (2007) to the extent that results are sensitive to the way tracking is implemented in each country. 5 This paper examines the consequences of South Korea’s equalization policy. 6 Under the new policy, students were assigned to high schools without using infor- mation on the student’s prior achievement. This policy was adopted by some regions within South Korea but not in others. This spatial variation permits a difference-in-difference research design. We study two distict cases in this paper; Ulsan that introduced the equalization policy in 2000 and seven cities in Gyeonggi Province where the policy was adopted in 2002. Figure 2.1 graphically describes what the equalization policy has caused. It shows that the number of students who were admitted to Seoul National University-considered to be the top school in South Korea- from each high school in our treatment regions has changed sig- nificantly. The number of student who go to Seoul National University has been a metric of school quality in South Korea. Between 1999 and 2004, the top-rank high schools in Gyeonggi Province had more than 30 students who are admitted to Seoul National University, while the low-rank high schools had none. After the equalization policy, however, the distribution has changed and the gap between high schools vanished considerably. The same pattern was observed in Ulsan. We find in one study that the transition to mixing system caused a reduction in the number of students who were admitted to top-ranked colleges. In the other study, students in the treated regions converged to the mean but the variance in college entrance test score declined. Tracking benefits high performing students who study more and grin from a superior learning environment. Heterogeneity across different subjects exists. The mixing system reduces the number of students who are good at math, whereas we find no evidence that the equalization policy hurts the right-tail of the distribution in Korean and English. This is in part 6 Tracking effects in South Korea have been explored in Kim and Lee (2003), Kang et al. (2007) Kim et al. (2008), Wang (2015). 6 because math usually shows greater instructional differentiation in response to ability tracking vis-a-vis verbal skills (Gamoran (1992)). We examine how teachers respond to their student mix. We find neither clear evidence that teacher-pupil interactionimprovednorthattrackingledschooltoemploymorequalifiedteacher. 7 We do not find evidence that ability homogeneous classroom enhanced teaching effectiveness; no statistically difference in teaching quality between the tracking and the mixing system is found. We also relate our results to the macroeconomics literature ((Gamoran and Mare (1989), Hanushek et al. (2006), Benabou (1993), Benabou (1996)) examin- ing the connection between human capital accumulation and ability tracking. Our results indicate that across-school tracking at the municipal level decreases edu- cational inequality to the extent that students’ academic performance are more dispersed. Mixing might increase the mean of the test score, but, simultaneously, it tends to wind up with fewer superstars. This brings up the discussion whether or not ability tracking contributes to increasing human capital. If the association betweeneducationattainmentandeconomicproductivitywerepositiveandstrictly convex, the dispersed academic outcomes would provide superior aggregate human capital because the smartest group plays a major role. If the average education levelrepresentedaggregatehumancapital, mixingsystemwouldbepreferable. Our back-of-the-envelope calculation implies that the decreased number of elites due to the transition from the tracking to the mixing system can decrease aggregate human capital. 7 Evidenceontrackingeffectonteachers’behaviorhasbeenmixedintheliterature. Dufloetal. (2011) find that tracking enables a teacher to provide more-tailored instruction, while Lankford et al. (2002) suggest poor-performing students tend to be matched with low-skill teachers. Booij et al. (2017) find that teachers do not adjust their teaching in response to whom they teach. 7 We motivate our empirical work by introducing a model of student effort. We model the heterogeneous tracking effect between high-achievement and low- achievement students. In this model, we draw a couple of implications. First, it shows that high-performance students are likely to benefit from tracking sys- tem, while the tracking impact on a low-performance students is ambiguous. Yet, if tracking discouraged high-achievement students too much due to difficulty in improving relative achievement, they are suffering under tracking as well. These implications guide our empirical work and provide insights into the possible mech- anisms for the effects we document below. The rest of the paper is organized as follows. Section 2 provides a conceptual framework. Section 3 describes the background. Section 4 outlines the data. Section5describestheempiricalstrategy. Section6discussestheresults. Section7 exploresthesuggestivemechanismsthroughwhichabilitytrackingaffectsstudents’ performance. Section 8 concludes the paper. 2.2 A Student’s Optimal Effort as a Function of Peer Effects In this section, we provide a simple model to explore heterogeneous tracking effect. The model predicts that tracking has a different impact, depending on the student’sabilityandrelativeachievementconcern. Itshowsthepossibleunderlying mechanismthroughwhichtrackingaffectsastudent’sperformance. Aseducational investment behaviors depend on the reference group students are surrounded by (BursztynandJensen(2015), Wang(2015)), weutilizeanon-cooperativegameset- ting in which individuals interact each other. Another key feature of the model is that we incorporate relative achievement into an utility function, as is in Tincani (2017). Without the relative achievement, it is always better to be with com- petent peers, meaning that low-performance students are always worse-off under 8 tracking system. However, if relativity concern influences educational investments, then whether or not tracking is detrimental to low-performance students becomes inconclusive. Building on Tincani (2017), we set up a model with two individuals (i and j) in school. An individual ‘i’ in school ‘s’ solves max e i,s U(y i,s ,R i,s )−C(e i,s ) s.t. y i,s =y(e i,s ;θ i,s ,θ j,s ,Qs) R i,s =R( e i,s e i,s +e j,s ;θ i,s ,θ j,s ,Qs), (2.1) where y i,s denotes absolute academic achievement, R i,s represents relative aca- demic achievement 8 , and e i,s is the effort level she exerts to study. θ i,s is her own academic endowment, while θ j,s denotes peer’s academical endowment. For sim- plicity, absolute achievement is affected not by that of her peer contemporaneously but by their prior endowment. In our empirical analysis, the endowment can be interpreted as prior achievement. Unlike Tincani (2017), we explicitly incorporate teacher quality in school (Q s ), and then relative achievement is determined by how much effort she exerts relative to her peer ( e i,s e i,s +e j,s ). 9 For simplicity, we consider the teacher quality to be independent to school-allocation system in this model. 10 8 In the model with two students, R i,s can be interpreted as gap in absolute achievement between two students. In the model in which n high types and m low types exist, it also can be considered to be each student’s rank in school. 9 Tincani(2017)assumesendowmentsandownabsoluteeffortsdeterminerelativeachievement. 10 In South Korea, the teacher allocation for public high schools is ruled by rotation system. Teachers must be transferred to a different school every four or five years within district, and this rule is strictly implemented by the government. This implies that it is a tall order for schools to maintain their teacher quality at high level in response to student allocation policy consis- tently, which makes our assumption plausible in South Korea’s context. However, as documented by Duflo et al. (2011), teacher quality might be closely linked with ability-tracking in another circumstance. 9 We later relax the assumption on teacher quality, and show how this changes our conclusion. We assume that ∂c(e i,s ) ∂e i,s > 0, ∂ 2 c(e i,s ) ∂e i,s 2 > 0, and ∂ 2 c(e i,s ) ∂e i,s ∂θ i,s < 0. This implies that the cost function is convex and that marginal cost for the high type is lower than those for the low type, which are standard in the literature. We also assume that y and R are twice differentiable and concave functions, respectively, and that the utility increases in y i,s and R i,s . Although Weinhardt and Murphy (2016) and Elsner and Isphording (2017) document academic rank has long-run impacts, we rule out that the relative achievement directly affects the absolute achievement. However, there is still a possible indirect pathway via effort. Seeking to improve their relative achievement in school, students may increase their study hour so that they achieve better an academic outcome. For simplicity, we add several assumptions as follows: A.1 Two types (θ i,s ∈{θ H ,θ L }) and two schools (s∈{M,T}). Under the mixing (non-tracking) system, a school consists of bothθ H andθ L , (θ H ,θ L ). Under the tracking system, homogeneous types are in school, (θ H , θ H ) or (θ L , θ L ). A.2 ∂ 2 y i,s ∂e i,s ∂θ i,s > ∂ 2 y i,s ∂e i,s ∂θ j,s > 0 A.3 ∂ 2 R i,s ∂e i,s ∂θ i,s > 0, ∂ 2 R i,s ∂e i,s ∂θ j,s = 0 Assumption A.1 outlines the basic model setting. Under the mixing system, both the high type and the low type study together, whereas under the tracking system the high type is with the high type and the low type is with the low type. Assumption A.2 implies that the marginal return to effort on absolute achievement depends not only on her own type but also on her peer’s type, and that own type influences the marginal return more than peer’s type does. Assumption A.3 consists of two parts. The former term represents that the marginal return to effort on relative achievement hinges on her own type; the more capable she is, 10 the higher the return is. The latter part implies that the total effects of peer’s ability on her marginal return to effort is zero. The rationale is that there are two offsetting forces. A high-performance peer provides a better study atmosphere, raisesmore-relevantquestions, andismorecapableofhelpingeachother. However, simultaneously,competitionbecomesfiercerwithahigh-typepeer. Itrequiresmore effort to improve relative achievement in school because a peer has higher marginal return and lower marginal cost. Because there is a lack of empirical evidence on this assumption, we assume that the two forces are equally strong so that the total effect is zero. Yet, we will relax the last assumption later and see how this affects our comparative statistics. Given the model, first-order conditions under the mixing system are Forthehightype : U 1 ∂y H,M ∂e H,M +U 2 e L,M (e H,M +e L,M ) 2 ∂R H,M ∂e H,M = ∂c H,M ∂e H,M (2.2) FortheLowtype U 1 ∂y L,M ∂e L,M +U 2 e H,M (e L,M +e H,M ) 2 ∂R L,M ∂e L,M = ∂c L,M ∂e L,M (2.3) First-order conditions under the tracking system are Forthehightypeschool : U 1 ∂y H,T ∂e H,T +U 2 1 4e H,T ∂R H,T ∂e H,T ( 1 2 ) = ∂c H,T ∂e H,T (2.4) Forthelowtypeschool : U 1 ∂y L,T ∂e L,T +U 2 1 4e L,T ∂R L,T ∂e L,T ( 1 2 ) = ∂c L,T ∂e L,T (2.5) 11 In equations (2)-(5), the left-hand side represents the marginal benefits of effort while the right-hand side shows marginal costs of effort. Each equation implies that higher marginal benefits or lower marginal costs lead students to exert more effort and to achieve better academic outcomes. Each effort level that satisfies each equation is a pure strategy Nash equilibrium. Our first point of interest is to compare the effort levels between the two types and to show who shows a better performance under the mixing school. Lemma 1. Under the mixing (nontracking) system, the high type exerts weakly more effort than the low type (e H,M ≥e L,M ). Hence, the high type outperforms the low type. Proof: See Appendix A.1 Intuitively, as the high type has a higher marginal benefit and lower marginal cost of effort than the low type, the high type exerts more effort. Holding teacher quality the same, with the production function in equation (1), we show the high type outperforms the low type under the mixing system due to more efforts and higher endowment. Our next key point of interest is to compare academic out- comes between tracking and mixing for each type. What the model predicts is summarized as follows: Proposition 1. The high type exerts more effort under the tracking the system than under the mixing system, while the low type changes in effort is ambiguous. There exists such that ifθ H −θ L <, then the low type would reduce efforts under the tracking system. Proof: See Appendix A.2 Holding the marginal cost function the same, the high type is better off under the tracking system due to more effort and direct spill-over effects from her peer. 12 An increased effort level under tracking is consistent with previous empirical find- ings. 11 On the other hand, the effect of the tracking system on the low type’s efforts is ambiguous. First, the low type reduces effort due to lower marginal bene- fitdrivenbylowerpeereffects. However, atthesametime, therelativeachievement is now solely determined by effort level because everyone in class shares the same endowment and subsequently the same peer effect. The fierce atmosphere leads students to exert more effort to improve their relative achievement. Given two off-setting forces, we cannot determine which is stronger, and it needs to be empir- ically tested. However, the model predicts that if heterogeneity between two types were small enough, the low type would reduce efforts under tracking because the negative force due to lost peer effect outweighs positive force driven by severer competition. Taking into account the fact that the low type is with other low type under the tracking system and given the production function in equation (1), it is more likely for the low type to be worse off under tracking. We conclude from the model that the high type benefits from the tracking sys- tem, while the low type suffers from it. However, as Duflo et al. (2011) document, if tracking leaded teachers in low type schools to provide tailored instructions or to reduce absenteeism, it would be more likely for the low type to be better off under tracking. Thisisbecausetheabsoluteachievementinequation(1)isalsoafunction of teacher’s quality in a school. 12 Hence, our model is not at odds with the theo- retical model in Duflo et al. (2011). It is worthwhile to note how the relaxation of assumption 3 changes our comparative statistics. Let us assume that the marginal 11 Bursztyn and Jensen (2015) show that students in honors class are less reluctant to take on extra effort than those in non-honors class. 12 Based on the previous findings(Duflo et al. (2011), Lankford et al. (2002)), teacher quality in school(Q s ) might affect marginal benefits of effort. However, we rule out this possibility for simplicity. 13 return to relative achievement decreases with peer’s type ( ∂ 2 R i,s ∂e i,s ∂θ j,s < 0), meaning that a competitive peer causes difficulty in improving their relative achievement. With this assumption, the conclusion becomes inconclusive. The high type takes advantage of higher marginal return to absolute achievement due to a competent peer, whereas one simultaneously suffers from stiff competition in terms of relative achievement. If a discouraging effect were large enough, the high type ends up with less effort and lower performance. The low type faces exactly the oppose situation. If tracking motivated the low type in absence of the high type, tracking would be beneficial to the low type. This model provides the insight that tracking effect is heterogeneous, which is consistent with a large body of the tracking literature. It depends on ability- type, whether or not teacher quality responds to student mix, and the extent to which peer’s competence is influential to relative achievement. Hence, a tracking effect should be empirically explored. It requires researchers to investigate aca- demic performance (y i,s ), educational investment behaviors (e i,s ), and teacher’s response in order to fully understand causal effects of ability-tracking in empirical works. Therefore, in the following, we use a wide variety of data sets to provide evidence on across-school tracking effect in South Korea. First, we empirically estimate how student allocation system and students’ performance are causally associated with difference-in-difference framework. Then, we explore underlying mechanisms through which ability-tracking affects students’s performance (y i,s ). Following what the model predicts, we deal with self-studying hours (e i,s ), self- evaluation (R i,s ), teacher-pupil interaction, and classroom atmosphere (Q s ). 14 2.3 South Korea’s Education Policy Dynamics Before 1974, high school allocation in South Korea was based on tracking. Stu- dents used to take a competitive municipal-level high school entrance examination at the end of their middle school years (grade 9). Based on the test score, students applied to schools within the district where they took the exam. If the number of applicants exceeded a school’s maximum capacity, students would be allocated according to the selection process that honors applicants whose scores are higher. Even though most high schools in South Korea were public schools, they could be ranked within the district in terms of academic performance (e.g., SAT scores or number of students who were admitted to top universities) 13 , and the rank across schools was known to the public. This process resulted in “an ability-homogeneous learning environment” under which students with similar ability study together (Wang (2015)). However, the high school-allocation system had created some public concerns. As parents wanted to send their kids to top-performing high schools, competition for better high schools had become extremely fierce, and the number of private tutoring institutions had grown at unprecedented rates. As a result, education costs increased significantly. Moreover, as noted by Gamoran and Mare (1989), Epple et al. (2002), Duflo et al. (2011), the tracking system winds up widening educational inequality in that well-performing students benefit, but poor-performing students suffer. The “Equalization Policy” (hereafter, EP), which can be considered to be the transition from the tracking to the mixing system, was introduced in 1974 to 13 The EP led to the “virtual nationalization” of private schools, as they lost control over the selection of students and had no incentives to adopt policies to attract students (Kim and Lee (2003)) 15 address the fierce competition and rising inequality pertaining to high school allo- cation. The EP abolished the competitive high school entrance exam, assigning students to high schools in their district no matter how well they did in middle school. The expansion occurred at a differential pace across the cities. Seoul and Busan implemented it in 1974, and it had been extended to other cities until 1981. 14 The EP did not expand between 1981 and 2000, but it is adopted by Ulsan and by seven cities in Gyeonggi Province (e.g. Anyang, Bucheon, Bundang, Goyang, Gunpo, Gwacheon, and Uiwang) in 2000 and in 2002, respectively. As a result, 61.05% of high schools are under the EP as of 2008 (Korean Educational Statistics Service). As tracking effects are heterogenous between educational capa- bility, each interest group evaluates the same policy in different ways based on where they are positioned. Through the policy implementation, majority of par- ents agreed upon the EP because they believed ability tracking at early age had made low-performance students less self-confident, and because cram schools had become more prevalent under the tracking system. 15 The supporters also argued that the secondary school tracking system pushed students into private tutor- ing at early age in order to get into better high school. They believed that the severe dependency on private tutoring hampers creative thinking and decreases students’ physical exercises. On the other hands, others objected the EP based on beliefs that ability-mixing might decrease students’ performance on average. They believed that teachers offer a standardized instruction rather than tailored one under the mixing system, which causes students to lose their appetite for 14 Daejeon, Chungju, Suwon, Chuncheon, Jeonju, and Jeju adopted the EP in 1979, while Changwon, Sungnam, Wonju, Gunsan, Iksan, Mokpo, Ahndong, and Jinju adopted the EP in 1980. 15 According to the poll, carried out by Korean Educational Development Institute in 2000, 71.2% of respondents welcome the EP. The sample size was 4,458. 16 studying. A few public hearings took place and a major newspaper criticize the expansion of the EP in the editorial. The divided views on the EP are consistent with what our model predicts in the previous section. Policy makers might under- stand the trade-off of the EP, but they have decided to adopt the EP in order to mitigate the negative impacts of stiff competition for high school entrance exam and address educational inequality. An interesting feature of the EP is that how the policy was implemented varies across districts and years. Some randomly allo- cated students into high school, while others used different mechanisms. However, no prior achievement is not considered in high school placements under the EP regardless of which allocation mechanism was used. This paper takes advantage of the EP in Ulsan city and in seven cities in Gyeonggi Province. After the EP was adopted, both regions started placing stu- dents in high school in the following way. First, all students submit a preference ranking of high schools, 16 each high school admits students who have listed it as their first priority and the system keeps assigning students to a school in priority order until either no slot remains or no student who has listed it in any order remains. If the number of applicants exceeds the target cohort size at any round, the students will be randomly chosen, which is the key difference from the tracking system. This is called the Boston Student Assignment Mechanism in the United States (Abdulkadiroglu and Sönmez (2003) and Abdulkadiroğlu et al. (2005)). 17 Figure 2.2 illustrates districts of interest. The top-left corner of South Korea indi- cates to the EP in Gyeonggi Province, while the bottom-right corner shows the 16 A student should mention explicitly his/her most preferred school. Then his/her second and third most preferred high schools should follow. A student may list up to 13 high schools. 17 The Boston Student Assignment Mechanism is not strategy-proof to the extent that each student has an incentive to misrepresent a school preference in order to avoid too a large risk. This misrepresentation also leads to Pareto inefficiency (Abdulkadiroglu and Sönmez (2003)). 17 region related to the EP in Ulsan. Dashed areas indicate the treatment group that experienced the EP in 2000 or in 2002, meaning that other shaded areas are con- sidered to be the control group. Since we use two different data sets corresponding to each case, for simplicity, we name two cases after the data set: GOMS repre- sents the case in Gyeonggi province and CSAT indicates the case in Ulsan. Figure 2.3 provides more detailed and magnified maps. In both maps, the non-shaded area indicates always-mixing and the shaded area shows always-tracking, while the dashed area indicates where the EP was implemented. The always-mixing and always-tracking regions are the control group, whereas the dashed regions are con- sidered the treatment group. On a side note, in South Korea, it is worth to note that there is no major difference between public and private high schools in terms of curriculum and students’ quality, especially, between late 1990s and early 2000s. Private schools had no control over student selection, but students are admitted into even private schools by the same process as public schools. Regardless of whether it is public or private, all high schools are under the Boston Mechanism without separating them. It implies that although students want to enroll into a private high school, there is no guarantee. This makes it less likely that elites rushed to private schools in response to the EP in order to benefit from ability- tracking. 18 By definition, the EP should reduce the variation of academic performances between schools to a large extent. If it were assumed that school quality does not differ within the district, one school should perform as well as others under the mixing system. However, it is also plausible that well-performing students still go 18 There are special-purpose high schools for science or foreign language in South Korea. They select their own students with different admission procedure, meaning that ability-tracking still takes place to some extent. However, in the empirical analysis, we drop individuals who graduate from the special-purpose schools because the inclusion confounds our definition of treatment. 18 to high school, which is previously known as a top school, to take advantage of better alumni or more-advanced facilities. For example, well-performing students might list a previously good school as a high priority, while poor-performing stu- dents might prefer a previously bad school for some other reason(s). Hence, it is crucial to test whether the EP, indeed, brought ability mixing across high schools. Figure 2.4 provides evidence that the EP contributed to reducing a performance gap between high schools. It shows the variance of the number of students who are admitted to Seoul National University, the most preferred institute in South Korea, from each high school in the treatment group. In both the GOMS and CSAT cases, the variances decreased significantly after the EP took place. 19 This implies that ability mixing took effect along with the EP. 2.4 Data In this section, we describe the data and the summary statistics. 2.4.1 Graduates Occupational Mobility Survey Toanalyzethetransitionfromthetrackingtothemixingsysteminseveralcities in Gyeonggi Province in 2002, we make use of the 2008-2013 waves of Graduates Occupational Mobility Survey (GOMS) 20 conducted by Korea Employment Infor- mation Service. GOMS is an ongoing short-term panel survey of a representative 19 The rate of decrease in variance is slower in the CSAT case than in the GOMS case in part because students often retake the college entrance exam. This leads the statistics of 2003 in the CSAT case to include students who enrolled in high school under the tracking system. As students are unlikely to take the exam more than three times, the variance has been decreasing consistently. 20 We exclude the first survey (2006 wave) because students in our cohort of interest?those born between 1983 and 1988?were not included in the survey but were still in school. GOMS survey was not conducted in 2007. 19 sample that targets college graduates 21 in South Korea. It had been designed to select18,000graduates(approximately3∼4%ofthepopulation)everyyearandto follow up with them two years later until the 2011 wave. However, it has collected only cross-sectional data since 2012. GOMS contains the name of the college from which a respondent graduated from and the information on the district where the respondent attended high school, along with a rich set of socioeconomics covari- ates. In accordance with education policy in South Korea, we define “academic birth cohorts” as those composed of students born between March and December in a certain year and those born between January and February in the following year. For example, the 1983 academic birth cohort includes those who were born between March and December in 1983 and those born in January or February in 1984. This is because the same academic birth cohort, not the calendar birth cohort, attends school together. We restrict our sample to graduates born between 1983 and 1988 in terms of the academic birth cohort because those younger than this generation are likely to be still in college in 2013, which means they are not yet surveyed. We define the control and treatment group, using the location of the high school and the academic birth cohort. Note that we exploit the sample that graduated from high school in Seoul, Incheon and Gyeonggi province to account for regional and cultural similarities as presented in figure 2.2 and 2.3. Table 2.1 provides the summary statistics for the GOMS data. We define the top 8 and top 15 based on the average of college entrance test scores. The major rationale behind why we use an admission data for colleges is that we cannot 21 GOMS includes graduates from 2- to 3-year colleges, 4-year colleges, as well as education colleges. 20 observe test score directly in GOMS data. 22 Given the rankings across colleges in South Korea, however, the top 8 and the top 15 are two of the most common measures that evaluate how well a student studies, although there is no official document that defines the top 8 and the top 15 explicitly. Around 8% of graduates are from the top 8, while 70.3% are from four-year colleges. 2.4.2 College Scholastic Ability Test For evaluation of the change in tracking policy in Ulsan Metropolitan City in 2000, we utilize College Scholastic Ability Test data (CSAT) between 2000 and 2007. 23 These are population data that include all scores of students who took the exam. Around 600,000-700,000 students take the exam annually, and the percentage of students who did not show up at the exam date is less than 5% on average between 2002 and 2007 (Korea Institute for Curriculum and Education). Taking into account regional and cultural similarities, we exploit the data from the southeast region as we did with the GOMS data. Despite the large sample size, the major disadvantage of the data is that no information of socioeconomic status, besides gender, exists. We make use of a percentile rank of Korean, math and English. As each student takes different electives, results from electives are excluded from our analysis. Since it is possible to take the exam for multiple times, on the other hand, we restrict the sample to the scores of the student who takes the exam for the first time. It takes a toll on estimating the mixing effect to include all samples due to the fact the data indicates only whether an exam taker takes 22 The similar attempt is found in Hahn et al. (2008). They exploit the dependent variable as whether students are admitted to the top three universities in South Korea: Seoul National University, Yonsei University and Korea University. 23 The government changed a structure of the exam significantly in 2008 so that we do not include scores from 2008 onwards. 21 it for the first time or not. Since the data does not say exactly how many times an exam taker has taken it if it exceeds one, we could not confirm in what year a student enrolled in high school if we included all samples. We define students in Ulsan Metropolitan City as the treatment group. Students who took the exam between 2000 and 2002 were under the tracking system. Table 2.2 reports the summary statistics of the CSAT data. The average of the percentile rank for the whole sample is 47.89, which is close to that for the control groups. What draws our attention is that there is a significant increase in all scores in the treated district since the EP was implemented. At first glance, it seems that on average students in the treated district benefited from the mixing system, but figure 2.5 and 2.6 provide another aspect. According to figure 2.5, the test scores for both total score and each subject are uniformly distributed except for both tails of the distribution for the entire sample. Once we focus on the treatment group, however, figure 2.6 shows the distribution had been altered after the school allocation system changed from tracking to mixing. It became a bell-shaped distribution under the mixing system, meaning that students are more likely to attain the test score around the mean under the mixing system than under the tracking system. This description suggests that the mixing system is better at fostering students’ performance on average, but it can be inferior at training the highest performing students. We return to this point in section 6. 2.5 The Empirical Approach In this section, we describe the empirical strategy employed. As noted by a largebodyofliterature(e.g. Bayeretal.(2007)andChoietal.(2014)), endogenous school choice or residential sorting results in a simple ordinary least squares (OLS) estimate bias. This is because it is a tall order to distinguish tracking(or mixing) 22 effect from other district characteristics. Following Kim et al. (2008) and Wang (2015), our approach is based on the linear difference-in-difference model. 2.5.1 Does Ability-Mixing Affect College Enrollment? For an individual i who was born in year t, graduated from high school in district j, and was surveyed in year s, the college enrollment is expressed as follows Y 1 ijst =β 1 Treat j ×Post t +β 2 X ijst +μ j +λ st +ε ijst , (2.6) where Treat j is the treatment dummy that takes on value one if a student grad- uated from high school in the treated district and that takes on value zero oth- erwise. Post t represents the time dummy that is one if a student was born after 1986 and zero otherwise. X ijst is a vector of covariates such as gender, father’s education, mother’s education, and parents’ income when a student graduated from high school. Our empirical specification also includes district fixed effect (μ j ) and survey-year fixed effect (λ st ), 24 as is standard in the difference-in-difference literature. We exploit top-8 enrollment, top-15 enrollment, enrollment into college in Seoul and four-year college enrollment as main outcome variables (Y 1 ijst ). 25 We take an advantage of Test Of English for International Communication (TOEIC) 26 scores as a dependent variable as well. 27 24 To allow for students born in the same academic year to differ across survey years, we do not use survey fixed effects and year fixed effects separately, but we include survey-year joint fixed effects 25 Top-8 and top-15 are defined by the average of CSAT scores of students who are admitted to a certain college as outlined in section 4.1. 26 TOEIC is a test to examine how well exam takes communicate in English. It consists of reading and listening comprehension tests. 27 We utilize not only raw scores but also three categorical outcome variables: above 700, above 780, and above 900. Such thresholds are based on the policy implemented by the government of 23 Within this regression framework, the effect of the EP (the transition from tracking to mixing system) in the treated districts is captured by coefficient β 1 . For example, if β 1 < 0, then the EP decreases students’ performance. If β 1 > 0, students in the treated districts are better off due to the EP. Forβ 1 to be unbiased, both the treated and the control group would have followed the parallel trajectory in the absence of the policy intervention. We will explore nonparametrically pre- trend of both the treated and the control group in the next section, finding that they began converging after the EP implemented. This implies that they are comparable and would have followed the parallel path. Another key assumption forourdifference-in-differenceframeworktobevalidisthattheinterventionshould nottriggermigrationfromonetowntoanothertown. Ifpeoplehadshoppedforthe preferableeducationpolicy, theEPwouldhavecatalyzepeopletoseekthedesirable education program. This educational shopping behavior jeopardizes our empirical strategy. Thus, it is worth testing whether any change in observables occurred in the treatment group after the EP. The last column of table shows p-values for the difference between before and after the EP. We find no significant change in most independent variables, except for gender. 28 This minimizes the possibility that our empirical strategy based on the difference-in-difference framework causes biased estimates. Furthermore, what needs to be addressed is that GOMS data targets only stu- dents who enroll in colleges. This sample design implies that very low-achievement South Korea. A score of 700 is the minimum to work for the government, and a score of 780 is the minimum to work at the United States Forces Korea. Korean soldiers need a TOEIC score above 900 to serve as interpreters in the army. 28 The difference in gender ratio is in part explained by the fact that all males in South Korea serve two years in the military. Most male students go into the army during college, which delays graduation for them. Hence, for younger cohorts, female students are more likely to graduate before 2013 than male students. 24 students or those who are never interested in studying are excluded from the sam- ple. As college enrollment rate was as high as 80% in South Korea in early 2000, the selection issue may not be too pressing but still restricts external validity of our study. However, analysis with CSAT data in the next section is rather free from a selection issue because it targets all high school students. Another possible concern is whether the education policy change from the tracking to the mixing systemtriggersTieboutmigration, meaningthatresidentsinthetreatmentdistrict may decide to migrate to other regions in an effort to find better educational envi- ronments. If this were true, then the high school enrollment rate might be affected by the treatment and our empirical strategy might be jeopardized. As discussed in Appendix C, however, we cannot find any statistically significant treatment effect on high school enrollment. Robust standard errors are clustered at the district level. 2.5.2 Does Ability-Mixing Affect A Student’s Test Score? For an individual i who was born in year t, graduated from high school in district j, the college enrollment test score is Y 2 ijt =β 1 Treat j ×Post t +β 2 Gender ijt +μ j +λ t +ε ijt , (2.7) whereTreat j takes on value one if a student is in treated district, and zero other- wise. Post t is one if a student took an exam before 2003, and zero otherwise. Due to a lack of covariates in the data, gender is the only control variable. Equation (7) also includes district fixed effect (μ j ) and year fixed effect (λ t ). We exploit a percentile rank as a dependent variable (Y 2 ijt ). We use not only total score but 25 also Korean, math, and English scores to explore which subject is influenced by the EP the most. In equation (7), β 1 captures the mixing effect on the college entrance test score in the treatment region. For β 1 to be valid, the parallel trajectory in the absence of the policy intervention and no migration assumption should be met. We will conduct the pre-trend analysis in section 6.1. To investigate whether the transitionfromthetrackingtothemixingsystemtriggersanychangeinpopulation composition or Tiebout migration, we compare the young population size and educational attainments in district level between 2000 and 2005 in Appendix C using the census data. Our analysis suggests that the likelihood that the treatment affects other demographics is rather small. Robust standard errors are clustered at the district level. 2.6 Results 2.6.1 Pre-Trend Analysis For the linear difference-in-difference approach described in equation (6) and (7) to be valid, both the treated and control groups would have followed parallel trajectory in the absence of the treatment. Analyzing the pre-trend, we demon- strate that the treated and control groups are not significantly different. Figure 2.7 presents the smoothing nonparametic graph of four outcome vari- ables of interest using the GOMS data. The vertical line at the year 1985 shows when the treatment occurred. The solid line represents the treatment groups, while the dashed line indicates the control groups. For most outcome variables, the treatment and the control groups show a parallel path before the intervention, but the gap between them has been decreasing ever since the EP was implemented 26 in the treated regions. It is worth noting that both the treatment and the control groups show declining trend in all outcome variables. This is mainly because the number of total college students had been growing constantly, while the number of students who are admitted to the good schools remained stable. Another cause is an increased number of colleges. Such new colleges are not usually considered to be good schools in South Korea. Thus, the number of students who enroll in a good school has shown the relative decrease. More details are described in Appendix. Figure 2.8 presents a regression-based pre-trend analysis. 29 All out- come variables, except for admission to the colleges in Seoul, show that the point estimates decreases after 1986. For both the top 8 and the top 15, the coefficients of interest become statistically different from zero at 10% level in 1986. This can be interpreted as evidence that the treatment broke the prior trajectory. Figure 2.9 illustrates the both ex-ante and ex-post trend using CSAT data. A vertical line indicates when the policy was implemented. In this figure, for all four outcome variables, both the treatment and the control group moved along the same path before the EP. They began to diverge after the intervention. This suggests that they are comparable, and that both the treatment and the control group would have followed a similar path in the absence of the EP. We also run the similar regression analysis. 30 Figure 2.10 shows that the probability of being in the top 95% started to decrease in 2004, a year after the treatment was implemented. Studentsinthetreatmentgrouphavebecomelesslikelytobein thebottom10%or 29 We estimate Y1 ijst = P 1988 Y=1984 β Y Treat j ×Year Y +β 2 X ijst +μ j +λ st +ε ijst , and present each β Y in figure 8. It presents annual treatment effects with the year of 1983 as a baseline. For the difference-in-difference framework to be valid, treatment effects should occur after the treatment was actually implemented. 30 We estimateY2 ijt = P 2007 Y=2001 β Y Treat j ×Year Y +β 2 Gender ijt +μ j +λ t +ε ijt , and present each β Y in figure 2.10. It implies how treatment effects have changed annually with the year of 2000 as a baseline. 27 bottom 5% ever since 2003. This provides strong evidence that the transition from tracking to mixing affects students’ academic performances. To address possible treatment effects on changes in population composition, which might confound our estimates, we present the time trends of each variables in Appendix C. We find little evidence that the EP affected students’ academic outcomes through a migration channel. 2.6.2 College Enrollment and TOEIC: GOMS Table 2.3 illustrates the extent to which the transition from the tracking to the mixing system affects college enrollments. Students in the treatment group are less likely to be admitted to the top 8. The probability to enroll into the top 8 colleges decreases by 1.6 percentage points. The rest of the outcome variables show similar results. The change to the mixing system results in decreased likelihood to be admitted to each category. In comparison with the mean of the outcome variable, our results imply that the treatment effect is bigger for top-ranked students. Given the fact that the percentage of students who study in the top eight colleges is 8.67 percent, on the one hand, the reduction represents a decrease by 18.3 percent. On the other hand, enrollment into four-year colleges remains relatively stable; it decreases by only 4.4 percent. 31 If the performance distribution across students was stable through secondary school 32 in part due to dynamic complementarity 31 Our finding is finding is consistent with Hahn et al. (2008) in which they show the change to the mixing system makes students be less likely to be admitted to the top three universities. Taking advantage of the longitudinal data framework with fixed, random effect, and the Tobit model, they document the consistent evidence of the negative mixing effects. However, our study is different from theirs for a few reasons. First, our empirical strategy is different. Second, we control for individual’s socioeconomic status, while they only control for school’s character- istics. Third, they investigate whether the ability-mixing affects enrollments to the top three universities, but we have variety in dependent variables. 32 Secondary school consists of middle school and high school in South Korea. 28 between early endowment and educational investments in later life (Cunha and Heckman (2007), Heckman (2007), Cunha and Heckman (2008)), table 2.3 shows top-ranked students suffer from the mixing system, while low-ranked students are relatively less affected. Table 2.4 shows whether the mixing system affects TOEIC scores. Mixing effectsarenotstatisticallydifferentfromzeroat10percentformostoftheoutcome variables, although probability to achieve above 700 decreases by 2.8 percent in column (2). Despite the fact that the TOEIC score is not a factor in determining college enrollment, this suggests that English would be the subject that drives the results in table 2.3. This is consistent with the previous findings that the ability to learn a second language decreases significantly after the age of 12(Knudsen et al. (2006), Newport (1990)). Since the change to the mixing system occurs above age 16 in our context, the effect on English education might be limited. This is also consistent with our results with CSAT data described in the next section. The chance to achieve high English scores in the college enrollment test is not affected when the tracking system is replaced by the mixing system. We will get into details in the following section. 2.6.3 College Entrance Test Score: CSAT Table 2.5 reports the impacts of the EP on the college entrance test score. It shows that in the treatment region fewer students are in the top tier (top five percent or top ten percent) at the exam, while, simultaneously, students are less likely to be left behind. The probability to score higher than the top five percent or the top ten percent decreases by 0.34 and 0.73 percentage points, respectively. Meanwhile, the chance to be in the bottom ten percent or in bottom five percent decreases by 5.92 and 3.19 percentage points, respectively. Our estimates imply 29 that students are more likely to score around the mean. As the positive effect on being out of the bottom outweighs the negative effect that drags students away from the right tail of the distribution, total score increases by 2.3 percentage points as seen in column (7). 33 We explore mixing effects on each subject: Korean, math and English. Our results, in table 2.6, show that the EP increased the probability to be out of the bottom regardless of subject, and all magnitude in column (4)-(6) are similar. On the other hand, only math shows statistically significant positive mixing effects on being a top tier at 10 percent level. Our results show that the chance to get math score higher than the top five percent decreased by 0.49 percentage points if students moved from tracking to mixing. As documented by Gamoran (1992), instruction for math is more flexible compared to that for language. The great instructional differentiation in math might cause the heterogeneity between subjects. 2.7 Discussion In this section, we test what the model predicts in section 2 and explore sug- gestive mechanisms under which the tracking system affects students’ academic 33 The positive effect on total test score seems to initially contradict the results in the previous section, but it can be rationalized for two reasons. First, in retrospect, GOMS data target only students who are admitted to colleges, which means students with very low test scores are excluded from our sample. In other words, GOMS data might represent students who score above the 75 percent quantile, given the fact that college enrollment rate is close to 80% in South Korea. By excluding students on the left tails, we might reach the consistent negative effects on college enrollment. However, the CSAT data includes students regardless of where students locate on the distribution of the test score, so we can find the positive effect on total score. Second, as outlined by the model in the section 2, the mixing or tracking effect on the low type is ambiguous. Since we deal with two different populations, GOMS and CSAT samples, mixed signs of treatment effect on low-performance students are consistent with what the model predicts. 30 performances, using a different data set. As we use different data sets with differ- ent populations, the analysis below cannot be interpreted as the direct mechanism through which the results in section 6 are derived. However, this analysis provides different prospects of ability tracking effects. As noted by the model in section 2, the tracking system affects students’ academic performance through various channels; studying effort, teacher’s quality, class atmosphere, and more. Thus, we shed light on plausible pathways though which students and teachers respond to schoolwide ability-tracking. 2.7.1 Data We use the 2004 and 2005 wave of Korean Education and Employment Panel (KEEP) for the analysis in this section. This is an ongoing longitudinal survey that selected 2,000 students from grade 9 (final grade in middle school) and 4,000 students from grade 12 (final grade in high school) in 2004. The subjects are followed up by more than 10 years so far in efforts to facilitate research pertaining to the education and labor markets for the younger generation. We make use of the baseline survey for 2,000 students in grade 9 in 2004 and the follow-up survey in 2005 because we intend to estimate an instant effect of tracking in the short term. In the case where key variables are not surveyed in the 2005 wave, we replace those with 2006 wave. For example, the query about teacher-pupil interaction was not carried out in the 2005 wave, so we exploit the information in the 2006 wave. This data includes a rich set of family background, information on schools and teachers, studying behaviors and whether students go to high school in a tracking region. The summary statistics of the data are presented in the Appendix F. 31 2.7.2 Empirical Strategy To investigate behavioral changes for both students and teachers caused by the tracking system, we exploit the unique educational context in South Korea. Due to the recognition that tracking across middle schools increases education costs considerably and expose students to too fierce competition at an early age, the government of South Korea abolished all tracking systems across the nation in 1971 and started assigning students to middle school regardless of how well they studied in primary school. However, tracking across high school still remains in some districts. Figure 2.11 illustrates relationships between a student’s own rank and peers’ rank in the same school in our data. Note that all ranks presented in figure 2.11 are ranks in middle schools not in high school, meaning that the ranks of two bottom graphs can be interpreted as prior ranks. Given the history of tracking and mixing in South Korea, we expect no salient association between ones own rank and peers’ rank both at the middle and high school levels under the mixing system. Conversely, we expect a positive relationship between those in high school under the tracking system. Figure 2.11 is consistent with what we expect. Thus, we utilize another difference-in-difference framework, with students in the region under high school tracking system defined as a treatment group. Students in the other regions are considered to be a control. 34 For an individual i who was surveyed in year t, studied in high school in district j, her academic outcome is Y 3 ijt =β 1 Treat j ×High t +β 2 Treat j ×High t ×Above i +β 3 High t +μ i +ε ijt , (2.8) 34 In a similar way, Wang (2015) estimates the tracking effects on non-academic outcomes. Unlike his work, we explicitly add a triple interaction term to explore the heterogeneity between high and low performance students 32 where Treat j takes a value of one if a student goes to high school in a track- ing district and zero otherwise. High t takes on value one if a student was sur- veyed when she was in high school, and zero if she was surveyed in middle school. Above i represents a dummy variable that shows whether student’s rank in middle school is above the median. We include Above i to explore heterogeneity in track- ing effect across prior ranks, as predicted by the model in section 2. Equation (8) includes individual fixed effect, and ε ijt is an unobservable disturbance. As the individual fixed effect takes into account all time-invariant individual charac- teristics, which include gender parents’ educational level and genetic information, additional covariates are not included. Our outcome variables (Y 3 ijt ) of inter- est include study hours, teacher-pupil relationship, teacher qualification and class atmosphere. All robust standard errors are clustered at the district level. Within the regression framework in equation (8), β 1 represents schoolwide tracking effects on students who were in the bottom half of the school in grade 9. The extent to which tracking affects students at the above half is captured by β 1 +β 2 . For both β 1 and β 2 to be valid, parents should not move based on knowledge of their kid’s ability. If parents sought for the most preferable education policy and migrated according to their belief, our difference-in-difference estimates would be confounded. In our sample, 7% of the sample migrated between 2004 and 2005. As it is not feasible to investigate their motivation behind the migration in our data, equation (8) hinges on the assumption that such migration has nothing to do with the shopping for the best educational policy. 35 35 For the robustness check, we exclude students who migrated and do the same analysis. Our results remain unaffected. 33 2.7.3 Hours of Studying First, we explore whether tracking affects studying behaviors. In section 2, the model predicts the high-performance student tend to increase their effort under the tracking system, whereas how the low-performance student changes effort in response to the tracking system is ambiguous. Table 2.7 presents changes in stu- dents’ self-studying hours depending on whether they are under tracking or not. We use three categorical outcome variables: studying less than 2 hours a week, more than 15 hours a week, or more than 20 hours a week. Table 2.7 shows that students in the bottom half reduce their study hours under the tracking system, whereas those in the top half increase their study hours. While the results in columns (1) and (2) are not statistically different from zero at the 10 percent level, all signs of the coefficients are consistent. We conclude that students whose rank was higher than the 25 percent quantile would be more likely to study more than 20 hours a week, if they moved from the mixing to the tracking system. We also identify the extent to which tracking affects private tutoring in Appendix E. The extent to which a student is involved in private tutoring has been considered to be a tool to improve academic outcomes in South Korea (Byun (2014), Ryu and Kang (2013)). Our results are consistent with what we find with self-studying hours in the sense that students in the top half are more likely to engage in private tutoring than those in the bottom half. This implies that tracking leads the high types to increase educational investment, although the tracking effect on private tutoring is not statistically significant at 10 percent. Table 2.8 provides a possible underlying mechanism through which the tracking system changes self-studying hours. We utilize a self-evaluation for Korean, math, and English, respectively, as outcome variables and see if they are affected under the tracking system. Table 2.8 shows that students in the bottom half of school in 34 grade 9 overestimate themselves under the tracking system, while those in the top half estimate themselves in the same way as they did in middle school or slightly underestimate themselves, especially for English. These results are consistent with the claim that the high types consider themselves to be relatively worse because they are exposed to high quality peer classroom. Such differences in self-evaluation might lead to the changes in self-studying hours reported in table 7. 2.7.4 Teacher-Pupil Interaction, Teacher’s Characteristics and Class Atmosphere Thetrackingsystemmayaffectateacher’sincentiveorteacher-pupilinteraction (Duflo et al. (2011)). If tracking affected a teacher’s behavior in a positive way, then all types would be better off under the tracking system. We use several subjective measures 36 related to teacher-pupil interaction. Table 2.9 shows that no one is affected by tracking regardless of prior achievement. We investigate the association between tracking and teacher quality. Due to no consensus on what defines a better teacher (Hanushek and Rivkin (2006)), we use a few relevant outcome variables. Following a large body of literature (Bird- sall (1985), Summers and Wolfe (1977), Rice (2003)), we exploit whether or not a teacher attains a masters degree or higher, total years of experience as a teacher, teaching experiences on the subject that a teacher is currently teaching and subjec- tive evaluation by an administrator in the school. Table 2.10 shows that teachers’ characteristics are no different regardless of whether a high school is under the tracking system or not. Results presented in column (1) through (4) show that no tracking effect is statistically significant at 10 percent level. As discussed earlier, in 36 These measures are based on a scale of five. We let the outcome of interest take on value one if it is four and above and take on zero, otherwise. 35 South Korea, the teacher allocation system based on the rotation keeps the teacher quality between schools balanced. This is because the teachers’ characteristics are no different. However, column (5) and (6) imply that students in the top half are more likely to experience a better education atmosphere, while those who used to lag behind at middle school tend to suffer from worse classroom environments. All in all, tracking effect in South Korea might be based on fierce competition or better educational atmosphere, not changes related to teachers. 37 2.7.5 Direct Peer Effects on Possible Mechanisms As a robustness check, we investigate direct peer effects on possible mechanisms explored in the previous section. We estimate, for a student i at time t, Y it = β 1 Peer it +β 2 High t +μ i +ε it , where Peer it is the mean of peer rank 38 evaluated at middle school, excluding oneself in the school that one attends, and High t takes on value one if a student was surveyed in high school and zero otherwise. As it includes the individual fixed effect, this reveals direct effects of how peers are composed of on study hours and on other school characteristics. Table 2.11 shows the higher the prior rank of the peers are, the more they study and the better class atmosphere is created, although all estimates, except column (4), are not statistically significant at 10 percent. The positive signs of all coefficients are consistent with what we find earlier. This reinforces the claim that increased study hours and better class atmosphere could be a plausible mechanism for determining students’ academic outcomes. 37 Our finding is consistent with Booij et al. (2017) in the sense that, unlike Duflo et al. (2011), that teachers at the University of Amsterdam do not respond significantly to composition of their student bodies. 38 We define the rank in the way that a higher percentage represents a better performance. It implies that the 100 percentile rank means the highest, while zero means the lowsest. 36 2.8 Conclusion Despitethewidespreaduseofacross-schooltrackingintheworldevidenceonits effect has been scarce relative to within-school tracking. In this paper, we provide the new evidence on the effects of across-school tracking, using the two cases of the EP in South Korea. Our difference-in-difference design in the first case shows that the transition from the tracking to the mixing system causes students to be less likely to advance to college. It hurts the top-ranked college enrollments more than the four-year college enrollments. In our second case in which we use the college entrance test score, we find that the EP causes the score distribution to be more bell-shaped. More students are distributed around the mean, while fewer students are distributed at both tails under the mixing system. We also provide evidence on the behavioral changes caused by across-school tracking. Students in the top half exert more effort and benefit from a desirable classroom atmosphere under the tracking system, while students in the bottom half reduce hours of self-studying. This might cause educational inequality between the high and the low types to be exacerbated and persistent (Gamoran and Mare (1989), Benabou (1993), Benabou (1996)). Our results bring up the discussion that whether or not ability-tracking con- tributes to increasing aggregate human capital. This is in line with what deter- mines aggregate human capital (Mulligan and Sala-i Martin (1997), Mulligan and Sala-i Martin (2000)). 39 Our empirical findings show that the tracking system causes educational inequality and stratification within a city to the extent that it produces more top-performing students and more students who lag behind. If an 39 Mulligan and Sala-i Martin (1997) propose the ratio of total labor income per capita to the wage of a person who is not educated at all as a sensible measure of aggregate human capital. 37 average wage (or educational attainment) level represented aggregate human cap- ital, the mixing system would be superior. If the number of the most productive people played a pivotal role, aggregate human capital would be higher under the tracking system. In order to provide the insight into human capital accumulation, we conduct a back-of-the-envelop calculation. We plot the relationship between the college entrance test score in 2004 and hourly wages 10 years later in figure 2.12. 40 It shows that higher test score is positively associated with higher hourly wage in the future. This relationship is an increasing convex curve. This implies that one city in which everyone attains the mean score makes less total income than the other city in which the academic performance is dispersed. In other words, given a society composed of two people, the combination of a genius and a fool can be superior to two normally-educated people. This argument is based on the strong assumption that the hourly wage reflects the true human capital or person’s productivity correctly. However, this back-of-the-envelop analysis pro- vides the insight that tracking can be justified on the efficiency grounds in some circumstances, although it is often at odds with educational equity. 40 We use a sample of students who were in grade 12 (final grade in high school) in 2004 using Korean Education and Employment Panel. 38 Figure 2.1: Enrollments in Seoul National University (SNU) Note: High school graduates in Gyeonggi Province and in Ulsan have been affected by the equalization policy since 2005 and 2003, respectively. 39 Figure 2.2: Research Design: Two Cases 40 Figure 2.3: Treated and Controls Region (a) GOMS: Gyeonggi Province (b) CSAT: Ulsan 41 Figure 2.4: Evidence on Equalization Policy: Variance of the Number of Top Students (a) GOMS: Gyeonggi Province (b) CSAT: Ulsan Note: Top students are defined as those who are admitted to Seoul National University 42 Table 2.1: Summary Statistics: GOMS Variable Whole Sample Controls Treated P-Value (A = B) Before (B) After (A) Outcome Variables Top 8 0.087 0.084 0.119 0.07 0.00*** (0.281) (0.278) (0.323) (0.255) Top 15 0.158 0.154 0.205 0.143 0.00*** (0.365) (0.361) (0.404) (0.35) College in Seoul 0.334 0.335 0.383 0.272 0.00*** (0.472) (0.472) (0.486) (0.445) 4-Year College 0.703 0.698 0.799 0.635 0.00*** (0.457) (0.459) (0.401) (0.482) Independent Variables Female (= 1) 0.494 0.496 0.36 0.633 0.00*** (0.5) (0.5) (0.48) (0.482) Mother, College Degree (=1) 0.175 0.17 0.188 0.198 0.3188 (0.38) (0.376) (0.39) (0.398) Mother, Graduate Degree (=1) 0.022 0.021 0.028 0.028 0.9704 (0.148) (0.143) (0.165) (0.165) Father, College Degree (=1) 0.267 0.259 0.294 0.298 0.7502 (0.442) (0.438) (0.456) (0.457) Father, Graduate Degree (=1) 0.079 0.079 0.084 0.077 0.3133 (0.27) (0.269) (0.278) 0.267 Parents’ Monthly Income (U.S.$) None 0.011 0.011 0.011 0.009 0.3929 (0.105) (0.106) (0.104) (0.093) 0 - 999 0.016 0.016 0.015 0.015 0.9184 (0.124) (0.125) (0.121) (0.123) 1,000-1,999 0.099 0.101 0.083 0.098 0.05* (0.299) (0.302) (0.276) (0.297) 2,000-2,999 0.22 0.224 0.217 0.188 0.0067*** (0.414) (0.417) (0.412) (0.391) 3,000-3,999 0.245 0.242 0.253 0.266 0.2680 (0.43) (0.428) (0.435) (0.442) 4,000-4,999 0.178 0.178 0.182 0.178 0.6606 (0.383) (0.383) (0.386) (0.382) 5,000-6,999 0.129 0.126 0.13 0.147 0.0602* (0.335) (0.332) (0.337) (0.354) 7,000-9,999 0.057 0.056 0.063 0.059 0.5809 (0.232) (0.23) (0.242) (0.236) Above 10,000 0.045 0.045 0.047 0.041 0.2596 (0.207) (0.207) (0.211) (0.197) Observations 29,142 23,086 3,162 2,894 43 Table 2.2: Summary Statistics: CSAT Variable Whole Sample Controls Treated P-value (A = B) Before (B) After (A) Total Score 47.894 47.83 47.366 49.747 0.00*** (25.51) (25.558) (26.728) (23.226) Korean 48.091 48.04 47.477 49.722 0.00*** (28.222) (28.258) (28.96) (26.709) Math 48.575 48.441 48.026 52.121 0.00*** (27.998) (27.987) (29.237) (26.825) English 47.678 47.661 46.675 48.931 0.00*** (28.098) (28.175) (28.486) (25.937) Female (= 1) 0.48 0.48 0.475 0.477 0.8022 (0.5) (0.5) (0.499) (0.499) Observations 1,105,705 1,018,790 40,129 46,786 44 Figure 2.5: Kernel Distribution of Test Score: Whole Sample 45 Figure 2.6: Kernel Distribution of Test Score: Treatment Group 46 Figure 2.7: Pre-Trend Analysis: Lowess Graph, GOMS 47 Figure 2.8: Pre-Trend Analysis: Regression Analysis, GOMS Note: In each graph, dots are point estimates, and lines represent confidence interval at 90 percent 48 Figure 2.9: Pre-Trend Analysis: Lowess Graph, CSAT 49 Figure 2.10: Pre-Trend Analysis: Regression Analysis, CSAT Note: In each graph, dots are point estimates, and lines represent confidence interval at 90 percent. 50 Table 2.3: Mixing Effects of Mixing on College Enrollments: GOMS (1) (2) (3) (4) VARIABLES Top 8 Top 15 In Seoul 4-year College Treat× Post -0.0159*** -0.0193** -0.0232*** -0.0310*** (Mixing Effect) (0.0056) (0.0086) (0.0087) (0.0090) Female (=1) 0.0150*** 0.1240*** 0.3095*** 0.3819*** (0.0052) (0.0068) (0.0110) (0.0089) Mother, College Degree (=1) 0.0459*** 0.0669*** 0.0655*** 0.0285*** (0.0068) (0.0087) (0.0093) (0.0063) Mother, Graduate Degree (=1) 0.0751*** 0.0915*** 0.0493** 0.0275* (0.0248) (0.0185) (0.0218) (0.0139) Father, College Degree (=1) 0.0467*** 0.0715*** 0.0886*** 0.0842*** (0.0045) (0.0052) (0.0074) (0.0070) Father, Graduate Degree (=1) 0.0753*** 0.1119*** 0.1459*** 0.1227*** (0.0092) (0.0116) (0.0131) (0.0090) Mean 0.0867 0.1584 0.3334 0.7025 Observations 27,621 27,621 27,621 27,621 R-squared 0.0662 0.1223 0.2215 0.3966 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at the district level. Controls include parents’ income when respondents were in high school 51 Table 2.4: Mixing Effects of Mixing on TOEIC Scores: GOMS (1) (2) (3) (4) VARIABLES RAW Scores Above 700 Above 780 Above 900 Treat× Post -4.7164 -0.0285* -0.0015 0.0049 (Mixing Effect) (5.5813) (0.0163) (0.0146) (0.0114) Sex 71.3920*** 0.1636*** 0.2129*** 0.0951*** (4.5038) (0.0126) (0.0140) (0.0096) Mother, College Degree (=1) 20.3836*** 0.0335*** 0.0724*** 0.0673*** (3.7727) (0.0102) (0.0135) (0.0141) Mother, Graduate Degree (=1) 29.3465*** 0.0583*** 0.1176*** 0.0868*** (8.4988) (0.0219) (0.0244) (0.0238) Father, College Degree (=1) 32.7445*** 0.0949*** 0.0870*** 0.0393*** (4.0116) (0.0109) (0.0130) (0.0114) Father, Graduate Degree (=1) 32.6858*** 0.0795*** 0.0931*** 0.0737*** (5.2716) (0.0142) (0.0177) (0.0168) Observations 9,224 9,224 9,224 9,224 R-squared 0.1903 0.1360 0.1497 0.0991 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at the district level. Controls include parents’ income when respondents were in high school 52 Table 2.5: Mixing Effects on College Enrollment Test Total Scores: CSAT hline (1) (2) (3) (4) (5) (6) (7) VARIABLES Top 5% Top 10% Top 25% Bottom 25% Bottom 10% Bottom 5% Test Score Treat× Post -0.0021*** -0.0048** -0.0077 -0.0727*** -0.0390*** -0.0117*** 2.3158*** (Mixing Effect) (0.0004) (0.0012) (0.0050) (0.0099) (0.0053) (0.0018) (0.3709) Female (=1) -0.0020** -0.0010 0.0203*** -0.0654*** -0.0397*** -0.0172*** 3.9661*** (0.0006) (0.0016) (0.0041) (0.0058) (0.0071) (0.0036) (0.0834) Observations 1,105,705 1,105,705 1,105,705 1,105,705 1,105,705 1,105,705 1,105,705 R-squared 0.0008 0.0013 0.0043 0.0166 0.0117 0.0057 0.0165 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at the district level. 53 Table 2.6: Mixing Effects on College Enrollment Test Subject Scores: CSAT (1) (2) (3) (4) (5) (6) (7) VARIABLES Top 5% Top 10% Top 25% Bottom 25% Bottom 10% Bottom 5% Test Score Korean Treat× Post -0.0016 -0.0019 0.0029 -0.0547*** -0.0442*** -0.0281*** 2.2425*** (Mixing Effect) (0.0012) (0.0020) (0.0032) (0.0076) (0.0068) (0.0042) (0.3628) Female (=1) 0.0093*** 0.0197*** 0.0512*** -0.0823*** -0.0522*** -0.0342*** 5.9898*** (0.0013) (0.0024) (0.0038) (0.0050) (0.0068) (0.0054) (0.1911) Math Treat× Post -0.0049** -0.0066** -0.0020 -0.0542*** -0.0381*** -0.0232*** 2.5639*** (Mixing Effect) (0.0013) (0.0023) (0.0040) (0.0071) (0.0041) (0.0027) (0.3494) Female (=1) -0.0138*** -0.0209*** -0.0171*** -0.0479*** -0.0283*** -0.0166*** 1.4273*** (0.0006) (0.0004) (0.0008) (0.0050) (0.0043) (0.0029) (0.1966) English Treat× Post 0.0007 0.0006 0.0014 -0.0579*** -0.0450*** -0.0258*** 2.3524*** (Mixing Effect) (0.0010) (0.0028) (0.0067) (0.0086) (0.0068) (0.0040) (0.4443) Female (=1) 0.0045* 0.0092* 0.0325*** -0.0708*** -0.0455*** -0.0277*** 4.6636*** (0.0021) (0.0037) (0.0065) (0.0034) (0.0050) (0.0036) (0.2050) Observations 1,105,705 1,105,705 1,105,705 1,105,705 1,105,705 1,105,705 1,103,346 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at the district level. 54 Figure 2.11: Relationship Between Student’s Own Rank and Peers’ Rank Note: This is constructed, using KEEP data. The average rank on the vertical axis in each graph represents an average of rank of peers, excluding oneself, in a reference group. All ranks mean how well students study in middle school. 55 Table 2.7: Tracking Effects on Study Hours (1) (2) (3) (4) VARIABLES ≤ 2 hours ≥ 15 hours ≥ 20 hours ≥ 20 hours Treat× High 0.0405 -0.1006 -0.1031** 0.1080* (Tracking effect) (0.1012) (0.0631) (0.0439) (0.0596) Treat× High× Above half -0.0331 0.1105 0.1511*** (0.1272) (0.0727) (0.0441) Treat× High× 25∼ 50% -0.1162** (0.0528) Treat× High× 50∼ 75% -0.2235*** (0.0628) Treat× High× 75∼ 100% -0.1878* (0.1029) Observations 2,271 2,271 2,271 2,271 R-squared 0.6062 0.5338 0.5345 0.5367 Notes: ***p<0.01,**p<0.05,*p<0.1. Robuststandarderrorsinparentheses. The standard errors are clustered at the district level. Table 2.8: The Low Types Overestimate Themselves Under Tracking (1) (2) (3) VARIABLES Korean Math English Treat× High 0.1201 0.1253** 0.1150** (Tracking effect) (0.0721) (0.0519) (0.0483) Treat× High× Above half -0.1226* -0.1228*** -0.1271** (0.0613) (0.0422) (0.0503) Observations 2,274 2,274 2,273 R-squared 0.6522 0.7000 0.6736 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at the district level. 56 Table 2.9: Tracking Effects on Teacher-Pupil Interaction Students ( ) a teacher Teachers ( ) a student (1) (2) (3) (4) VARIABLES Respect Like Get Interested in Understand Treat× High -0.0365 -0.1197 0.0786 -0.0447 (Tracking effect) (0.0860) (0.0772) (0.0602) (0.1078) Treat× High× Above half -0.0283 0.0536 -0.1205 0.0289 (0.0817) (0.0616) (0.0972) (0.0823) Observations 2,134 2,134 2,134 2,132 R-squared 0.5854 0.6157 0.5918 0.5998 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at the district level. 57 Table 2.10: Tracking Effects on Teacher’s Quality and Class Atmosphere (1) (2) (3) (4) (5) (6) VARIABLES M.A. Degree Experience Subject Experience Teacher’s Ability Teacher-Pupil Closeness Class Atmosphere Treat× High -0.0192 -0.0731 -0.0241 -0.0243 -0.2531** -0.0976 (Tracking effect) (0.0853) (0.1196) (0.0784) (0.1101) (0.1022) (0.1272) Treat× High× Above half -0.0498 -0.0175 0.0526* -0.0678 0.0704 0.1645** (0.0665) (0.0616) (0.0281) (0.0737) (0.0631) (0.0741) Above half 0.0140 0.0591 -0.0029 0.0176 0.0111 0.0241 (0.0224) (0.0461) (0.0232) (0.0108) (0.0123) (0.0212) Observations 1,722 1,719 1,675 2,061 2,068 2,068 R-squared 0.0747 0.1984 0.1780 0.2486 0.2003 0.1973 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at the district level. 58 Table 2.11: Direct Peer Effects on Possible Mechanism (1) (2) (3) (4) VARIABLES Study Hours Study Hours Teacher-Pupil Class ≥ 15 hours ≥ 20 hours Closeness Atmosphere Direct Peer Effect 0.0024 0.0019 0.0014 0.0072*** (0.0019) (0.0016) (0.0018) (0.0026) Mean of Peers’ Rank (%) 59.89 59.89 59.97 59.97 Observations 1,718 1,718 1,617 1,617 R-squared 0.6838 0.6469 0.6275 0.6756 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in paren- theses. The standard errors are clustered at the district level. 59 Figure 2.12: The Total CSAT Score and The Hourly Wage 10 Years Later (a) CSAT Score And Future Wage Are Positively Correlated (b) The Convex Association Note: This is constructed using the Korean Education and Employment Panel data. 60 Chapter 3 Estimating the Gains from New Rail Transit Investment: A Machine Learning Tree Approach 3.1 Introduction Major urban rail transportation projects increase travel speeds in cities and thus facilitate shorter commutes, labor market matching and consumer shopping and leisure opportunities. Housing located close to new transport nodes often increases in value as the demand to live close to fast public transit increases local demand to live there (McMillen and McDonald (2004), Blake (2016), Pivo and Fisher (2011)). Real estate developers will seek to build new housing units close to these new stations. In recent decades, Asia’s major cities have made major investments in new subways (Gonzalez-Navarro and Turner (2016)). Cities ranging from Beijing, to Shanghai to Singapore have invested billions in new subways. In this paper, we study how the real estate market in Seoul has been affected by the construction of a major new subway. The line number 9 (hereafter LINE9) subway connects the Southern part of the city with the Gangnam District. This is one of the richest parts of the city. The opening of new transit stations may increase nearby property values by bothloweringcommutetimesbetweentheoriginanddestinationandbypotentially stimulating new “consumer city” amenities near the new transit stations (Fejarang 61 (1993), Baum-Snow and Kahn (2000)), Hess and Almeida (2007), and Nelson and McCleskey (1990)). On the other hand, Bowes and Ihlanfeldt (2001) suggests that public transit access can have negative local effects if it increases nearby criminal activity. Though a majority of studies have found that property values increase as transit access increases, a few studies find evidence of a price penalty associated with new transit stations. Based on a meta-analysis of 57 studies, Debrezion et al. (2007) concludes that every 250 meters closer to a station is associated with a 2.4% increase in property values. Past research has tested for heterogeneous effects of transit stations Cervero and Duncan (2002) show the effects vary with transit technology. 1 . Duncan (2008) show that based on data from San Diego that the transit premium for multifamily housing is three times larger than that for single-family housing. Few studies have explored the treatment heterogeneity across several dimensions of apartment attributes. Our methodological approach builds on past hedonic studies that use panel estimation strategies to recover estimates of the causal effects of new transit access (Kahn (2007), Billings (2011), Zheng and Kahn (2013), Gibbons and Machin (2005)). A distinguishing feature of our study is to use machine learning to pare downthepossiblenon-linearitiesinthehedonicpricingfunction. Thetypicalhedo- nic analysis includes a large vector of housing attribute control variables. It would be computationally cumbersome to include a full set of interactions between each of these control variables and the treatment indicator. Our solution to this challenge is to use the regression tree approach from machine learning (ML) (e.g., Breiman et al. (1984) and Friedman et al. (2001)). 1 They find regional commuter rail system almost 6 times more increased property values than the city-wide light rail system did in San Jose, California. 62 Past ML research has focused on predicting outcome variables using high- dimensional explanatory variables. A recent literature has used ML methods to estimate causal effects (Zeileis et al. (2008), Beygelzimer and Langford (2009), Su et al. (2009), Foster et al. (2010), Dudík et al. (2011), Imai et al. (2013), Athey and Imbens (2015), and Taddy et al. (2016). Building on Athey and Imbens (2015), we apply ML methods in using a difference-in-difference approach to estimate conditional average treatment effects. This estimation strategy imposes few com- putational burdens. In our tree approach, we create dummy variables indicating whether the treatment has occurred or not and whether the housing unit is in the treatment area (i.e. close to the new transit stations). The ML algorithm splits the sample on these attributes as well as on the physical attributes of the housing unit. This approach allows us to test how housing price appreciation differs for treated units versus control units while allowing these effects to vary by housing unit and community attributes. Based on our ML approach, we document that there is considerable variation in the conditional average treatment effect (CATE) across the apartment types. Some apartments types experience greater price appreciation than others. For example, one “winner" from the treatment is an apartment in the upper 25% of the apartment size distribution featuring 3 rooms, 2 baths that is less than five yearsoldandislocatedwithinonekilometerofoldtransitintheSeochocounty. We discuss the methodological advantages of our approach and also report estimates of the hedonic capitalization effect using a log-linear hedonic model (Redfearn (2009)). Asavalidationtestofourestimates, westudywhetherdevelopersofnewapart- ments are building units with the features that our ML estimates yield the highest marginal revenue. We document a positive correlation between our estimates of 63 the real estate price appreciation gains from train network proximity and the spe- cific type of new housing built by a developer. These findings support our claim that we have recovered key non-linearities of the true underlying pricing gradient and how they change over time. 3.2 Seoul’s New Subway Construction and Project Financing Seoul’s first subway line was built in 1974. Over the last four decades, the subway system expanded to cover five lines. Since 2000, Seoul’s government has built three additional subway lines(lines 6, 7 and 8). The last subway expansion plan is the introduction of LINE9. LINE9 was first designed in 1997. The detailed blueprint was released in 2000, and the ground-breaking construction ceremony took place in 2002. It began its service on July 24th 2009. As of 2014, 39% of trips in Seoul use subways or railways. Figure 3.1 and 3.2 display the early subway network and the LINE9. The total cost of this project was US$818 million 2 . 46.7% percent of the total costs were subsidized by the Seoul metropolitan government, and the METRO9, a privatecompany,coveredtherest. TheMETRO9operatesLINE9forthreedecades without paying any rental fees while the Seoul metropolitan government owns it. The Seoul metropolitan government guarantees a minimum profit level for the first fifteen years of the project. 3 In 2005, the Korea Transport Institute predicted that 243,196 riders per a day in 2014 would use LINE9. However, the actual ridership has been 384,423 riders a day. This prediction stands in contrast to the U.S literature that argues that transit agencies routinely over-state the ridership of 2 The construction costs are based on an exchange rate of 1100won/ US$1. 3 The Seoul metropolitan government promised this private company 90 percent of the expected profits for the first five years, 80 percent for the next five years, and 70 percent for the last five years. 64 a new subway before it is built (Kain (1990)). Such strategic predictions increase the likelihood that the project is funded. 3.2.1 The Demand for Housing Close to Transit Seoul’s residents rely on public transit. In 2014, cars accounted for 22.8% and buses accounted for 27%, while subway and light rail take 39%. The share of trips by taxi is 6.8%.Standard network logic suggests that the value of subway access increases in the set of potential destinations one can reach in a short time. A fast train that connects to a desirable city sub-center should lead to gentrification along its nodes, and transit improvements (McMillen and McDonald (1998),Glaeser and Kahn (2001) and Baum-Snow et al. (2005)). If such a train is fast enough then it could reduce the demand to live very close to the destination because people can decentralize while still having access to the destination area. Glaeser et al. (2008) documents that poor people live close to slow public transit, while rich people are attracted to fast public transit in centralized cities such as Boston and New York City. LINE9 significantly reduces travel times within Seoul. To document this fact, we calculate the travel time between each apartment unit to twenty major des- tinations before and after it is built, based on the average train’s speed of 50 kilometers per hour and a walking speed of 4 kilometers per hour. Table 3.1 presents the one way reduction in travel time (measured in hours) to 20 major destinations in Seoul. 4 For example, across our sample, the average apartment resident experienced a reduction in travel time to Gangnam by roughly 5 minutes 4 The estimated travel time is based on the assumption that travelers walk to the closest subway station and take a subway. 65 each way. Those living within a 1 kilometer radius of new transit enjoyed a 14.4 minute reduction in one way travel time to Gangnam. This is a 35% reduction. While the new train reduces commute times, we do not believe that its effects are large enough to cause important general equilibrium shifts in the entire Seoul housing market. Starting with the work of Sieg et al. (2004) there has been a growing recognition that local public goods improvements can have general equi- librium effects on a given city. They studied how Clean Air Act regulations sharply reduced pollution in major sections of Los Angeles and this caused a reshuffling of the population such that richer people moved to previously poorer polluted areas of the city. A hedonic researcher who ignores this migration effect would likely over-state the role of clean air improvements as the sole cause of real estate price appreciation. In our setting, we believe that such GE effects are a second order concern. As we discuss in the next section, the new train’s treatment area is only a small physical area of Seoul. 3.2.2 The Supply of Housing Close to the New Transit Stations When LINE9 was completed, there were 322 residential apartment complexes within a kilometer of the new transit stations. Since LINE9 opened the owners of these properties began enjoying a capitalization effect that we will estimate below. As we will document in section 5.1, we do not find evidence of a capitalization effect caused by the announcement of the LINE9 construction. A key assumption in our difference-in-difference approach is identifying the treatment date. The plan for LINE9 was announced in the year 2000 but it was only completed years later. In section 5.1, we test and reject the hypothesis that the subway construction plant had an ex-ante capitalization effect. 66 Once the new subway opens, nearby land becomes more valuable in these “treated” areas. Thus, real estate developers have incentives to upgrade existing structures and to build new structures. But, Seoul features stringent construction regulation. It takes an average of 33.3 months to build a new apartment complex (Jeon et al, 2010). Redeveloping existing housing entails overcoming many reg- ulatory obstacles. Each urban housing redevelopment project proposal in Seoul undergoes a nine stage process that includes a strict safety investigation. For the typical redevelopment project completed between the years 2000 and 2015, it took an average of 8.7 years to complete the reconstruction process. Seoul’s regulations also require developers to supply a certain proportion of small apartment types. A U.S literature has studied how regulations limits housing supply (see Glaeser et al. (2005)). While developers face many restrictions in building, they will have a greater incentive to do so if the marginal revenue from building an apartment is higher. The total revenue a developer collects from producing apartments of certain type in a given location is the price per unit multiplied by the units sold. Our ML estimates provide an estimate of the former. If each developer is a price taker, then facing the non-linear hedonic pricing function (their revenue curve) they will have an incentive to supply new housing that offers greater revenue. Below, we will use data on the new housing supply by developers combined with our CATE estimates to study this. 67 3.3 The Empirical Approach 3.3.1 The OLS Model Following Kahn (2007), Billings (2011), Zheng and Kahn (2013) and Gibbons and Machin (2005), we begin by estimating average treatment effects of the LINE9 on apartment prices using a difference-in-difference estimator. For the apartment type i in district j at time t, its price is expressed as follows: Log(Price ijt ) =β 1 Line9 i +β 2 Line9 i ×AFTER t +β 3 X ijt +μ j +λ t +ε ijt , (3.1) where Line9 i is distance between the apartment type i and the closest LINE9 station and AFTER t takes one if time period is after the LINE9 opened, and 0 otherwise. X ijt is a set of the apartment characteristics except proximity to the LINE9, and μ j and λ t are the district fixed effect and the quarter fixed effect, respectively. ε ijt is the error term. To specify the treatment area we split the area with G groups,G ={1,...,G}, based on the distance between the LINE9 station and the apartment. For apart- ment i in district j at time t, its price is expressed as follows: Log(Price ijt ) = G X g=1 α g I{Group i =g} + G X g=1 β g I{Group i =g}×AFTER t +γX ijt +μ j +λ t +ε ijt , (3.2) where Group i is the group dummy of apartment i that takes a value inG = {1,...,G}. In the empirical analysis in Section 5, we consider three groups (G = 3). The first group includes the apartments within 1km of transit stations. The second group includes between 1km and 2km from a transit station, and the third group 68 includes all other apartments. For both econometric specifications, we allow serial correlation in ε ijt within the district of “Dong”. For OLS to yield consistent estimates of the average treatment effects, the unobserved error term ( ij1 ,..., ijT ) must be uncorrelated with the "treatment" variables even after we control for the observed apartment characteristics and the two sets of fixed effects. If β 2 measured the "average" price effect associated with the treatment, the creation of such new subway stations may have several effects on apartments nearby. First, it reduces travel times to destinations. Second, once the new stations open, this may trigger the opening of new restaurants and stores close to the new stations. In this case, the LINE9 causes both a reduction of commute times, say, to Gangnam and an improvement in the quality and quantity of local restaurants and stores. We will return to this point below. We recognize that home prices reflect future expectations of local amenity changes. If home buyers anticipate that the new train would raise future rents, then they may bid more aggressively for houses before the LINE9 opens. In section 5.1 below, we will study trends in real estate prices in the treatment areas and the control areas before the actual opening of the line. We find that there is little evidence of an anticipation effect in the treated areas. 5 3.3.2 The Machine Learning Approach Our Machine Learning approach allows us to disaggregate the average treat- ment effect associated with new transit access along a high dimensional set of 5 Some papers provide empirical evidence that housing prices rise in advance of when new transit lines open (McDonald and Osuji (1995), Knaap et al. (2001), McMillen and McDonald (2004)). However, Gibbons and Machin (2008) argue that the impact of transport improvements are heavily dependent on the economic context, and that if housing is treated as consumption goods rather than as assets, then anticipation effects can be small. 69 observed attributes. For those interested in the economic incidence of public poli- cies, this ML approach provides more precise estimates of which incumbent apart- ment owners are the biggest winners from the city’s public goods investment. We follow the general supervised machine learning approach to grow our regres- sion tree. The detailed algorithm is described in the appendix. We define apart- ments within one kilometer of a LINE9 station as the treatment group, whereas those more than one kilometer away from it are considered to be in the control group. We have chosen this definition based on the OLS results presented in table 3.3. This definition is consistent with the earlier literature (Bartholomew and Ewing (2011)). Another issue to address is a double-treatment effect. As the aver- age of direct distance between the LINE9 stations is 1.1km, some apartments have two new stations within 1km. Using our methods, we cannot address this double treatment effect. In our analysis, we treats these data points as in the treatment group but do not attempt to estimate a separate treatment effect for this subset. According to Athey and Imbens (2015), our approach represents a single tree model because the treatment dummy, the time dummy and all covariates are included in the single tree. We can extend our approach to the two tree model or the four tree model, based on how splitting variables are included when the tree grows. If the post-treatment effects and the pre-treatment effects are estimated separately from two different trees with sub-sample of T = 1 and T = 0, respec- tively, then it is referred to as the two tree model. In implementing our machine learning approach, the main assumption we are making is that both the treated and controls would follow a similar trajectory in the absence of the intervention. We discuss pre-trends below to address the issue. We recognize that the LINE9’s geographic placement was not randomly deter- mined. Thus, we are conducting a conditional analysis. Given the new transit 70 stations that were built how has it affected real estate pricing? This approach is relevant for an ex-post evaluation of who are the winners and losers of this invest- ment. Our approach cannot be used to predict what will be the future impact of a new Seoul subway in another location. 3.4 Data In this section, we describe the data and the summary statistics. 3.4.1 Apartment Data We use apartment price data provided by the Ministry of Strategy and Finance of South Korea. This covers more than 90% of entire apartments in South Korea since 2000 and contains a rich set of apartment characteristics, including size, the number of rooms and bath and parking spaces. Since our goal is to investigate the effects of LINE9 on apartment prices, we restrict our sample to the locations where LINE9 passes. In figures 3.1 and 3.2, the light green area represents our districtsofinterest. Thesedatarestrictionsresultinoursamplethatincludes1,102 apartmentcomplexesand4,161apartmenttypes. Marketpricesaresurveyedbased on an apartment type rather than at the apartment unit. This means that the price data represents the average price of all apartment types that share the same characteristics within the same complex. For example, 84 square meter apartment units with two beds and a bath within the same complex are considered to be the same product and thus have an identical price in our data. 6 Our data has a 6 We are interested in the value of a certain apartment type, not individual apartments. An apartment complex has a limited number of apartment types. Under a certain apartment type, there are many homogeneous units. For example, an apartment complex has 600 units, but they can be categorized into four different types, meaning that each type has 150 units on average. We cannot observe transaction prices of individual units but we observe an appraisal of the type. The appraisal process uses each property’s arms-length transaction sale price and then an 71 panel structure such that the price for each apartment type has been surveyed on a weekly basis. We use the quarterly average price for our analysis. As shown in Table 3.2, the average apartment has three beds and 1.7 baths, and it is as old as 8.2 years. 3.4.2 Geographic Information Data Geographical information data are obtained from the Seoul Metropolitan Gov- ernment. It provides administrative borders, locations of bus stops and hospital, and all subway systems including LINE9. Figure 3.2 shows the locations of LINE9 subway stations. Using ArcGIS, we measure the distance between center of each apartment complex and the closest LINE9 station. This is a key variable in our analysis. Our control group consists of apartments more than one kilometer away from the new transit. 7 As shown in table 3.2, the mean distance between an apartment and the closest LINE9 station is 1.92 kilometers, and each apartment has other subway station, excluding LINE9, within 0.7 kilometers on average. Our sample of apartments consists of those in districts where the LINE9 passes through. Roughly 42.4% of Seoul residents lived in apartments in 2014. Apartments in Seoul are organized into complexes. The “complex” is composed of several apart- ment buildings. In our sample, each “complex” features an average of 5.5 apart- ment buildings. Each apartment building contains many apartment units where households reside in. All “apartment units” can be classified into a few number averaging takes place. Though our price data has some measurement error due to this process, this is classical error. 7 In order to control for the direct impact of buses and hospitals on apartment price from benefits from the new subway, we also construct one kilometer buffers for each apartment to count the number of bus stops and hospitals within 1km. These are utilized as controls along with the apartment characteristics. 72 of “apartment type” that share the same apartment characteristics e.g. size, the number of rooms and baths to name but a few. Within the same “apartment type”, it is reasonable to assume that apartment units are homogenous. Table 3.2 shows that each complex has 435 “apartment units” in our sample, meaning that each “apartment building” contains more than 80 “apartment units’". The Seoul housing stock is quite young. The average age of a Seoul apartment in our data is eight years. It is worth noting that the supply of apartments in Seoul has been expanding since the mid 1970s. The city’s growing population and rapid economic development since the 1970s catalyzed the need for high-density residen- tial structures. The development plan for Gangnam caused a massive apartment supply increase in the 1980s. Our data shows that the oldest apartment building is 46 years old, but a large fraction of apartments were built between 1997 and 2007. 3.5 Results 3.5.1 The Pre-Treatment Trend In conducting a difference in difference study it is important to demonstrate that the pre-trends for the treatment and control groups are not statistically differ- ent. In Figure 3.3, we define the treatment group as the set of apartments within 1 kilometer of LINE9 transit station and the control group is the set of those apart- ments located more than 2 kilometers away. In figure 3.4, the treatment group we further refine this set to represent the apartments located within 1/2 of a kilometer of the closest LIEN9 station while the controls are the same as in figure 3.3. These figures are based on apartments located in districts where LINE9 passes through. Both figure 3.3 and figure 3.4 show that the pre-trends are parallel, which implies 73 that both the treated and the controls would have followed the similar path in the absence of the intervention. Figure 3.5 shows that the gap between the treated and controls has been decreasing significantly after LINE9 opened. Each bar in figure 3.5 represents the coefficient for interaction between the dummy of within 1 kilometer and the estimated year dummy along with a 90 percent confidence interval. 8 This shows when LINE9 started affecting apartment prices, and the new transit station effects becomes statistically significant at 10% after 2009 when LINE9 opened. This implies that the treated and the untreated had experienced a similar path prior to LINE9, meaning that they would have fol- lowed the same trajectory in the absence of LINE9 even though detailed blueprint was announced at the early period. Our pre-trend analysis indicates that the dif- ference in difference approach is suitable for estimating the impact of LINE9 on apartment prices. 3.5.2 OLS Results Our first set of results builds on earlier work studying the consequences of Seoul’s investment in transit infrastructure (see Kim et al. (2005), Cervero and Kang (2011), Bae et al. (2003), Agostini and Palmucci (2008) and Ahlfeldt (2013)). Table 3.3 reports results from a linear hedonic pricing regression. Controlling for structure attributes, the double difference approach indicates that an extra kilometer reduction in the distance from the LINE9 station is associated with a 1.7% increase in the home’s price. We further explore these results by includ- ing distance to transit dummies. All else equal, properties within 1 kilometer of 8 We estimate Log(Price ijt ) = β 1 Within1km i + P 2015 Y=2000 β Y Within1km i × YEAR Y + β 3 X ijt +μ j +λ t +ε ijt where Within1km i takes one if an apartment type i has the new station within 1km, and zero otherwise. YEAR Y is a year dummy and X ijt is a set of apartment type i’s characteristics in district j at time t. μ j and λ t are a district fixed effect and a quarter fixed effect, respectively. 74 the transit experience a 4% price appreciation compared to those more than two kilometers away from transit (see column 3). Column 4 documents that there is heterogeneity in the treatment effects across apartments’ size and age. The larger an apartment is, the smaller the price premium is. Old apartments benefited less from the LINE9 than new ones did. Totestwhetherornotananticipationeffectconfoundourestimates, wepresent rentregressionsusingthesameparametricspecification. Theseresultsarereported in the appendix. If there is an anticipation effect or if speculative demand played a major role in determining the LINE9’s price appreciation, then housing prices would have experienced a larger increase than rents. Equilibrium rents are less subject to an anticipation effect. However, the rent results are qualitatively either quite similar to or larger than our results from the house price regressions. This suggests that the anticipation effect is limited. 3.5.3 The Machine Learning Results The ML approach yields 142 estimates of the treatment effect. 9 In figure 3.6, we present a histogram of these estimates. With standard errors calculated by the bootstrap, all estimates are reported in appendix. Table 3.4 shows the top-tier or the low-tier leafs. For example, 17.8% of the apartment types in the top 10% leafs are smaller than the 25% quartile, while 21.3% are larger than the 75% quartile. Based on our estimates, we find that 89 are positive and 53 are negative. One way to interpret the results is that the demand for a certain apartment type is low. One explanation for the negative treatment effects is suburbanization. Negative 9 We present the regression tree constructed by our data in appendix. First, the entire sample is split into two sub-samples based on its size. Then one sample is divided by its size again, while the other sample is split by whether or not it is located in Gangnam. Our algorithm keeps splitting the samples based on apartment attributes until it reaches the terminal condition described above. 75 leafs are associated with many apartments in Gangnam (CBD) which suggests that some residents are willing to pay less for this desirable location when they can more easily access it from other locations. The new fast subway encourages center city residents to decentralize (Baum-Snow (2007)). Negative externalities caused by, in part, increased noise (Diao et al. (2016)) or higher crime (Bowes and Ihlanfeldt (2001)) might be another mechanism. As shown in table 3.5, most apartment types featuring a low CATE (the Bottom 10% or Bottom 25%) have other subway transit stations within one kilometer. This finding suggests that there are diminishing marginal returns to access to the quantity of transit lines. A transit hubbing hypothesis would posit that such multi-nodal points would be even more valuable. Comparing column 4 in table 3.3 with table 3.4, we document the differences in the estimated treatment effects between the OLS model and the ML model. Table 3.3 implies that small apartment benefit more from LINE9, but table 3.4 shows that the low CATE groups are characterized by small apartments. In addition, the linear hedonic model’s estimates of the treatment effect do not statistically vary across distances to other existing subway station. Our ML model shows most apartments in the low CATE group have another transit station within one kilometer. The OLS model indicates new apartments experience greater price premium, but a distinct linear association between apartment age and treatment effect is not observed in the ML model. 3.5.4 Developer Responses to the Shifting Real Estate Price Gradient If we have recovered the true underlying gradient, then the non-linear pricing function sketches out the developer’s revenue function for producing different new housing units. Assuming smooth cost functions with respect to apartment size, 76 if developers can earn a large marginal revenue for bundling certain features then they have a profit incentive to build these in. To be specific, developer i supplies apartment type j to maximize the following profit function. max j∈J Π ij =π ij + ij π ij =R ij −C ij (L,P,B) B =B(size) (3.3) where R ij represents revenue of apartment type j and C ij is a cost function of constructing apartment type j. L indicates required amounts of land, and P is costs related to attaining permits. B denotes building costs that hinge mainly on size, and ij is a random component. The probability that developer i supplies apartment type j is Pr{Y i =j} =Pr{max(Π i1 ,..., Π iJ ) = Π ij } (3.4) where Y i indicates an apartment type chosen by developer i. If ij is independent and identically distributed with Gumbel (type 1 extreme value) distributions 10 , then the probability that type j is chosen by developer i is as follows (McFadden et al. (1973)). Pr{Y i =j} = exp(π ij ) P J j=1 exp(π ij ) (3.5) We do not have any cost of construction data, but our ML estimates provide infor- mation on the shape of the revenue function. We test whether new construction is positively correlates with our estimates of the revenue function. Potential buyers are more willing to pay for more attractive apartment types. Our CATE estimates 10 Its cumulative density function is F( ij ) =exp(−exp(−ij)) 77 provide a proxy for the revenue a developer will receive from selling a given type of apartment. This suggests that the flow of new construction’s attributes should be positively correlated with our CATE estimates. We study this by constructing three histograms in figure 3.7. These histograms are based on properties built at three points in time; before 2002, between 2002 and 2009, and after 2009. These three stages can be thought of as the before, middle period and after the construction of LINE9. The histograms display the share of all housing units as a function of each of their respective CATEs. We find that units built before 2002 (when developers at that time were unaware of what the future treatment effects of LINE9 would be) build housing units that are symmetrically distributed around zero. In the post-period, the new units built feature positive CATE estimates. We interpret this as evidence that developers are focusing their efforts on constructing what the market signals is scarce and valued. In addition, we estimate CATE i = β 0 +β 1 Age i +β 2 Age 2 i +β 3 X i +ε i . Age i represents how old an apartment is in years, and X i is a vector of apartment characteristics. In this analysis, apartments within one kilometer from the LINE9 transit stations are only included. Table 3.5 shows that the CATE and apartment’s age are negatively associated, and that the relationship is not sensitive to model specification. Thisimplies thatrealestatedevelopers respondto the heterogeneous positive demand shock and began providing the apartments offering the greatest return given the non-linear hedonic pricing gradient. 78 3.5.5 Testing Two Explanations for the Price Appreciation Effects In this section, we explore two potential reasons for why transit access is asso- ciated with rising real estate prices. One explanation is reduced travel time to pop- ular destinations and the other is that new “consumer city" retail and restaurants co-agglomerate near the new train stations. 11 We test each of these by augmenting our linear hedonic regression to include additional explanatory variables and then we test if the capitalization of transit effect changes. In table 3.6, we report results where we return to the parametric hedonic speci- fication reported in equation (1). Across the eight regressions reported in table 3.6, we include different combinations of extra control variables to test if the treatment effect shrinks as we control for these variables. We use the distance between each apartment and the LINE9 station in column (1) to (4), and we use the dummy variable that indicates whether an apartment locates within a kilometer from the LINE9 station. We add travel times to 20 key destinations in column (2) and (6), while we control a measure of the new restaurants and the retails co-agglomerated near the new transit lines in column (3) and (7). 12 All controls are included in columns (4) and (8). The first four columns show that the treatment effect does not shrink much as the travel time vector and the the restaurant and retail store count variables are included separately. However, column (4) indicates that the treatment effect shrinks around 20% and becomes no longer statistically different from zero at 10%. This implies that the travel time saving and the creation of a local “consumer city” are the main reasons for the capitalization effect. Columns 11 Transportation innovation causes, in some cases, local amenity development that generates additional price premiums (Tu and Eppli (1999), Dronyk-Trosper (2017), Billings (2015). We cannot test whether this happens in Seoul due to data limitation. 12 We use the count of restaurants and retail establishments and the number of employees in those industries at the “Dong" level. “Dong" is the smallest administrative level. The data is drawn from the Seoul metropolitan government 79 (5) to (8) provides another prospective that reductions in travel time is more influ- ential mechanism behind price appreciation. Apartments within a kilometer from the LINE9 station experience a price premium of 3.36%. Controlling for travel times makes the treatment effect not statistically different from zero at the 10% significance level, while the treatment effect is still statistically significant when we control for the count of retail and restaurants. The findings suggest that the price appreciation is mainly caused by travel time savings rather than by a “consumer city” effect. WealsotakeourpanelCATEestimatesfromtheMLprocedureandwecompare these leaf specific estimates to those obtained when we conduct a “long difference" ML estimation. In this second case, we only keep the data for the first year and the last year of our sample and we rerun the ML estimator. In figure 3.8, we graph the relationship between the long run CATE and the short run CATE. The slope is 0.42. This suggests that the CATE effects shrinks over time. The first possible explanation is that the local “consumer city" effect is small as time passes. Another explanation is that there is a general equilibrium effect as developers build new desirable housing units (as revealed by the CATE responses by developers). As the developers engage in this activity, increase in supply lowers the equilibrium prices. 3.5.6 Estimating the Value of Time We study what is the implied value of time for different Seoul residents if all of the observed capitalization effect is due to time savings. To study this, we first regress the rent for apartment i in district j at time t on each travel time to twenty major destinations presented in table 3.1 with apartment type fixed effect as follows. 80 Rent ijt = 20 X g=1 β g Hours igt +X jt +μ i +λ t +ε ijt (3.6) where Hours igt represents travel time between apartment i and destination g at time t, and X jt includes counts of restaurants and retail shops and the number of employees in those industries in district j at time t. μ i is apartment type fixed effect and λ t is quarter fixed effect. The main reason we use the rent data is to rule out any speculative demand that may affect the property price, and focusing on instant benefits. Though an apartment is not located in the vicinity of the transit station, travel time from the apartment to each destination changed because riders might use a faster route after LINE9 opened. This reveals the correlation between an hour reduction to each destination and rent. We find that tenants are likely to pay US$ 1,454,545 more as one travels to Kangnam(CBD) an hour earlier (Table 3.7, A). Note again that rent is not monthly payments but two-year deposit in advance unlike the U.S. and many countries. Tenants put down deposits at the first day of contract and retrieve them when they move out. No other fee is paid to home owners for renting. This suggests that willingness to pay to be an hour closer to Kangnam is not the amount of deposit per-se, but foregone interest that tenants would earn if they lived in their own apartment. Assuming an interest rate of 2%, the opportunity cost for two years is US$ 29,090(Table 3.7, B), which means tenants that sacrifice US$ 39 everyday (Table 3.7, C). We compare our estimated value of saving an hour in commute time to Gang- nam to the taxi fare in Seoul to cross-validate our estimates. Based on the current taxi fares, riders pay US$ 2,73 for first 2km, even though they travel less than 2km. Beyond2km, riderspayUS$0.09forevery142m. Withanaveragespeedof35.4km in Seoul (The Korea Transport Institute, 2011), the estimated taxi fare to travel 81 for an hour is US$ 24.11, which implies that riders pay US$ 48.22 for a round- trip. Moreover, traveling speed becomes slower during rush hours due to traffic congestion. For commuters to travel 35.4km during rush hours, it costs $29.13 in the morning and $29.84 in the evening, respectively. This back-of-the-envelop calculation implies that a commuter would pay $58.97 for roundtrip, should she travel only by a taxi during rush hour. She would save $19.97 everyday as a net effect by moving to the region where she is able to travel to Gangnam an hour faster. 3.6 Conclusion Over the years 2000 to 2009, US$818 millions were spent to build a new subway in Seoul, South Korea. Such place based investments offer the opportunity to explore how a city’s urban form and real estate pricing are affected by such an investment. This paper has used ML methods to contribute to the urban transit infrastructure effects literature. Our paper implements a difference in difference empirical design. We find that the introduction of the train is associated with apartment price appreciation for certain leafs but actually lowered apartment price growth in other neighborhoods. We posit that the fast train is most likely to reduce prices for apartments in the destination area of Gangnam because people can now decentralize and still access this location by using the fast train. The notable feature of our study is our ability to document significant heterogeneity on observable dimensions. The payoff for urban research from ML methods is the ability to search across a large number of dimensions of heterogeneity at low cost. Such conditional average treatment effects disaggregate the overall average treatment effect that has been the typical object of interest in earlier real estate studies. By estimating the CATEs our work has new 82 implications for estimating the economic incidence of public transit improvement projects. 83 Figure 3.1: Map of Seoul 84 Figure 3.2: LINE9 85 Table 3.1: Travel Time to Major Destination in Seoul Whole Sample Within 1km Destinations Category Traveling Time Traveling Time Difference Traveling Time Traveling Time Difference before LINE9 after LINE9 before LINE9 after LINE9 (Hours) (Hours) (Hours) (Hours) (Hours) (Hours) Kangnam CBD 0.514 0.42 0.094 0.669 0.429 0.24 Yeouido Business 0.459 0.356 0.103 0.499 0.289 0.21 Myungdong Business 0.525 0.468 0.057 0.563 0.46 0.103 Hongik University Entertainment 0.462 0.428 0.034 0.502 0.435 0.067 Express Bus Terminal Bus Terminal 0.507 0.359 0.148 0.65 0.38 0.27 Shinchon Entertainment 0.48 0.432 0.048 0.511 0.435 0.076 Sadang Entertainment 0.674 0.462 0.212 0.71 0.423 0.287 Gimpo Airport Airport 0.911 0.46 0.451 0.928 0.358 0.57 Incheon Airport Airport 1.655 1.606 0.049 1.672 1.594 0.078 Seoul Zoo Entertainment 0.774 0.568 0.206 0.813 0.529 0.284 Gwanghwamun Business 0.517 0.462 0.055 0.558 0.456 0.102 Kungook University Entertainment 0.577 0.543 0.034 0.667 0.561 0.106 Nambu Bus Terminal Bus Terminal 0.511 0.427 0.084 0.67 0.44 0.23 Kangbyun Bus Terminal 0.593 0.544 0.049 0.701 0.557 0.144 Jongro Old CBD 0.536 0.483 0.053 0.578 0.478 0.1 Apgujeong Entertainment 0.534 0.474 0.06 0.654 0.484 0.17 Yeoungdeungpo Train Station 0.422 0.403 0.019 0.472 0.407 0.065 Seoul Train Station Train Station 0.49 0.427 0.063 0.528 0.418 0.11 Dongdaemun Entertainment 0.493 0.466 0.027 0.573 0.485 0.088 Korea University Entertainment 0.622 0.592 0.03 0.705 0.61 0.095 Notes: Estimated traveling time is based on the assumption that travelers walks to the closest subway station and take a subway, with walking speed of 4km/hour and subway running at 50km/hour. 86 Table 3.2: Summary Statistics Variable Mean Std. Dev. N Subway Distance to line9 (km) 1.915 1.244 265600 Distance to closest other line (km) 0.702 0.560 265600 Apt Characteristics Area (m 2 ) 94.976 39.501 265600 Room 3.131 0.959 265344 Bath 1.744 0.507 260381 Age, in Years 8.205 9.946 265600 Parking spaces within Complex 546.053 777.993 265600 Number of Apartment units within Complex 435.59 558.62 265600 Number of Apartment buildings within Complex 5.597 9.057 265600 Bus stops within 1km 62.863 19.662 265600 Hospitals within 1km 2.452 1.772 265600 87 Figure 3.3: The Pre-Treatment Trend: 1km vs 2km (Lowess Graph) Notes: Vertical line represents when LINE9 opened. 88 Figure 3.4: The Pre-Treatment Trend: 0.5km vs 2km (Lowess Graph) Notes: Vertical line represents when LINE9 opened. 89 Figure 3.5: Treatment Effect Estimates Over Time Notes: Each circle indicates the coefficient on the interaction between a "within 1km dummy"and the calendar year. Each bar represents a 90 percent confident interval. 90 Table 3.3: OLS Estimates of the Value of Rail Access (1) (2) (3) (4) VARIABLES Log(Price) Log(Price) Log(Price) Log(Price) Distance (km) 0.0339* (0.0193) Distance (km)× AFTER -0.0174** (0.0078) Log(Distance, km) 0.0138 (0.0181) Log(Distance, km)× AFTER -0.0246** (0.0103) Within 1km -0.0785** -0.0641** (0.0367) (0.0254) Between 1∼ 2km -0.0253 (0.0400) Within 1km× AFTER 0.0392* (0.0205) Between 1∼ 2km× AFTER 0.0224 (0.0214) Within 1km× AFTER 0.4073*** (0.0970) Within 1km× AFTER× Size (m 2 ) (1) -0.0017** (0.0006) Within 1km× AFTER× Other Line (km) (2) 0.0092 (0.0101) Within 1km× AFTER× Room (3) -0.0178 (0.0285) Within 1km× AFTER× Bath (4) -0.0269 (0.0233) Within 1km× AFTER× Age (5) -0.0117** (0.0051) Within 1km× AFTER× Age 2 (6) 0.0001 (0.0001) Joint F-value (1)∼ (6) 11.19 (P-value) (0.000) Observations 201,985 201,985 201,985 201,985 R-squared 0.9079 0.9076 0.9078 0.9102 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at the district(“Dong”) level. Controls include size, the number of room and bath, parking spaces, age, age squared, distance to other closest station, the number of bus stops within 1km, the number of hospitals within 1km, whether it has named brand, the number of households within complex and the number of apartment building within complex. District fixed effect and quarter fixed effect are included 91 Figure 3.6: The CATE Distribution 92 Table 3.4: Apartment Characteristics in Each CATE Group Variables Top 10% Top 25% Bottom 10% Bottom 25% (CATE) (CATE) (CATE) (CATE) Apartment Characteristics Size (m 2 ) 0∼ 66.24 (=1) 0.178 0.154 0.343 0.347 66.24∼ 84.88 (=1) 0.323 0.216 0.137 0.214 84.88∼ 114.93 (=1) 0.286 0.345 0.260 0.236 114.93∼ 301.45 (=1) 0.213 0.286 0.260 0.203 Room (Number) 3.132 3.175 3.288 3.225 Bath (Number) 1.80 1.822 1.671 1.700 Apartment’s Age Less than 5 yrs (=1) 0.273 0.269 0.387 0.274 Between 5∼ 10 yrs (=1) 0.662 0.611 0.208 0.275 More than 10 yrs (=1) 0.065 0.120 0.405 0.451 Another Nearby Station (=1) 0.555 0.76 0.893 0.982 (Within 1km) District Yeongdeungpo 0.065 0.093 0.120 0.162 Dongjak 0 0.063 0.225 0.177 Gangnam 0.086 0.160 0.368 0.276 Gangseo 0.470 0.302 0.135 0.166 Seocho 0.291 0.337 0.046 0.096 Yangcheon 0.088 0.045 0.107 0.123 The Average of CATE 0.08 Number of types with positive impacts 89 Number of types with negative impacts 53 Observations 201,530 93 Figure 3.7: The Empirical Distribution of New Construction as a Function of the CATE (a) Before 2002 (b) Between 2002 and 2009 (c) After 2009 94 Table 3.5: New Apartment Yields High CATE (1) (2) (3) (4) VARIABLES CATE CATE CATE CATE Age -0.0169** -0.0140** -0.0119* -0.0080 (0.0073) (0.0065) (0.0062) (0.0062) Age 2 0.0004** 0.0003** 0.0003** 0.0002 (0.0001) (0.0001) (0.0001) (0.0001) Other Controls No No Yes Yes District Fixed Effect No Yes No Yes Observations 878 878 878 878 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at the dis- trict(“Dong”) level. Apartments within 1km from the LINE9 sta- tions are only included. Controls include size, the number of room and bath, parking spaces, age, age squared, distance to other clos- est station, the number of bus stops within 1km, the number of hospitals within 1km, whether it has named brand, the number of households within complex and the number of apartment building within complex. 95 Table 3.6: Rail Transit Capitalization: The Role of Travel Time Savings and the Local Consumer City (1) (2) (3) (4) (5) (6) (7) (8) VARIABLES Log(Price) Log(Price) Log(Price) Log(Price) Log(Price) Log(Price) Log(Price) Log(Price) Distance (km) 0.0256 0.0181 0.0251 0.0182 (0.0189) (0.0185) (0.0187) (0.0185) Distance (km)× AFTER -0.0172** -0.0156* -0.0153* -0.0138 (0.0078) (0.0090) (0.0077) (0.0087) Within 1km -0.0478* -0.0328 -0.0447* -0.0314 (0.0244) (0.0253) (0.0244) (0.0254) Within 1km× AFTER 0.0336* 0.0248 0.0284* 0.0225 (0.0173) (0.0256) (0.0166) (0.0256) Travel Times No Yes No Yes No Yes No Yes Retails and Restaurants No No Yes Yes No No Yes Yes Observations 185,745 185,745 180,569 180,569 185,745 185,745 180,569 180,569 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at the district(“Dong”) level. Controls include size, the number of room and bath, parking spaces, age, age squared, distance to other closest station, the number of bus stops within 1km, the number of hospitals within 1km, whether it has named brand, the number of households within complex and the number of apartment building within complex. District fixed effect and quarter fixed effect are included 96 Figure 3.8: Long Difference Result 97 Table 3.7: Estimates of the Value of Time The Estimated Value of an Hour Correlation b/w An hour reduction in travel time to CBD and 2-year rent deposit US$ 1,454,545 (A) Interests for two years (Interest rate 2 %) US$ 29,090 (B = A× 0.02) Daily opportunity costs (2 year = 730 days) US$ 39 (C = B / 730) Estimate Taxi Fare for an Hour Basic Fare (First 2km) US$ 2.73 Approximate Extra Fare US$0.09 per 142m Average Estimated Driving Distance in an Hour (With an average speed of 35.4km/hour, 2011) 35.4km Average Estimated Taxi Fare to go 35.4km US$ 24.11 Traveling Speed in Morning Rush Hours* (8-9 AM) 29.3km/hour Traveling Speed in Evening Rush Hours* (6-8 PM) 28.6km/hour Estimated Taxi Fare to go 35.4km in Morning Rush Hours* US$ 29.13 (= 24.11× 35.4 29.3 ) Estimated Taxi Fare to go 35.4km in Evening Rush Hours* US$ 29.84 (= 24.11× 35.4 28.6 ) * Taxi fare in South Korea is determined by distance as well as traveling time. Due to traffic congestion, we expect taxi fare to be higher during rush hours if a commuter travels the same distance. All numbers are based on back-of-the- envelop calculation. 98 Chapter 4 Is 1+1 more than 2? Joint evaluation of two public programs in Tanzania 4.1 Introduction In-utero and early life investments in health and education have been found to have long run impacts on educational attainments (Almond et al. (2017)). How- ever, notmuchisknownabouthowearlylifeinvestmentsinhealthandineducation interact in determining the education attainment of individuals. We further this discussion - we study the joint impact of a health policy and an education policy in Tanzania on the educational attainments of individual exposed. Cunha and Heckman (2007) propose a theoretical framework that considers the formation of human capital as a dynamic process with the complementarity between investments at different stages of life. They suggest that investments in human capital later in life are likely to be more productive for individuals who receive higher investments in early life than for those who received lower invest- ments in early life. They term this ‘dynamic complementarity’ in the production of human capital. A major empirical challenge in testing the model of dynamic complementarity is the endogeneity of investments at different points in life. As a result, the empirical evidence in favor of this model of complementarity is limited. A small number of studies that evaluate the joint causal impacts of two public 99 programs or shocks affecting individuals at different stages in their lives fail to find any evidence in favor of ‘dynamic complementarity’ (Adhvaryu et al. (2015); Maya and Miriam (2016); Gunnsteinsson et al. (2016); Malamud et al. (2016)). How- ever, as we discuss in detail ahead, it mostly due to their data or methodological limitations. We use information from Kagera Health and Development Survey (KHDS) to examine the joint effects of two public programs, the Iodine Supplementation Program (ISP) and the Primary Education Development Program (PEDP), on the grade attainment of children who were 10 to 13 year old at the time of the survey. We find that exposure to ISP, a health policy that targeted pregnant women and, consequently, their in-utero babies, was negatively associated with completedschoolingofthoseexposed. PEDPabolishedallprimaryschoolfeesand, as expected, had a positive impact on educational attainment. We also find sig- nificant negative interaction effects of ISP and PEDP on educational attainments - individuals who were exposed to both ISP and PEDP had lower educational attainments by the time of the survey than individuals not exposed to either or one of the two programs. We show that the the two programs and their interaction have impacts on primary school starting age that mirror their impacts on grade completed by 2004. ISP exposure is associated with a delay in primary school starting age. PEDP had a negative effect on starting age. The interaction of the two programs is positively correlated with starting age. The association of the two programs and their interaction with educational attainments almost vanish when we control for primary school starting age. Individuals who delay entering school spend more time working on the family farm and doing household chores. 100 This suggests that delayed entry is more likely due to positive returns from pre- school training (Bommier and Lambert (2000)) and less likely due to malnutrition problems (Glewwe and Jacoby (1995)). Next, the ratio of the impacts of the two programs and their interaction on educational attainment by the time of the survey and on primary school starting age provides us with a measure of the rate at which individuals convert years in school into completed years of schooling. We find that in comparison to individuals exposed to PEDP but not ISP, those exposed to ISP are better at converting years in school into completed years of schooling. This is consistent with Field et al. (2009)claimthatthoseexposedtoISPsawanimprovementintheircognition. This is also an indirect evidence of dynamic complementarity - ISP exposure improves the productivity of each year spent in school. This paper contributes to the literature in two ways. First, we re-evaluate the impactofISPonschoolingattainmentsforindividualsinKageraregionofTanzania andpresentresultsthathelpreconcilethedivergentfindingsoftwopreviousstudies (Field et al. (2009) and Bengtsson et al. (2013)) on the impact of ISP on school- ing. We underline the importance of careful consideration of behavioral responses to ISP exposure to better understand the reduced form impact of ISP. Second, we contribute to the methodological discussion around identifying ‘dynamic comple- mentarity’ by illustrating the need for more cautious interpretation of the reduced magnitudes of the interaction of two exogenous shocks as evidence for or against complementarity. Consequently, we use an alternative strategy to present what we believe is the first piece of evidence in favor of ‘dynamic complementarity’ from developing countries. The remainder of the paper is organized as follows. Section 2 provides a brief background of ISP and PEDP. Section 3 discusses the existing literature. Section 4 101 describes the data and the empirical strategy. Section 5 presents the main results and robustness checks. Section 6 concludes. 4.2 Background 4.2.1 Iodine Supplementation Program (ISP) Lackofpropernutrientinuteroorduringearlylifeisdetrimentaltothephysical and cognitive development of individuals (Barker (1990); Cao et al. (1994); Barker (1995); Barker et al. (2002); Zimmermann et al. (2005)). One such important nutrient is iodine, essential for the synthesis of thyroid hormones. Adequate levels of these thyroid hormones in pregnant mothers are important for physical and mental development of a fetus. Especially, sufficient stock of iodine in a pregnant mother’s body in the first trimester of her pregnancy is extremely crucial for the cognitive development of the baby in-utero. Brain development during this period is sensitive to minor adjustments in thyroid hormone and mild maternal iodine deficiency can impair the full cognitive development of an individual (Dugbartey (1998); Pop et al. (1999)). PeoplefromTanzania, likethosefrommanyAfricancountries, traditionallysuf- fered from high rates of Iodine Deficiency Disorder (IDD). According to a Tanzania nationwide survey of iodine levels in the early 1970s, about 40% of the Tanzanian population lived in iodine deficient areas and 25% of the population was estimated to have had IDD. The prevalence among pregnant and lactating women was as high as 52% (Van der Haar et al.,1988). In response, beginning in 1986, the Tan- zania Food and Nutrition Center (TFNC) started distributing iodized oil capsules (IOC) to individuals in districts where more than 10% of school children had some 102 symptoms of goiter. The program, known as the Iodine Supplementation Pro- gram (ISP), was expanded to 27 districts covering 7.3 million population by 1994 (Peterson et al. (1999)). This program was one of the largest and most intensive iodine supplementation programs in the world (Peterson, 2000). The program was scheduled to begin in 1988 and planned to distribute iodized oil capsules containing 400 mg of iodine amongst males and females aged 2 to 45 years and a dose of 200 mg for children aged 12 to 23 months (Peterson et al. (1999)). However, the time line was not strictly followed. Four districts received the supplementation in 1986 and only 10 had received it by 1988 while two districts did not receive it until 1992. The coverage rate was never perfect in any district and the average coverage rate was 64% (See Table C.1). The delays in the program start date, in all cases, were due to administrative issues arising from the logistical challenges of distributing IOC throughout the district (Peterson, 2000). However, despite the delays, according to a conservative estimate from Peterson et al. (1999), the program protected 12 million individuals from iodine deficiency (ID). Theprogramwasconsideredasuccess, withseveralpreviousevaluationsfinding reductioninvisibleandtotalgoiterrate(VGR,TGR)attributabletoISP(Peterson (2000); Kavishe (2000)). In the early 1990s, a success of ISP led to the Universal Salt Iodization (USI) program initiated by Tanzanian government. After the USI was introduced, ISP was used to complement USI, focusing on districts not yet reached by the USI. Thus, during this period, the absence of the ISP program in a district does not necessarily indicate that the individuals in the district are unprotected from IDD. Fieldetal. (2009)analyzetheimpactofISPongradeattainmentofthechildren of treated pregnant mothers using the Tanzania Household Budget Survey 2000 103 (THBS 2000). They find that ISP had significant positive impact on completed years of schooling of treated children by the time of the survey. They find that treated children, who were still in school at the time of the survey, had completed 0.345 more years of education. This, they conjecture, must have been due to the improvement in cognition of those who received the iodine supplementation. In contrast, using information from the 1999, 2004, and 2010 waves of Demographic and Health Survey, the 2008 wave of National Panel Survey, and the 2000 wave THBS, Bengtsson et al. (2013) find that the estimated impact of ISP on grade attainment is not consistent across datasets and often negative in sign. The impact is positive and significant for only the THBS 2000 sample. They use a slightly different model of iodine depletion over time than the one in Field et. al (2009) and find much smaller magnitudes for the impact of ISP on grade attainments. They explore the robustness of their findings across different definitions of ISP treatment and across different criteria for selecting the sample and find no evidence ofasignificantconsistently. Theyinvestigatetheattenuationbiasthatmightresult from selective migration and incomplete birth information and conclude that these would not explain the differences between their results and that in Field et. al (2009). The main purpose of our study is to document the existence of dynamic com- plementarity in the production of human capital and our evaluation of ISP is not directly comparable to either to these studies. However, our findings help in recon- ciling the apparently contradictory findings from Field et al. (2009) and Bengtsson et al. (2013). 104 4.2.2 Primary Education Development Program (PEDP) Tanzania school system consists of seven years of primary school, four years of secondary school and two years of upper secondary school. There are two national examinations in primary school - one at the end of the 4th and another, primary school leaving exam (PSLE), at the end of the 7th grade (Government Report, 2005). Students need to pass the examination at the end of grade four to progress to grade 5 and the PSLE to advance to secondary school. Children are expected to enroll in primary school at the age of seven and complete primary school by the age of 13 (Ministry of Education and Culture, 1995). However, delays in enrollment, dropouts and grade repetitions are common. In January 2002, Tanzanian government launched the Primary Education Development Program (PEDP) wherein tuition fees and other mandatory cash contributions to schools were abolished (Tanzania Education Report, 2006). The primary purpose of PEDP was to ensure the enrollment of all 7 to12 year olds by 2005. The net enrolment rate in primary school in the year preceding the launch of the Primary Education Development Plan (PEDP) was less than 50%. The program began by targeting those who were seven to eight years old in 2002, indi- viduals born in 1993 or 1994. The coverage of the program was extended to 11 and 12 years old in 2004 (9 and 10 years old in 2002). However, the effort and impact for these children was substantially lower and delayed. As a result, individuals born in 1993 and 1994 were fully exposed to PEDP while those born before 1993 were partially or never exposed to PEDP. Due to PEDP, net enrollment rates went up significantly from 66% in 2001 to 97.3% in 2007. The program worked towards bringing down the cost of primary education by abolishing all tuition fees. Moreover, a $10 capitation grant was also introduced 105 and controlled by school committees. This was intended to cover some of the addi- tional school-based costs. However, substantial indirect costs, such as an expense for instructional materials, remained, the provision of which has not been sufficient to date. 4.2.3 InteractionofISPandPEDPandtheQuestionofDynamicCom- plementarity If the ISP treated individuals indeed had higher cognitive ability than the untreated individuals, this could imply both a higher benefit and a higher oppor- tunity cost of schooling for the treated children. In the light of the possibility, the reduction of schooling cost due to PEDP could potentially have differential impact on the ISP treated and untreated individuals. Since there was a fair degree of overlap between the two programs in terms of the cohorts treated, a careful examination of interaction between these two programs is warranted. Of late, there has been a rising interest in studying interactions between two shocks to human capital formation in developing countries. The primary moti- vation for studying such interactions is to shed light on the production function of human capital in developing countries. In particular, many studies examine if inputs at different points in life into the production of human capital exhibit any complementarity. However, as mentioned before, endogeneity of the level of inputs at different points in life is a major empirical challenge. A small number of studies have employed the ‘lightening strike twice’ (Almond and Mazumder, 2013) iden- tification strategy - exogenous variation in the exposure to two public programs or shocks that affect individuals at different stages in their lives (Adhvaryu et al. (2015); Maya and Miriam (2016); Gunnsteinsson et al. (2016); Malamud et al. (2016)). 106 Adhvaryu et al. (2014) examine the interaction between early life adverse rain- fallconditionsandProgresaconditionalcashtransferinMexico. Theyfindthatthe conditional cash transfer enabled individuals, who were otherwise lagging behind due to adverse rainfall shocks in early life, to catch up. Malamud et al. (2016) estimate the joint effect of access to abortion facilities at the time of conception and access to better school later on. Although they find no significant interac- tion effect, they acknowledge that their results do not count as evidence against dynamic complementarity as behavioral responses by individuals or their parents between first intervention and second intervention could dampen the joint effect. In addition to assuming that the two sources of variations in investments are orthogonal to each other, these studies also assume that an individual’s uptake or compliance or avoidance or mitigation efforts in response to the second shock does not depend on her first program’s treatment status. This second assumption might easily be violated. We use an empirical specification similar to the ones in these studies to study the interactions between the two programs, ISP and PEDP. However, we do not interpret the sign of the interaction as evidence for or against dynamic complementarity. Instead, we use a comparison of the ratio of the impact of ISP and PEDP on completed schooling by 2004 and primary school starting age to shed light on the dynamic complementarity in the production of education. 4.3 Data and Empirical Strategy 4.3.1 Data We use information from the Kagera Health and Development Survey (KHDS), a survey representative of the population of the Kagera region from Tanzania. Located in the northwestern corner of Tanzania, Kagera is one of Tanzania’s 30 107 administrative regions. Kagera is Tanzania’s fifteenth largest region and accounts for more than three percent of the country’s area (CIA (2010)). During 1980s, Kagera suffered from high rates of IDD. As a result, four of its seven districts were targeted by ISP, the first one starting in 1989. Next, the timeline of the KHDS survey waves overlap favorably with the high prevalence of IDD and subsequent high intensity of ISP. KHDS households were originally interviewed in four waves from 1991 to 1994. Follow-up surveys were then carried out in 2004 and 2010. Therefore, it covers the implementation phase of both ISP and PEDP and still allows analysis of short and medium run outcomes like height and educational attainment. KHDS is one of the longest-running African panel data set with an impressive tracking rate of around 90%. (Beegle et al. (2006), De Weerdt et al. (2012)). Due to the overlap between the program and the survey timelines, KHDS is a suitable survey to study the programs and their impact. We use the 1991-1994 and 2004 waves for information on individual’s educational attainments, primary school starting age, parental investments in the child and a variety of covariates. To calculate iodine exposure intensity, we use the district-year coverage rates from Field et al. (2009). We match this coverage rate for each year for each district with the corresponding observation from KHDS using the year and name of the district information contained in KHDS. We follow Field et al. (2009) in their calculation of the probability that an individual benefited from the supple- mentation. An individual’s probability exposure depended on whether and when the iodine supplementation program was implemented in the district of a district vis-à-vis her mother’s first trimester of pregnancy. In that, we make the assump- tion that mothers, through out their pregnancy, lived in the district where they delivered their child. The details about the method followed are provided in the next section. We restrict our sample to the cohorts born between 1991 and 1994. 108 We do not include cohorts born after 1994 because nation-wide iodine supplemen- tation (USI) began in late 1994. In addition, since PEDP (started in 2002) fully affected both 7 years-old and 8 years-old, cohorts born after 1992 were treated by PEDP and those born in 1991 and 1992 were not treated. We do not include the cohorts born before 1991 to avoid more serious recall bias in the 1991-1994 waves and to balance then number of PEDP treatment and control group across cohorts. Consequently, while the variation in ISP treatment is at the level of cohorts and districts, the PEDP treatment varies only across cohorts. However, since we make use of information from a small number of adjacent cohorts in a period with no other major government program in the region, we believe that the bias due to time-variant unobservable will be minimal. The main reason we do not use information from other nationally representa- tive surveys like the Tanzanian Demography and Health Surveys (TDHS) or the Tanzania Household and Budget Surveys (TBHS) is that the relevant waves from these surveys do not have information on the district of birth of individuals. Inter- nal migration across regions in Tanzania is common (Kudo (2015)). Kagera region is an ideal setting in this context because migration outside Kagera is relatively low. Moreover, KHDS boasts of a high tracking rate of individuals even when they move. The information allows us to restrict our attention to individuals who report not having moved in the last ten years and report being a part of the household in preceding years. This helps us minimize the attenuation bias from migration. While children born in 1991 and 1992 were born twelve and eleven years before the 2004 wave, respectively, the probability that they moved in the first two years of their birth is relatively small. 109 4.3.2 Iodine Exposure As described before, sufficient levels of iodine are most crucial in the first trimester. Therefore, the child of an iodine deficient mother who received an iodized oil capsule in the first month of any year would not be protected unless the child was born in the eighth month of that year or later. Following Peterson et al. (1999) and Field et al. (2009), we assume that the timing of the distri- bution was uniform over the months of any year that the district received the supplementation. We also maintain the assumption in Field et al. (2009) that, conditional on the starting month, it took three months to complete the distribu- tion of these capsules. Therefore, for a district that received the supplementation program in the first month of the year t, children born in the first seven months in that district were not protected by the supplementation program. Research shows that the body stock of iodine depletes at a certain rate after every such iodine supplementation. To account for this depletion, we use the method used in Field et al. (2009). For those born in the eighth month or later, protection, there- fore, depended on whether the program started early enough to have reached their mothers in time (first trimester or earlier) and whether their mothers had retained adequate amounts of iodine throughout their first trimester after accounting for the depletion of body iodine stocks with time. The detailed table of probability of protection calculation is reproduced from Field et al. (2009) in the appendix. For instance, we present here the calculation forthosebornintheeighth, theninthandthetenthmonthofyeart. Forthoseborn in month 8, probability of protection is equal to the probability that the program started in January that year (equal to 1/12 using uniform timing assumption) and their mothers were reached in that very month (equal to 1/3 using three-month diffusion time assumption.) Therefore, it is equal to 1/36. For those born in the 110 ninth month, the program reached their mother in the first trimester if it started in January (1/12) and reached them by February (2/3) or if it started in February (1/12) and reached them in February itself (1/3), therefore, the probability of protectionconditionalontreatmentinthatyearis1/12. ForthoseborninOctober, the program reached their mothers in time if it started in January (1/12) and reached the mother by March (1) or if it started in February (1/12) and reached them by March (2/3) or if it started in March (1/12) and reached them in March itself (1/3). Therefore, the probability of protection conditional on treatment in that year is 1/6. Given the assumption on the rate of depletion made in Field et al. (2009), one that we maintain here, the stocks of iodine retained in the body would be above the required levels for 24 months after the administration of the pill. Therefore, one does not need to adjust for depletion for these months. Finally, this calculated probability is multiplied by the coverage rate in a particular district in a particular year to get the final treatment probability. 4.3.3 Empirical Specification We begin by examining the direct impact of the iodine exposure on educa- tional attainments at the age of 10-13 in 2004. We follow Field et al. (2009) and Bengtsson et al. (2013), where treatment is considered to vary exogenously at the district-birth year level after we control for several observables and apply some fixed effects. Y 1idb =α 1 +β 11 ∗ID 1idb +γ∗X 1idb +τ 1b +ω 1d + 1idb (4.1) where Y 1idb is the years of schooling completed by an individual i born in district d in year b by 2004. It depends on ID 1idb . the probability that individual i’s mother was treated by the ISP program in the first trimester of her pregnancy. 111 This treatment probability is calculated as explained in the previous section. X 1idb is a vector of covariates that include a dummy each for whether the mother and father have some education or not, a dummy for gender of the individual, a dummy each for whether the individual belongs to the majority tribe or religion, and total land ownership of the household to which individuali belongs. 1 2 Standard errors are clustered at the district-year level in order to allow for arbitrary correlation in the error terms within each cohort in a district. 3 Our specification is closer to that used in Bengtsson et. al (2013) and differs from Field et al. (2009) in that it is more parsimonious with respect to the controls variables used. Since the treatment occurred before birth, many of the potential controls run the risk of being impacted by the treatment. For example, as pointed outbyBeckerandTomes(1976)andempiricallyverifiedbyRosenzweigandWolpin (1980), fertility decisions are endogenous to the quality of children, a dimension that ISP treatment might have affected. Therefore, we exclude controls for birth order, number of children, distance to secondary school and health clinic, food security measures, home ownership, housing quality, as used in Field et. al. (2009), and a dummy for household’s urban residence, as used in Bengtsson et. al (2013). 1 Land in rural areas were regulated by the Tanzanian government under the Village Land Act beginning in 1999. To check for robustness, we replace the land ownership variable with the value of livestock owned in an alternative specification. The results, not presented here, remain very similar. 2 Our sample has a very small percentage of HIV positive individuals. Out of 1784 individuals for whom we clinical diagnosis, only four were diagnosed as HIV positive. Out of the 4240 individuals for whom we have self diagnosis information, 10 diagnosed themselves to be HIV positive. Given the small percentage of HIV positive individuals, we do not include HIV status as a control. 3 Since the number of districts is just seven, we prefer the district-year level clustering. Since the number of clusters is relatively small, we repeat our analysis with cgm wildboot cluster method to correct for standard errors (Cameron et al. (2008). The results (available on request) remain unchanged. 112 Unlike Field et. al (2009), we do not use household fixed effect specification in our main analysis. We believe that households where mothers gave birth twice within a span of four years are different than those with one birth during the period and excluding household with only one child born during this period will lead to substantial selection biases. While using the month of birth information for the assignment of treatment probability would lead to more accurate assignment, we do not have the month of birth information for a fairly large number of individuals in our sample. Therefore, we follow Field et. al (2009) in our main specification and assign treatment probabilities on the basis of month of birth. In section ??, we check the robustness of our results to the assignment of treatment probability on the basis of month of birth for a smaller sample of individuals for whom we have the month of birth. Since the treatment status of the PEDP program is based on the year of birth, we cannot use birth fixed effects in specifications that look to evaluate the impact of PEDP in addition to ISP. Instead, we replace fixed effects in year of birth by a quadratic term in age. To show that this quadratic term approximates the year of birth fixed effects closely, we re-estimate (1) with the birth year fixed effect replaced by a quadratic in age. We, then, look at the combined impact of ISP and PEDP on completed years of schooling using the specification: Y 2idb =α 2 +β 21 ∗ID 2idb +β 22 ∗P 2idb +β 23 ∗ID 2idb ∗P idb +γ 2 ∗X 2idb +τ 2 ∗age+δ 2 ∗age 2 +ω 2d + 2idb (4.2) For individual i, living in district d and born in year b, ID 2idb represents the probability that individual i’s mother received iodine supplementation during the first trimester of her pregnancy. P 2idb indicates individual i’s exposure to PEDP 113 and takes value ‘1’ if the individual was born in 1993 or 1994, ‘0’ otherwise. Our specification includes district fixed effects (ω d ), a quadratic in age, a dummy each forwhetherthemotherandfatherhavesomeeducationornot, adummyforgender of the individual, a dummy each for whether the individual belongs to the majority tribe or religion, and total land ownership of the household to which individual i belongs. β 21 and β 22 represent the independent impacts of ISP and PEDP on the schooling attainments, respectively. Coefficient β 23 is a measure of heterogeneity in the impact of PEDP by ISP exposure status. To provide suggestive evidence for the mechanism we propose, we begin by showing that the ISP and PEDP treatment statuses and their interaction predict the primary school start age and individual’s involvement in household work or work on family farm in a manner that is consistent with the impact of these three variables on years of schooling. For this we use a specification that is similar to (2), except now the outcome variable is the age at which the individuals start primary school, probability that the individual worked on-farm or at home in the last week, or the number of hours worked on-farm or at home in the last one week. Weestimatetherateatwhichchildrentreatedbyoneorbothoftheseprograms convert years at school into completed years of schooling by taking a ratio of estimated impact of these two treatments and their interaction on completed years of schooling and primary school starting age. We interpret these rates measures of the dynamic complementarity. A higher value of this ratio for those exposed to ISP compared to those not exposed to ISP would imply that the former group makes better use of each year spent in school. 114 4.4 Results 4.4.1 School Grade Attainment and Primary School Starting Age Table 4.2 presents the impact of ISP exposure on completed schooling by 2004. The columns differ in the controls used in the specification. For example, columns (1), (3), (5), and (7) include age or birth year fixed effects to account for time varying unobservable factors that might have impacted schooling levels in those years. Columnc (2), (4), (6), and (8) replace the birth year fixed effect with a quadratic term in age. It is clear from the comparison of the coefficient across columns that a quadratic terms in age closely approximates year of birth fixed effects in our analysis. Both the ISP coefficient magnitudes and the R-squared fit of the model remains virtually unchanged. Controlling for tribe, religion and total land makes almost no difference to the estimated impact of ISP on grade attainment. When discussing the results, we will prefer the coefficient estimates from the specification with the full set of controls and quadratic in age, similar to the one used in column (8). According to the estimates, ISP exposure is associated with 0.70 fewer years of completed schooling. Conditional on non-zero probability of exposure, the average probability of exposure to ISP is 0.31. Therefore, those exposed to ISP, on an average, had completed 0.21 (0.70 * 0.31) fewer years of school. At a first glance, the negative impact of ISP on grade attained is puzzling. There is no a priori reason to expect a negative impact on grade attainment of a supplementation which is expected to improve the cognition of those exposed. It also seems to contradict the results from Field et. al (2009) that those exposed to ISP had completed more schooling. However, once we examine the behavioral responses to ISP exposure, the negative association between ISP exposure and 115 grade attainment in no longer a puzzle. But since the primary objective of the paper is to examine how the two policies interacted, we discuss the joint impact of these two policies before we document the behavioral response. In table 4.3, we examine the joint impact of the two programs and their inter- action on years of schooling completed by the time of the survey in 2004. The coefficient estimates in column (3) suggest that for those who were not exposed PEDP the impact of ISP remained comparable to the estimates from table 4.2. However, there was a significant level of heterogeneity in the impact of PEDP by the ISP exposure status. Those not exposed to ISP but exposed to PEDP had completed 0.18 extra years of education by the time of the survey compared to those not exposed to either of the two programs. However, those exposed to ISP and PEDP had, on average, completed 0.19 years of schooling (-0.71 * 0.31 + 0.18 - 0.47 * 0.31 = -0.19). They were comparable to those exposed to only ISP and not PEDP who were lagging behind those who did not get exposed to either of the two programs by 0.22 years (-0.71 * 0.31). The negative interaction effect is equally perplexing. Why will a reduction in the cost of schooling hurt those who, most likely, have better cognition. One advantage of using KHDS for our analysis is that it contains information on pri- mary school starting age. By examining the primary school starting age, a choice variablesforindividualsortheirparents,wecaninvestigateiftherewereanybehav- ioral responses to the policies. Table 4.4 reports the impact of the two policies and their interaction on primary school starting age. The estimated coefficients seem to mirror the impact of the two policies and their interaction on completed school- ing. Those exposed to PEDP alone start school at a younger age than those not exposed to either of the two programs. Those exposed to ISP only or both the programs enter school later than those in the omitted category. On comparing 4.3 116 and 4.4, it is clear that the association of ISP exposure, PEDP exposure, and their interaction with completed schooling is, at least, partly explained by changes in primary school starting age in response to these treatments. In the next section, we provide suggestive evidence to further explain why such a response might have arisen. To be able to interpret the interaction coefficient as evidence in favor of or against dynamic complementarity, one has to make the assumption that in the absence of dynamic complementarity, the impact of the second policy on those who were exposed to the first policy must be equal to the independent impact of the second policy on those who were not exposed to the first policy. However, since ISP changes the primary start school age, the cost and benefit from PEDP for those exposed to ISP might no longer be same as for those who were not exposed to ISP. The difference in cost and benefits from PEDP might, therefore, also invoke different behavioral response. However, since coefficient estimates of the impacts of these two programs and their interaction on completed schooling and primary school starting age from tables 4.3 and 4.4, respectively, are still unbiased, a ratio of coefficient estimates for each of these policies and their interaction will be an indicator of how productive a particular subgroup is in school. That is. ∂(years of schooling) ∂(school starting age) = ∂(years of schooling) ∂(exposure to program X) ∗ ∂(exposure to program X) ∂(primary school starting age) (4.3) where X ∈{ISP,PEDP,ISP∗PEDP}. We compute the conversion rate for the subgroups in table 4.5. If those exposed to PEDP but not to ISP started school one year earlier, they would have have attained 0.39 extra years of com- pleted schooling. In comparison, those exposed to ISP alone would have attained 0.99 extra years of school. This suggests that ISP exposure makes individuals 117 more productive at school. If we consider years in school as an input in the pro- duction function of human capital, the productivity of this input is higher for those who benefit from the in-utero iodine supplementation. This is an evidence of dynamic complementarity. We have to be careful when trying to make a sim- ilar deduction for those who were exposed to both the programs. Their rate of conversion should we a weighted average of the three conversion rates calculated in the table. However, what should be the weights is not clear. However, for any combination of non-trivial weights, their conversion rate will be better than those who were exposed to PEDP but not ISP, lending further support to the dynamic complementarity argument made above. 4.4.2 Delay in Starting Primary School But why might those exposed to ISP delay start of primary school more than those not exposed? Late entry into primary school is very common in Tan- zania (Burke (1998); Bommier and Lambert, (2000)) and elsewhere in Africa (Glewwe and Jacoby (1993, 1995); De Vreyer, Lambert, and Magnac(1998). Sev- eral hypotheses have been proposed to explain this delay in enrolment - exis- tence of liquidity constraints (Jacoby (1994)), malnutrition problems (Glewwe and Jacoby (1995)), considering children too young to be in school (Burke (1998)), and pre-school training (De Vreyer, Lambert, and Magnac (1998)). There is no reason to believe that ISP exposure of child was correlated with credit constraints that her family faced, especially because ISP exposure depended on the timing of first trimester of pregnancy vis-a-vis supplementation and not on supplemen- tation alone. Therefore, we focus on the next two most important hypothesis - malnutrition problem and pre-school labor force. 118 Delay due to Worse Health If those exposed to ISP delay starting school because they are malnourished, we might expect it to be reflected in their height-for-age. Low height-for-age is an indicator of stunted growth reflecting a process of failure to reach linear growth potential is often associated increased risk of early exposure to adverse conditions such as illness and/or inappropriate feeding practices. Column (1) of table 4.6 presents the association between an individual’s ISP exposure status and height for age. Those exposed to ISP, indeed, are shorter in 2004. However, it is not clear why those exposed to ISP had worse growth. In-utero iodine supplementa- tion, especially in such low doses, has no adverse impacts on physical growth (Isa Zaleha et al. (2000)). Most individuals from the sample were interviewed at least once during the first four waves of KHDS between 1991 and 1994. Height mea- surements were also taken. Unfortunately, the number of individuals from each wave that we have height information on is small. However, since the selection for being interviewed during any of these years was unrelated to ISP exposure status, examining association between ISP exposure status and height during these waves might still be informative. Columns (2)-(4) present the association between ISP and height for age during these waves. Even though the standard errors are too large to interpret these coefficients without caution, the height for age during the early years for individuals exposed to ISP seems to be higher than for those not exposed. If the ISP exposure had an adverse impact on the physical health of those exposed, one might expect to see an effect on height for age early on. A second explanation for lower height attainment that seems to be consistent withthetrendinheightdifferencesacrosswavesisthatparentsofthosenotexposed to ISP responded, either to their exposure status or to their lower cognition, by making compensatory investment in them. That might explain how the initial 119 height advantage of those exposed to ISP was reversed by 2004. However, previous studies from developing countries have mostly found that parental response in such scenarios is often to reinforce the advantage that on of their children might have (Rosenzweig and Schultz (1982), Li et al. (2010), Adhvaryu and Nyshadham (2014)). Most of these studies use a sibling fixed effects specification to check for reinforcement or compensation within families. Our main sample consists of children born from 1991 to 1994. Households where mothers gave birth twice or more within a span of four years are different than those with one birth during the period. Therefore, excluding household with only one child born during this period will lead to substantial selection biases. Therefore, the results of sibling fixed effects analysis must be taken with a grain of salt. The results are presented in table 4.7. Column (1) and (3) look at the associa- tion of ISP exposure status with years of completed schooling by 2004 and height for age in 2004, respectively. Since, here, we are interested in the impact of ISP alone and including those born earlier than 1991 could, potentially, reduce some selection bias, in columns (2) and (4), our sample consists of all those born between 1989 and 1994. 4 However, the results do not indicate any compensatory response within the household. Most of estimated coefficients, even though not significant, are positive, consistent with reinforcement and not compensation. This suggests the negative impact of ISP exposure on education and height are identified from individuals with differential exposure to ISP born to households where theirs was the single birth during this period (table??). The results in 4.7 do not rule out the possibility that households with one child born during this period and not exposed to ISP tried to compensate for the lack of ISP exposure. 4 Kagera first received the program in one of its district in 1989. 120 Delay due to Child Labor Next, we turn to the hypothesis with maximum empirical support in previous works - pre-school training. According to the 2013 US Department of Labor report on worst forms of child labor, as of 2011, over 25% of the Tanzanian children aged 5-14wereengagedintheworstformsofchildlabor. Alittleover20%ofthechildren aged 7-14 were combining work and school. Using information from the 2000 wave of the Tanzania Household and Budget Survey, Kondylis and Manacorda (2010) findover60%ofchildrenaged7-14engagedinsomeformofproductiveactivityand around 40% combining work and school. Children worked on the family farm or did household chores. The average number of hours worked every week was a little over 25 and around 20% of those who did not attend school reported the reason as work or perceived uselessness of schools. Beegle et. al (2006) use information from the 2004 wave of KHDS and find that children aged 7-15 were found to have worked a little over 18 hours in the week prior to their interview. Beegle and Burke (2004) find the 10-15 year olds were working close to 9 hours on farming activities and between 11-15 hours on household chores. These findings are consistent with 2000-2001 integrated labor force and child survey by the Tanzanian Ministry of Labor, Youth Development and Sports under International Labor Organization’s International Program on Elimination of Child Labor. According to the report, of the total number of children aged 5-17, 39.6 % were involved in economic activities and 47.8% were engaged in housekeeping activities. Amongst those engaged in economic activities, more than three quarter of them (78.8%) worked as unpaid family members in their family farm or shamba and another 17.99% work as un-paid family members in non- agricultural estab- lishment. An estimated 34% of the total working children worked for more than 4 121 hours per day or 30 hours per week. Beegle et al. (2007 NBER) use crop and rain- fall shocks as instrumental variables for child labor and find that child labor has negative effects on completed years of schooling. One of the ways in which child labor affects educational attainment of children in Tanzania is through delayed enrolment. Even though children in Tanzania are expected to enroll in primary school at the age of seven, enrollment is almost always delayed by two, three, or even four years (Burke (1998); Bommier and Lambert (2000)). The returns to schooling in Tanzania are lower than other countries in the region (Knight and Sabot (1990); Mason and Khandker (1997)). Since the coun- try agricultural practices mostly use traditional production methods, the returns to education in agriculture are low (Mason and Khandker, 1997). Our findings are, therefore, not very surprising. Beegle and Burke (2004) find that children in the Kagera region were not attending school due to household demand of child labor and high opportunity cost of schooling. De Vreyer, Lambert, and Magnac (1998), Bommier and Lambert (2000) and Beegle and Burke (2004) argue that the main reason for delay in starting school in African countries, and in Tanzania in particular, is the high opportunity cost of going to school. De Vreyer, Lam- bert, and Magnac (1998) present a model where a household’s decision is similar to a portfolio choice among three assets - physical assets, ‘general’ human capi- tal accumulation for the children through schooling, and ‘specific’ human capital accumulation for the children through participation in family economic activities. Bommier and Lambert (2000) use information from the Human Resource Develop- ment Survey conducted by the World Bank, the Dar-es-Salaam University, and the Tanzanian government in 1992-1993 on 5000 households to test the model. They show that the parents send their children to school later and for a smaller period 122 of time since Tanzania had high returns from accumulation of the ‘specific’ human capital. From table 4.5, it does seem that ISP exposure made the exposed children smarter. This, in turn, might have increased their opportunity cost of schooling more than those not exposed. As a result, the ISP treated children might have chosen to start school later. Moreover, if they were aware that they were better at converting years in school into completed years of schooling, this might have incentivized them further to delay schooling. This would imply that those exposed to ISP were working more often than those not exposed before school. In 2004, at the time of the survey, all the individuals from the sample were in school. It would have been ideal if we had information on the working status of these individuals before they started school. Unfortunately, KHDS collected information on involvement in market and non market labor activities only for the week preceding the interview date. We assume that the number of hours worked in the week preceding the survey is correlated with the number of hours worked every weekinyearsprecedingtheirenrollmentinprimaryschool. Usinginformationfrom THBS 2000, Kondylis and Manacorda (2010) find enrolled children from all over Tanzania spent close to forty hours in school every week. They report that hours of work among children in school was approximately half that of children out of school. The alternative assumption that ISP treated children who enrolled later worked less than those who were not exposed and enrolled at younger age is less plausible. Most children generally work at home and on the family farm. These activities may include but may but may not be limited to working in the fields or tending to livestock (categorized as farm activities in KHDS) or collecting water, fetching firewood, cleaning the house, preparing meals, and time spent caring for other 123 children or sick household members (categorized as household chores in KHDS). Less than 0.5% of the children in our sample were engaged in wage work outside the family farm. Therefore, we focus on work on family farm and household chores only. Table 4.8 presents the association between program exposures and number of hours worked in different activities preceding the survey. ISP exposure seems to increase the number of hours worked on both family farms and unpaid family chores. The coefficients, even though insignificant for the activities separately, are in the right direction and large in comparison to the mean number of works worked in these activities by the individuals in the sample. Moreover, when we combine the activities, those exposed to ISP are working over five hours extra more than those not exposed. The impact of PEDP exposure, even though positive, is small and insignificant. However, the coefficient for the interaction large in columns (2) and (3), and significantly so for hours spent on household chores. The results suggest that pre-school work is one of the reasons behind delayed enrollment of those exposed to ISP. While we find suggestive evidence in favor of both worse health and more pre- schoolworkforthoseexposedtoISPaspossiblereasonsbehinddelayedenrollment, the evidence is rather weak. Therefore, we do not want to claim one or both of these as the only or even the strongest mechanism. What is clear, however, is that ISP invoked different behavioral responses from different subgroups and one needs to take those responses into consideration when evaluating ISP and its interaction with PEDP. 4.5 Conclusion There is now a broad consensus amongst demographers, sociologists and economists alike that the diffusion of modern economic growth to the developing 124 regions requires human capital accumulation by the population in these regions (Counts (1931); Inkeles (1969); North (1973); Davis et al. (1971); Rosenberg et al. (1986); Easterlin (1981); Easterlin (2009)). A higher level of human capital is desirable in its own right (Pigou (1952); Adelman (1975); Grant (1978); Grant (1978); Streeten et al. (1981); Sen (1984)). However, poor access to information and quality infrastructure, low levels of incomes, and imperfect credit markets in these regions limit the possibilities of private investment in human capital accumu- lation. State run policies, therefore, are of extreme importance in ensuring higher levels of human capital (Easterlin (1981)). Given the limited state budget, the decision of whether or not to roll out a particular program depends a lot on the cost benefit analysis of the program. Traditionally, the cost benefit analyses of such development programs is based on the evaluation of the single program as if it was implemented in isolation. However, if two independent programs interact in important ways, a partial equilibrium analysis might greatly understate the net benefitsofsuchprograms. Insuchscenarios, itbecomesessentialtojointlyevaluate the impact of the two (or more) programs, allowing for possible complementarity between the programs. Keeping this in mind, we evaluate the Iodine Supplementation Program and Primary Education Development Program in Tanzania. We find that ISP treat- ment was associated with lower schooling achievements for the exposed kids in 2004. The effect operated entirely through delays in enrollment. We provide sug- gestive evidence that this behavioral response of delaying enrollment was because those exposed to ISP were in worse health and spent more time working on the family farm or in the house. This, we conjecture, might have been because their improved cognition made them better at these jobs. More importantly, we find that those exposed to ISP were better at converting years in school into completed 125 years of schooling - a sign of dynamic complementarity between ISP exposure led improved cognition and time spent in school. The result that government policies interact in important ways might explain why the short run impacts of many programs dissipate in the long run. The results also underscore the need to raise the dimensionality of the policy space to be considered. However, it is impossible to evaluate the combined effect of all sort of different policy exposures and determine how they interacted. Perhaps a better combinations of theoretical, non-experimental, quasi-experimental and experimental methods need to be developed to handle the situation. 126 Figure 4.1: Iodine Supplementation Program in Tanzania (from Field et al. (2009)) 127 Figure 4.2: Trends in years of education and primary school strating age before treatments 0 5 10 15 20 Lowess 20 40 60 80 100 Age Schooling (ISP treated districts) Schooling (ISP untreated districts) Starting age (ISP treated districts) Starting age (ISP untreated districts) 128 Figure 4.3: Trend in completion of appropriate grade for age before treatments -.05 0 .05 .1 Lowess - Completed apropriate grade for age 20 40 60 80 100 Age ISP treated districts ISP untreated districts 129 Figure 4.4: Trend in height before treatments 150 155 160 165 Lowess - Height (in cms) 20 40 60 80 100 Age ISP treated districts ISP untreated districts 130 Table 4.1: Summary Statistics Outcomes Control Treatment Ages 10-11 Mean SD Mean SD Years of Schooling 1.87 1.00 1.44 0.96 Primary school start age 7.98 1.02 8.22 1.15 School Progression 0.82 0.30 0.79 0.40 HAZ in 2004 130.50 8.99 127.77 7.61 Proportion with Vaccination card 0.92 0.85 Tb vaccination 1.00 0.97 Measles vaccination 1.00 0.92 Tetanus vaccination 0.46 0.39 Polio vaccination 0.52 0.55 Ages 12-13 Mean SD Mean SD Years of Schooling 3.09 1.38 2.78 1.42 Primary school start age 8.57 1.45 9.01 1.46 School Progression 0.79 0.25 0.81 0.24 HAZ in 2004 141.21 8.47 139.64 8.44 Proportion with Vaccination card 0.95 0.99 Tb vaccination 0.99 0.99 Measles vaccination 0.94 0.97 Tetanus vaccination 0.80 0.88 Polio vaccination 0.84 0.86 Independent variables Control Treatment Ages 10-11 Mean SD Mean SD Protection due to ISP 0 0 14.26 17.17 Age 10.34 0.47 10.13 0.34 Mother has any education 0.95 0.21 0.92 0.27 Father has any education 0.92 0.27 0.92 0.27 Household land per capita 0.48 0.53 0.55 0.47 Proportion Sex = Male 0.54 0.48 Tribe = Mhaya 0.93 0.37 Religion = Catholic 0.65 0.53 N 133 185 Ages 12-13 Mean SD Mean SD Protection due to ISP 0 0 70.05 27.72 Age 12.57 0.50 12.55 0.50 Mother has any education 0.97 0.17 0.89 0.32 Father has any education 0.95 0.21 0.88 0.32 Household land per capita 0.56 0.56 0.80 0.66 Proportion Sex = Male 0.47 0.48 Tribe = Mhaya 0.94 0.01 Religion = Catholic 0.65 0.50 N 161 87 131 Table 4.2: Impact of Iodine Supplementation Program on completed years of schooling (1) (2) (3) (4) (5) (6) (7) (8) VARIABLES Years of education Iodine Supplementation Program -0.70*** -0.70*** -0.69*** -0.70*** -0.69*** -0.70*** -0.69*** -0.70*** (0.12) (0.13) (0.12) (0.13) (0.12) (0.12) (0.12) (0.12) Age fixed effect YES NO YES NO YES NO YES NO Quadratic in age NO YES NO YES NO YES NO YES Religion dummy NO NO YES YES NO NO YES YES Tribe dummy NO NO NO NO YES YES YES YES Land ownership control YES YES YES YES YES YES YES YES Mean of dependent variable 2.20 2.20 2.20 2.20 2.20 2.20 2.20 2.20 Mean ISP treatment probability 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 Observations 518 518 518 518 518 518 518 518 R-squared 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at district-year of birth groups. Other controls include a dummy each for whether the mother and father have some education or not, a dummy for gender of the individual, and district fixed effects. Table 4.3: Impact of ISP and PEDP on completed years of schooling (1) (2) (3) VARIABLES Years of education Iodine Supplementation Program (ISP) -0.70*** -0.71*** (0.12) (0.11) Primary Education Development Program (PEDP) 0.13 0.18** (0.15) (0.07) ISP * PEDP -0.47* (0.26) Mean of dependent variable 2.20 2.20 2.20 Mean ISP exposure probability 0.31 0.31 Observations 518 518 518 R-squared 0.36 0.35 0.36 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at district-year of birth groups. Controls include a quadratic in age, a dummy each for whether the mother and father have some education or not, a dummy for gender of the individual, a dummy each for whether the individual belongs to the majority tribe or religion, controls for total land holdings of the household, and district fixed effects. 132 Table 4.4: Impact of ISP and PEDP on primary school starting age (1) (2) (3) VARIABLES Primary school starting age Iodine Supplementation Program (ISP) 0.77*** 0.74*** (0.16) (0.15) Primary Education Development Program (PEDP) -0.47** -0.47** (0.19) (0.18) ISP * PEDP 0.26 (0.21) Mean of dependent variable 2.20 2.20 2.20 Mean ISP exposure probability 0.31 0.31 Observations 518 518 518 R-squared 0.17 0.16 0.17 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at district-year of birth groups. Controls include a quadratic in age, a dummy each for whether the mother and father have some education or not, a dummy for gender of the individual, a dummy each for whether the individual belongs to the majority tribe or religion, controls for total land holdings of the household, and district fixed effects. Table 4.5: Conversion of an additional year into additional years of schooling Treatment School starting age Years of schooling ∂(yearsofschooling) ∂(schoolstartingage) PEDP only −0.47 0.18 −0.38 ISP only 0.74 −0.71 −0.96 ISP * PEDP 0.26 −0.47 −1.8 Notes: ∂(years of schooling) ∂(school starting age) = ∂(years of schooling) ∂(exposure to program X) ∗ ∂(exposure to program X) ∂(primary school starting age) , whereX∈ {ISP,PEDP,ISP∗PEDP} 133 Table 4.6: Impact of ISP on height of the child (Height-for-age) (1) (2) (3) (4) (5) Height for age Z-score in VARIABLES 2004 1994 1993 1992 1991 ISP -0.46** -2.34 3.33** 1.79 3.80 (0.21) (1.45) (1.40) (1.51) (2.48) Observations 501 102 118 128 145 R-squared 0.04 0.09 0.08 0.17 0.13 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at district-year of birth groups. Controls a dummy each for whether the mother and father have some education or not, a dummy each for whether the individual belongs to the majority tribe or religion, controls for total land holdings of the household, and district fixed effects. We used the WHO Child Growth Charts and WHO Reference 2007 Charts for our height for age analysis. Table 4.7: Within household impacts of ISP (1) (2) (3) (4) VARIABLES Years of education Height for age in 2004 ISP 0.24 0.22 0.78 -0.39 (0.59) (0.46) (0.87) (0.47) Observations 132 335 119 298 R-squared 0.86 0.86 0.66 0.67 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at the level of the household. Controls include a dummy for gender of the individual, age and sibling fixed effects. 134 Table 4.8: Impact of ISP and PEDP on hours worked (1) (2) (3) In the last week, how many hours did you work [...]? VARIABLES on the family farm in unpaid work in total ISP 1.97 2.07 5.43*** (1.46) (1.75) (1.93) PEDP 1.97 0.63 1.72 (1.18) (1.20) (1.08) ISP * PEDP -1.85 10.33* 7.62 (3.07) (5.61) (8.69) Mean of dependent variable 4.51 5.49 10.18 Mean ISP treatment probability 0.32 0.32 0.32 Observations 540 540 540 R-squared 0.04 0.05 0.04 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at district-year of birth groups. Controls include a quadratic in age, a dummy each for whether the mother and father have some education or not, a dummy for gender of the individual, a dummy each for whether the individual belongs to the majority tribe or religion, controls for total land holdings of the household, and district fixed effects. 135 Chapter 5 Conclusions This dissertation explores two education programs and an urban development plan. Chapter 2 documents that the student mix in secondary school affects stu- dents’ academic performance. Students are exposed to different studying environ- ment according to where or not they are tracked, and they respond differently based on their prior achievement. Chapter 3 deals with the effects of subway tran- sit station on apartment price. A great deal of heterogeneity in apartment price premium has been found according to the machine learning method. It is also doc- umented that the real estate developers responded to the positive demand shock and provided popular apartment types in order to maximize their profit in the treated area. Chapter 4 investigates the dynamics of human capital development, using to adjacent exogenous shocks. Parents delayed the age at which children treated by ISP in-utero. The similar compensation pattern has been found with investment in health. Themaincontributionofthisdissertationtotheeconomicsliteratureistwofold. First, all three chapters highlight heterogeneity in treatment effect. 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Physiology and pharmacology of iodized oil in goiter prophylaxis. Medicine, 80(1):20–36. Zeileis,A.,Hothorn,T.,andHornik,K.(2008). Model-basedrecursivepartitioning. Journal of Computational and Graphical Statistics, 17(2):492–514. Zheng, S. and Kahn, M. E. (2013). Does government investment in local pub- lic goods spur gentrification? evidence from beijing. Real Estate Economics, 41(1):1–28. 147 Appendix A Supplementary Material for Chapter 2 A.1 Proof of Lemma 1 To prove lemma 1, we assume thate H,M <e L,M and show this contradicts other assumptions made earlier at the end. Subtracting the equation (3) from equation (2), we obtain the following. U 1 ∂y H,M ∂e H,M −U 1 ∂y L,M ∂e L,M +U 2 e L,M (e H,M +e L,M ) 2 ∂R H,M ∂e H,M −U 2 e H,M (e L,M +e H,M ) 2 ∂R L,M ∂e L,M = ∂c H,M ∂e H,M − ∂c L,M ∂e L,M (A.1) Given e H,M < e L,M and ∂ 2 c(e i,s ) ∂e i,s ∂θ i,s < 0, it is straightforward to show that the right-hand side in equation (9) is less than zero. On the other hand, ∂y H,M ∂e H,M > ∂y L,M ∂e L,M holds because the high type exerts more efforts than the low type and because of assumption A.2, so thatU 1 ∂y H,M ∂e H,M −U 1 ∂y L,M ∂e L,M is positive. It is also trivial to see that e L,M (e H,M +e L,M ) 2 ∂R H,M ∂e H,M > e H,M (e L,M +e H,M ) 2 ∂R L,M ∂e L,M not only because we assume e H,M < e L,M earlier but also becauseR i,s is concave and assumption A.3 holds. Putting these all together, the left-hand side in equation (9) is negative, which contradicts equality. Hence, we prove that e H,M ≥e L,M 148 A.2 Proof of Proposition 1 B.1. High Type We assumee H,T <e H,M first and show a contradiction later, as we have done in appendix A. Subtracting equation (4) from equation (2), we obtain the following. U 1 ∂y H,M ∂e H,M −U 1 ∂y H,T ∂e H,T +U 2 e L,M (e H,M +e L,M ) 2 ∂R H,M ∂e H,M −U 2 1 4e H,T ∂R H,T ∂e H,T ( 1 2 ) = ∂c H,M ∂e H,M − ∂c H,T ∂e H,T (A.2) As we assume e H,T <e H,M earlier, it is trivial that the right-hand in equation (10) is positive. On the other hand, by assumption A.2 and e H,T < e H,M , it is easy to show U 1 ∂y H,M ∂e H,M < U 1 ∂y H,T ∂e H,T . By lemma 1, e H,M > e L,M , and assumption A.3, ∂R H,M ∂e H,M ( e H,M e H,M +e L,M ) < ∂R H,T ∂e H,T ( 1 2 ). e L,M (e H,M +e L,M ) 2 increases in e L,M due to lemma 1. Lemma 1 also impliese L,M ranges between zero ande H,M . Ife L,M is equal toe H,M , then e L,M (e H,M +e L,M ) 2 becomes 1 4e H,M that is maximum. If e L,M takes value of zero, then e L,M (e H,M +e L,M ) 2 is also zero that is minimum. Since both the maximum and the minimum are less than 1 4e H,T by the assumption at the beginning and e L,M (e H,M +e L,M ) 2 is monotonicallyincreasing,theleft-handsideinequation(10)isnegative. Hence,the assumption, e H,T < e H,M , contradicts other assumptions pertaining to functions in equation (1). 149 B.2. Low Type We set up the initial assumption, e L,T > e L,M , first and show a contradiction later as we have done in appendix A. Subtracting equation (5) from equation (3), we obtain equation (11) as follows. U 1 ∂y L,M ∂e L,M −U 1 ∂y L,T ∂e L,T +U 2 e H,M (e L,M +e H,M ) 2 ∂R L,M ∂e L,M −U 2 1 4e L,T ∂R L,T ∂e L,T ( 1 2 ) = ∂c L,M ∂e L,M − ∂c L,T ∂e L,T (A.3) As we assume e L,T > e L,M at the beginning, the right-hand side in equation (11) is negative. On the other hand, U 1 ∂y L,M ∂e L,M −U 1 ∂y L,T ∂e L,T > 0 holds because of both the initial assumption and assumption A.2. By assumption A.3 and lemma 1, it is straightforward to show ∂R L,M ∂e L,M ( e L,M e H,M +e L,M ) > ∂R L,T ∂e L,T ( 1 2 ). The last piece of the proof is to compare between e H,M (e L,M +e H,M ) 2 and 1 4e L,T . By lemma 1, e H,M (e L,M +e H,M ) 2 decreases in e H,M , and e H,M ranges between e L,M and infinity. If e H,M equals e L,M , then e H,M (e L,M +e H,M ) 2 takes the maximum that is greater than 1 4e L,T by the initial assump- tion. In this scenario, the initial assumption contradicts equation (11), so that we prove e L,T <e L,M holds. If e H,M goes to infinity, then e H,M (e L,M +e H,M ) 2 takes zero, the minimum that makes U 2 e H,M (e L,M +e H,M ) 2 ∂R L,M ∂e L,M −U 2 1 4e L,T ∂R L,T ∂e L,T ( 1 2 ) negative. In this scenario, the initial assumption can be valid. Hence, it is ambiguous to deter- mine under what condition the low type exerts more efforts generally. However, as e H,M (e L,M +e H,M ) 2 is monotonically decreasing with e H,M , there always exists such that if θ H −θ L <, then e L,T <e L,M holds regardless of functional forms. 150 A.3 Test for Tiebout Migration For equation (6) not to be biased the policy change from the tracking to the mixing system should not trigger migration. As documented by Tiebout (1956) and Benabou (1993), it is plausible for residents to migrate in an effort to seek better educational services. If this were true, then the estimates from equation (6) could be biased in both directions, depending on who migrates between the high and low type. Due to limitations in the data, we cannot access which type moves, but we can test whether the change to the mixing system causes high school enrollment in the treated region. With high school enrollment in a district each year as an outcome variable, we estimate equation (6) by OLS. Column (1) in table A.1 shows that no statistically significant difference between the control and the treatment group at 10% is found. We also estimate Y 1 ijst = P 1988 Y=1984 β Y Treat j × Year Y +β 2 X ijst +μ j +λ st +ε ijst with the same outcome variable to compare annual change in high school enrollments with that in 1999 as a baseline. Column (2) in table A.1 implies that the intervention does not cause migration between districts in the GOMS case. As high school enrollment data before 1999 are not available, we cannot test if the intervention causes that in the CSAT case. Hence, we use the census data and compare the control and treatment district in terms of population size and education level in districts; we utilize the population of 10- to 14-year-olds and 15- to 19-year-olds and the number of residents who attain a bachelor’s degree and who receive a master’s degree. Figure A.1 shows that both the control and treatment group move in the same direction from 2000 to 2005. This implies that the possibility of Tiebout migration is marginal. 151 Table A.1: Evidence that High School Enrollment Is Not Affected By Treatment, GOMS (1) (2) VARIABLES High school Enrollments High school Enrollments Treatment× After 306.8419 (282.8117) Treatment× Year 2000 -23.1128 (177.1945) Treatment× Year 2001 118.9426 (206.3606) Treatment× Year 2002 110.4352 (288.9192) Treatment× Year 2003 342.2591 (390.1286) Treatment× Year 2004 563.9044 (434.2090) Observations 388 388 Data: KESS Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Figure A.1: Evidence that Refutes Tiebout Migration, CSAT 152 A.4 Appendix A.4 Growing number of colleges and college students Figure 6 shows that the number of students who graduate from the top 8 or the top 15 colleges has been declining over time. Figure A2 shows both the number of college students and that of colleges have been increasing over time, but the number of students who go to the top schools remain constant during the same period. Therefore, the ratio of top school students to total college students had decreased in the period of our interest. Figure A.2: Growing number of colleges and college students 153 A.5 Tracking Effects on Private Tutoring In section 7, we show that the students in the top half exert more studying effort under the tracking system, while those in the bottom half reduce study hours. This is consistent with what the model in section 2 predicts. Since another major investment in education is private tutoring in South Korea, it is worthwhile to explore whether investment in private tutoring moves in the same direction as self-study hours. Table A2 shows the extent to which the tracking system results in private tutoring. 1 As a result, it shows students who used to be within the 25% quantile are involved in private tutoring the most no matter which outcome variables are used, 2 although all estimates are not statistically significant at 10%. This provides evidence on that tracking leads the high type to exert more studying effort. Table A.2: Tracking effects on Private Tutoring (1) (2) (3) (4) VARIABLES Private Tutor Private Tutor Log(Expenditure) Log(Expenditure) Treat× High -0.0255 0.0045 -0.4580 -0.1233 (Tracking effect) (0.0714) (0.1269) (0.2671) (0.6681) Treat× High× Above half -0.0094 0.1835 (0.0721) (0.3559) Treat× High× 25∼ 50% -0.0765 -0.2916 (0.1541) (0.7610) Treat× High× 50∼ 75% -0.0187 -0.2377 (0.1692) (0.7887) Treat× High× 75∼ 100% -0.0514 -0.5149 (0.1626) (0.6827) Observations 2,274 2,274 2,236 2,236 R-squared 0.6587 0.6591 0.7102 0.7104 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at the district level. The KEEP data are used. 1 With private tutoring as an outcome variable, we estimate equation (8) 2 Weuseadummyvariableofprivatetutoringandnaturallogarithmofexpendituresonprivate tutoring 154 A.6 Summary Statistics for KEEP Table A.3: Summary Statistics: KEEP Variable Mean Std. Dev. N Study hours (per week) Less than 2 hours 0.391 0.488 2562 More than 15 hours 0.138 0.345 2562 More than 20 hours 0.085 0.279 2562 Private Tutoring Tutoring (=1) 0.678 0.467 2565 Expense on Private Tutoring(US$ per month) 201.487 279.87 2515 Teacher-Pupil Interaction Students respect a teacher (=1) 0.705 0.456 2410 Students like a teacher (=1) 0.516 0.5 2410 Teachers are interested in a student (=1) 0.708 0.455 2410 Teachers understand a student 0.563 0.496 2407 Teacher Quality Master degree or above (=1) 0.356 0.479 1934 Experience (years) 13.406 7.779 1931 Experience on a certain subject 12.642 7.723 1930 Subjective evaluation on teacher (Good=1) 0.762 0.426 2323 Study Atmosphere Teacher-pupil closeness 0.746 0.435 2334 Class Atmosphere (Good=1) 0.573 0.495 2334 155 Appendix B Supplementary Material for Chapter 3 B.1 The Machine Learning Algorism Following Rubin (1974), Heckman (1990) and Abadie (2005), we defineY 0 (i,t) as the potential outcome that apartment i attains in period t if untreated, and define Y 1 (i,t) as the potential outcome that apartment i attains in period t if treated. ThetreatmenteffectisY 1 (i,t)−Y 0 (i,t). Thefundamentalproblemisthat econometrician cannot observeY 1 (i,t) andY 0 (i,t) at the same time. Econometri- cians observe the realized outcome,Y (i,t) =Y 0 (i,t)·(1−D(i,t))+Y 1 (i,t)·D(i,t), where D(i,t) takes one if treated, and zero otherwise. Due to the missing data problem, it is impossible to identify individual treatment effects, which leads researcher to focus on average treatment effects on the treated under the assump- tion that the average outcomes conditional on X for the treated and the untreated would have followed similar trends if not exposed to any treatment. 1 As in 1 In the next section, we will present evidence that the treated and the untreated follow a parallel path. 156 Heckman et al. (1997), the conditional average treatment effect on the treated is expressed as follows. E[Y 1 (i, 1)−Y 0 (i, 1)|X,D(i, 1) = 1] = {E[Y (i, 1)|X,D(i, 1) = 1]−E[Y (i, 1)|X,D(i, 1) = 0]} −{E[Y (i, 0)|X,D(i, 1) = 1]−E[Y (i, 0)|X,D(i, 1) = 0]} (B.1) As noted by Abadie (2005), the estimation process is burdensome; four conditional expectations need to be estimated nonparametrically, and the number of observa- tions may not be large enough to estimate conditional expectation when X is high dimensional. To address the innate limitations of DID estimator Abadie (2005) suggests the semiparametric approach, and Athey and Imbens (2006) proposed the generalized identification method that provides entire counterfactual distribution of outcomes that would have been realized both for the treated and the untreated, respectively. In an empirical application, Bajari and Kahn (2005) estimate a hedo- nic model non-parametrically. However, recent development of supervised machine learning enables researchers to estimate conditional expectations using the regres- sion tree. Athey and Imbens (2015) propose the conditional average treatment effect approach in a context where the unconfoundedness assumption holds. We extendthismodeltotheDIDcontextbyincorporatingthetreatmentdummyalong with the time dummy as splitting variables in the process of growing a regression tree. We follow the general supervised machine learning approach to grow our regression tree. (Friedman et al. (2001), Breiman et al. (1984) and Athey and 157 Imbens (2015) 2 ). Let first Q is (ˆ τ;α,X,Y obs ) and Q os (ˆ τ;α,X,Y obs ) denote in- sample goodness-of-fit measure and out-of-sample goodness-of-fit measure, respec- tively, as follows. Q is (ˆ τ;α,X,Y obs ) =− 1 N N X i=1 (Y obs i − ˆ τ(X i )) 2 −α·K Q os (ˆ τ;α,X,Y obs ) =− 1 N N X i=1 (Y obs i − ˆ τ(X i )) 2 , (B.2) where K is the number of leafs in the tree, and α is penalty term to avoid an extremely large tree. ˆ τ(X i ) is a sample average of Y i in leaf. The regularization parameter α is chosen by cross validation, minimizing Q os (ˆ τ;α,X,Y obs ). Let T M denote a tree with M nodes: R 1 ,R 2 ,...,R M . We model the response as a constant ˆ τ(·;T m ) in each node and consider the splitting variable j among J explanatory variables and threshold j thr for each region. Using j and j thr , we split parent node(m) into two child nodes(2m and 2m+1). R 2t (j,j thr ) ={X|x j ≤j thr } and R 2t+1 (j,j thr ) ={X|x j >j thr } (B.3) For each j = 1,...,J, we fix α and find the value j thr,∗ that solves max j thr Q is (ˆ τ(·;T x thr j M );α,X,Y obs ) (B.4) whereT x thr j M is a new candidate tree generated by splitting the parent node into the children nodes with the threshold of j thr . The following stopping rule is applied; 2 Athey and Imbens (2015) develop five supervised machine learning algorithms for the cases where the unconfoundedness assumption is met. Our approach is based on the single tree with the observed outcome among the five. 158 • If max J j=1 Q is (ˆ τ(·;T x thr,∗ j M );α,X,Y obs )≤ Q is (ˆ τ(·;T M );α,X,Y obs ), then stop splitting and R m becomes a terminal node • If max J j=1 Q is (ˆ τ(·;T x thr,∗ j M );α,X,Y obs )>Q is (ˆ τ(·;T M );α,X,Y obs ), then we fol- low the steps described below. – If N R 2m < 10 or N R 2m+1 < 10 , stop splitting and then parent node R m becomes a terminal node where N R 2m and N R 2m+1 are the number of observations in the child node are R 2m and R 2m , respectively. A very large tree may overfit the data, and it is difficult to interpret average treatment effect within leafs that contain only a single unit (Athey and Imbens (2015)) – If N R 2m ≥ 10 and N R 2m+1 ≥ 10, split the node, using variable j ∗ = argmax j Q is (ˆ τ(·; T x thr,∗ j M );α,X,Y obs ) with the threshold of j thr,∗ • We iterate this process until all of the nodes become terminal nodes and then define T α as the tree based on the final iteration for a given α, . In order to choose the optimal penalty parameter, α, we utilize 10-fold cross- validation, minimizingQ os (ˆ τ;α,X,Y obs ). Breiman et al. (1984) prove that a finite number of relativeα exist, though possible ‘α’s are a set of continuous values. This implies that there is the unique T i that minimizes Q os (ˆ τ(·;α);X te ,Y te,obs ) within the interval [α i ,α i+1 ). Taking advantage of the algorithm Breiman et al. (1984) proposed, we construct a sequence of the optimal trees T (α) =<T 0 ,T 1 ,...,T n >, corresponding to each relative α i (See Breiman et al. (1984) for more details). We partition the entire sample into ten subsamples. With only k-1 the training subsamples except the kth subsample, we generate a sequence of tree, T k (α), using the method described above. With the kth test sample, we estimate the 159 prediction error, using Q os (ˆ τ (k) (·;α);X te ,Y te,obs ). For each k, we iterate using the same procedure and find the optimal α ∗ that solves arg max α 1 K K X k=1 Q os (ˆ τ (k) (·;α);X te ,Y te,obs ), where K = 10. (B.5) With the optimalα ∗ , we defineT α ∗ and ˆ τ α ∗ (x) to be the optimal tree and the final estimator, respectively. In the process of creating the regression tree we include the treatment dummy (D) along with the time dummy (T) and other covariates (X) as splitting variables as we did in the linear specification. The treatment dummy equals one if the distance between the apartment and LINE9 station is less than one kilometer, zero otherwise. Likewise, the time dummy equals one if the year is after the opening of the line and equals zero otherwise. The outcome variable of interest is the log of apartment price (Y), and the covariate vector X includes the apartment size(m 2 ) 3 , the number of rooms, the number of baths, years of depreciation 4 , distance to other existingsubwaytransitstation 5 andeachdistrictdummy. Wetakeadvantageofthe constructed regression tree and use a sample average in each leaf as the conditional expectation, E(Y|X = x,D = d,T = t). Building on Athey and Imbens (2015), we estimate the conditional average treatment effect(CATE) in DID context as CATE ={E[Y|X =x,D = 1,T = 1]−E[Y|X =x,D = 0,T = 1]} −{E[Y|X =x,D = 1,T = 0]−E[Y|X =x,D = 0,T = 0]} (B.6) 3 We construct a categorical variable, using 25%, 50% and 75% quartile. One represents the smallest group and four is the largest group 4 We use a categorical variable that takes on the value of one if less than five years have passed and equals two if between five and ten years have passed, and three otherwise. 5 We use a dummy that equals one if the distance between the apartment and the existing other station is less than 1km, and equals zero otherwise. 160 B.2 LINE9 Effects on Rent This section reports an effect of LINE9 on rent price. Note that the rent here is not monthly payments but two-year deposit unlike the U.S. and many countries. If an anticipation effect or a speculative demand had played a major role in price appreciation due to LINE9, prices would have experienced a bigger premium than rents. This is because rents are less subject to an anticipation effect. Empiricalstrategyfortherentsarethesameasequation(1)and(2), butwereplace Log(Price ijt ) withLog(Rent ijt ). In comparison to table 3, table A1 reports bigger treatment effects. For every a kilometer closer to LINE9 station, an apartment experiences of 2.03% premium . If an apartment locates within 1km from the LINE9 station, rents are 6.26% higher than those more than two kilometers away from the new station. Both of them imply that the treatment effect comes from direct benefits like travel time savings or growing retail activities rather than an anticipation of future price hike. Assuming heterogeneous buyers, some who are patient enough to wait for a long time may buy properties in advance and expect a price appreciation later. However, our results show that such cases are not big enough. This justifies that we define the date of opening as a treatment. 161 Table B.1: Impacts of LINE9 on Rent (1) (2) (3) (4) VARIABLES Log(Rent) Log(Rent) Log(Rent) Log(Rent) Distance (km) 0.0117 (0.0181) Distance (km)× AFTER -0.0203*** (0.0060) Log(Distance, km) 0.0120 (0.0138) Log(Distance, km)× AFTER -0.0365*** (0.0084) Within 1km -0.0619* -0.0516* (0.0326) (0.0278) Between 1∼ 2km -0.0042 (0.0282) Within 1km× AFTER 0.0626*** (0.0194) Between 1∼ 2km× AFTER 0.0108 (0.0197) Within 1km× AFTER 0.2555*** (0.0896) Within 1km× AFTER× Size (m 2 ) -0.0020*** (0.0005) Within 1km× AFTER× Other Line (km) 0.0426*** (0.0127) Within 1km× AFTER× Room 0.0081 (0.0208) Within 1km× AFTER× Bath 0.0024 (0.0202) Within 1km× AFTER× Age -0.0102* (0.0053) Within 1km× AFTER× Age 2 0.0002* (0.0001) Observations 199,742 199,742 199,742 199,742 R-squared 0.9102 0.9105 0.9105 0.9124 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at the district level. Controls include size, the number of room and bath, parking spaces, age, age squared, distance to other closest station, the number of bus stops within 1km, the number of hospitals within 1km, whether it has named brand, the number of households within complex and the number of apartment building within complex. District fixed effect and quarter fixed effect are included 162 B.3 Conditional Average Treatment Effects Size Room Bath Old Other Transits District CATE S.E N (Category) (No.) (No.) (Category) Within 1km (Name) 1 1.0573 0.0509 201 Top 25% 3 2 < 5 yrs Yes Seocho 2 0.9023 0.0993 360 Bottom 25% 1 1 > 10yrs Yes Yeongdeungpo 3 0.8203 0.0968 96 Top 25% 5 2 5∼ 10yrs No Yangcheon 4 0.6403 0.0780 208 Bottom 25% - 50% 3 1 5∼ 10yrs Yes Seocho 5 0.5959 0.0442 1179 Bottom 25% - 50% 3 2 < 5 yrs Yes Seocho 6 0.5524 0.0630 536 Top 25% - 50% 4 2 < 5 yrs Yes Seocho 7 0.5453 0.0551 787 Top 25% - 50% 4 2 5∼ 10yrs Yes Gangnam 8 0.5011 0.0726 1530 Bottom 25% - 50% 3 2 5∼ 10yrs No Gangseo 9 0.4972 0.0941 628 Top 25% 4 2 5∼ 10yrs No Gangseo 10 0.4637 0.0470 532 Bottom 25% 2 1 5∼ 10yrs Yes Gangseo 11 0.4396 0.0911 1586 Top 25% - 50% 3 2 5∼ 10yrs No Gangseo 12 0.4328 0.1324 228 Top 25% 3 2 5∼ 10yrs Yes Seocho 13 0.4118 0.0283 757 Bottom 25% 3 1 5∼ 10yrs Yes Gangseo 14 0.3929 0.0838 369 Top 25% 4 2 < 5 yrs No Yangcheon 15 0.3896 0.1328 544 Top 25% 4 2 5∼ 10yrs No Yangcheon 16 0.3752 0.1224 79 Bottom 25% - 50% 3 1 < 5 yrs Yes Seocho 17 0.3686 0.0421 2023 Top 25% 4 2 < 5 yrs Yes Seocho 18 0.3603 0.0998 917 Bottom 25% - 50% 3 2 < 5 yrs No Gangseo 19 0.3562 0.0482 2076 Top 25% - 50% 3 2 5∼ 10yrs Yes Gangnam 20 0.3320 0.0336 2615 Top 25% 4 2 5∼ 10yrs Yes Seocho 21 0.3315 0.0338 1956 Bottom 25% 1 1 5∼ 10yrs Yes Gangnam 22 0.3268 0.0562 958 Top 25% - 50% 3 2 > 10yrs Yes Gangseo 23 0.3026 0.1400 344 Top 25% - 50% 4 2 5∼ 10yrs No Gangseo 24 0.3002 0.0660 229 Top 25% 4 2 < 5 yrs Yes Gangseo 25 0.3000 0.0708 300 Top 25% 4 2 5∼ 10yrs Yes Gangseo 26 0.2869 0.0679 652 Top 25% 4 2 < 5 yrs Yes Yeongdeungpo 27 0.2832 0.0817 260 Top 25% - 50% 4 2 5∼ 10yrs No Yangcheon 28 0.2691 0.0626 816 Top 25% 5 2 > 10yrs Yes Yeongdeungpo 29 0.2588 0.3020 256 Bottom 25% 3 2 < 5 yrs Yes Seocho 163 30 0.2518 0.1381 572 Bottom 25% 2 1 5∼ 10yrs Yes Dongjak 31 0.2484 0.0416 1078 Top 25% - 50% 3 2 < 5 yrs Yes Dongjak 32 0.2387 0.0350 1994 Top 25% - 50% 3 2 5∼ 10yrs Yes Seocho 33 0.2366 0.0744 748 Bottom 25% - 50% 3 1 > 10yrs Yes Gangseo 34 0.2356 0.1374 1380 Top 25% - 50% 3 2 > 10yrs Yes Yeongdeungpo 35 0.2231 0.0551 1359 Bottom 25% - 50% 3 2 5∼ 10yrs Yes Dongjak 36 0.2228 0.1401 840 Top 25% - 50% 4 2 5∼ 10yrs Yes Seocho 37 0.2191 0.0881 1018 Bottom 25% - 50% 3 2 < 5 yrs Yes Dongjak 38 0.2157 0.0499 368 Top 25% - 50% 4 2 5∼ 10yrs Yes Gangseo 39 0.2155 0.0255 334 Bottom 25% 3 1 < 5 yrs Yes Gangseo 40 0.2130 0.2038 104 Bottom 25% - 50% 3 1 5∼ 10yrs Yes Yeongdeungpo 41 0.2117 0.0335 690 Top 25% 4 2 < 5 yrs Yes Dongjak 42 0.2029 0.0788 986 Top 25% - 50% 3 2 < 5 yrs No Gangseo 43 0.1985 0.0564 1582 Top 25% - 50% 3 2 5∼ 10yrs Yes Gangseo 44 0.1957 0.0408 1483 Top 25% - 50% 3 2 < 5 yrs Yes Seocho 45 0.1817 0.0559 1507 Bottom 25% - 50% 3 2 > 10yrs Yes Yeongdeungpo 46 0.1784 0.0587 1835 Bottom 25% 2 1 > 10yrs Yes Seocho 47 0.1781 0.0397 1162 Top 25% - 50% 3 1 > 10yrs Yes Seocho 48 0.1735 0.0286 658 Bottom 25% 3 1 5∼ 10yrs Yes Dongjak 49 0.1710 0.0573 689 Bottom 25% 1 1 > 10yrs Yes Seocho 50 0.1694 0.0838 384 Top 25% - 50% 4 1 > 10yrs Yes Seocho 51 0.1618 0.1552 186 Top 25% - 50% 4 2 < 5 yrs No Yangcheon 52 0.1478 0.1407 1792 Bottom 25% - 50% 3 2 5∼ 10yrs Yes Seocho 53 0.1435 0.0523 441 Bottom 25% - 50% 2 1 > 10yrs Yes Seocho 54 0.1313 0.0666 2001 Bottom 25% - 50% 3 2 < 5 yrs Yes Gangseo 55 0.1303 0.0307 1107 Bottom 25% - 50% 3 2 < 5 yrs No Yangcheon 56 0.1153 0.0447 2543 Bottom 25% - 50% 3 2 5∼ 10yrs Yes Gangseo 57 0.1106 0.0554 950 Top 25% 4 2 5∼ 10yrs Yes Yeongdeungpo 164 58 0.1099 0.0371 2543 Bottom 25% 2 1 > 10yrs Yes Yeongdeungpo 59 0.1045 0.0419 846 Bottom 25% 2 1 5∼ 10yrs Yes Seocho 60 0.0999 0.0611 464 Top 25% 6 2 > 10yrs Yes Seocho 61 0.0987 0.0350 1351 Top 25% - 50% 3 2 5∼ 10yrs Yes Dongjak 62 0.0982 0.0541 1148 Bottom 25% - 50% 3 2 > 10yrs Yes Gangseo 63 0.0961 0.0401 613 Top 25% - 50% 4 2 5∼ 10yrs Yes Dongjak 64 0.0904 0.0941 285 Top 25% - 50% 4 2 < 5 yrs Yes Yeongdeungpo 65 0.0900 0.0642 756 Bottom 25% 2 1 > 10yrs No Yangcheon 66 0.0897 0.0358 1696 Top 25% - 50% 3 2 5∼ 10yrs Yes Yeongdeungpo 67 0.0855 0.0580 163 Bottom 25% 3 2 < 5 yrs Yes Yeongdeungpo 68 0.0830 0.1016 636 Bottom 25% - 50% 2 1 > 10yrs Yes Yeongdeungpo 69 0.0717 0.0527 1196 Top 25% - 50% 3 2 < 5 yrs Yes Gangseo 70 0.0669 0.0409 1736 Bottom 25% - 50% 3 2 5∼ 10yrs No Yangcheon 71 0.0649 0.0509 3232 Top 25% 4 2 > 10yrs Yes Seocho 72 0.0646 0.0737 259 Bottom 25% - 50% 2 1 5∼ 10yrs Yes Seocho 73 0.0620 0.1077 2230 Top 25% 4 2 < 5 yrs Yes Gangnam 74 0.0538 0.0659 256 Top 25% - 50% 4 1 > 10yrs Yes Yeongdeungpo 75 0.0501 0.0450 3062 Bottom 25% - 50% 3 1 > 10yrs Yes Yeongdeungpo 76 0.0383 0.0599 1632 Bottom 25% - 50% 3 2 > 10yrs Yes Seocho 77 0.0382 0.0813 280 Top 25% 5 2 > 10yrs No Yangcheon 78 0.0272 0.1807 1792 Top 25% - 50% 3 2 > 10yrs Yes Gangnam 79 0.0242 0.0384 1332 Bottom 25% 1 1 > 10yrs Yes Gangnam 80 0.0242 0.0626 275 Bottom 25% - 50% 3 1 > 10yrs Yes Dongjak 81 0.0238 0.0625 524 Bottom 25% 3 1 5∼ 10yrs No Yangcheon 82 0.0218 0.1027 2108 Bottom 25% - 50% 3 1 > 10yrs Yes Seocho 83 0.0208 0.0534 337 Top 25% - 50% 4 2 < 5 yrs Yes Gangseo 84 0.0160 0.2436 832 Bottom 25% - 50% 2 1 > 10yrs No Yangcheon 85 0.0158 0.0339 1504 Top 25% 4 2 > 10yrs Yes Yeongdeungpo 86 0.0095 0.0493 484 Bottom 25% 3 1 > 10yrs Yes Seocho 87 0.0056 0.2432 202 Bottom 25% - 50% 3 1 < 5 yrs Yes Gangseo 165 88 0.0052 0.0733 1644 Bottom 25% 3 1 > 10yrs Yes Yeongdeungpo 89 0.0001 0.1002 632 Top 25% - 50% 4 2 < 5 yrs Yes Gangnam 90 -0.0060 0.0963 484 Top 25% - 50% 4 2 > 10yrs Yes Seocho 91 -0.0221 0.0615 1800 Top 25% 5 2 > 10yrs Yes Seocho 92 -0.0225 0.0295 1476 Bottom 25% 1 1 5∼ 10yrs Yes Seocho 93 -0.0227 0.0416 460 Top 25% - 50% 4 2 5∼ 10yrs Yes Yeongdeungpo 94 -0.0309 0.0377 567 Bottom 25% 3 2 < 5 yrs Yes Dongjak 95 -0.0336 0.0945 1132 Bottom 25% - 50% 3 2 > 10yrs Yes Dongjak 96 -0.0338 0.1179 685 Top 25% - 50% 4 2 > 10yrs Yes Gangnam 97 -0.0339 0.0440 576 Top 25% - 50% 3 1 > 10yrs Yes Yeongdeungpo 98 -0.0388 0.0227 1268 Bottom 25% 3 1 5∼ 10yrs Yes Yeongdeungpo 99 -0.0446 0.0821 1386 Bottom 25% 2 1 > 10yrs Yes Dongjak 100 -0.0573 0.0358 409 Bottom 25% 3 2 < 5 yrs Yes Gangseo 101 -0.0726 0.0813 228 Top 25% 3 2 > 10yrs Yes Seocho 102 -0.0838 0.0843 512 Top 25% - 50% 3 2 < 5 yrs No Yangcheon 103 -0.0856 0.0595 594 Top 25% 5 2 5∼ 10yrs Yes Seocho 104 -0.0876 0.0605 731 Top 25% - 50% 3 2 5∼ 10yrs No Yangcheon 105 -0.0893 0.0697 64 Bottom 25% 2 2 5∼ 10yrs Yes Gangnam 106 -0.0903 0.0376 891 Top 25% - 50% 3 2 > 10yrs Yes Dongjak 107 -0.0921 0.1467 1540 Bottom 25% 3 1 > 10yrs Yes Gangnam 108 -0.1024 0.0567 976 Top 25% 4 2 > 10yrs No Yangcheon 109 -0.1057 0.0498 477 Top 25% 5 2 < 5 yrs Yes Seocho 110 -0.1136 0.0607 488 Top 25% - 50% 3 1 > 10yrs No Yangcheon 111 -0.1150 0.0339 963 Bottom 25% - 50% 3 2 < 5 yrs Yes Yeongdeungpo 112 -0.1233 0.0580 440 Bottom 25% 3 2 5∼ 10yrs Yes Dongjak 113 -0.1238 0.0487 1072 Bottom 25% 3 1 > 10yrs Yes Gangseo 114 -0.1242 0.0646 812 Top 25% - 50% 4 2 > 10yrs Yes Yeongdeungpo 115 -0.1435 0.0530 1016 Top 25% 4 2 5∼ 10yrs Yes Dongjak 116 -0.1474 0.0420 1028 Bottom 25% - 50% 3 2 > 10yrs No Yangcheon 166 117 -0.1553 0.0472 1516 Bottom 25% - 50% 3 2 5∼ 10yrs Yes Gangnam 118 -0.1634 0.0256 1686 Top 25% - 50% 3 2 > 10yrs Yes Seocho 119 -0.1643 0.0500 685 Top 25% - 50% 4 2 > 10yrs Yes Dongjak 120 -0.1717 0.0645 400 Bottom 25% 3 2 5∼ 10yrs Yes Gangseo 121 -0.1920 0.1078 332 Bottom 25% 3 2 < 5 yrs No Gangseo 122 -0.2003 0.0544 260 Top 25% 5 2 < 5 yrs Yes Gangnam 123 -0.2014 0.0762 463 Bottom 25% 3 1 5∼ 10yrs Yes Seocho 124 -0.2141 0.0746 132 Bottom 25% 3 2 5∼ 10yrs Yes Yeongdeungpo 125 -0.2169 0.0367 323 Bottom 25% 3 2 < 5 yrs No Yangcheon 126 -0.2245 0.1132 1237 Bottom 25% 2 1 > 10yrs Yes Gangseo 127 -0.2270 0.0344 1447 Bottom 25% - 50% 3 2 5∼ 10yrs Yes Yeongdeungpo 128 -0.2487 0.0639 180 Top 25% 5 2 5∼ 10yrs Yes Dongjak 129 -0.2540 0.0429 601 Top 25% 5 3 < 5 yrs Yes Seocho 130 -0.2682 0.0444 877 Bottom 25% 3 1 5∼ 10yrs Yes Gangnam 131 -0.2702 0.0552 1250 Top 25% - 50% 3 2 < 5 yrs Yes Yeongdeungpo 132 -0.2711 0.0995 396 Bottom 25% - 50% 3 1 5∼ 10yrs Yes Gangseo 133 -0.2756 0.0446 1244 Top 25% 4 2 > 10yrs Yes Dongjak 134 -0.2802 0.0632 282 Top 25% - 50% 4 2 > 10yrs Yes Gangseo 135 -0.3010 0.1898 1155 Bottom 25% - 50% 3 2 < 5 yrs Yes Gangnam 136 -0.3031 0.0416 628 Bottom 25% 2 1 5∼ 10yrs Yes Gangnam 137 -0.3075 0.1423 1463 Top 25% - 50% 3 2 < 5 yrs Yes Gangnam 138 -0.3865 0.0449 784 Bottom 25% 3 1 > 10yrs No Yangcheon 139 -0.4003 0.1888 132 Bottom 25% 2 1 5∼ 10yrs No Yangcheon 140 -0.4321 0.0486 833 Bottom 25% 3 1 > 10yrs Yes Dongjak 141 -0.5024 0.2278 120 Top 25% 5 2 5∼ 10yrs Yes Yeongdeungpo 142 -0.5619 0.0661 470 Top 25% 4 2 > 10yrs Yes Gangseo Note: Bootstrap standard errors are reported. 167 B.4 The Regression Tree Result 168 Appendix C Supplementary Material for Chapter 4 C.1 The ISP treatment definition This section draws heavily from Field et al. (2009). Information has been reproduced for clarity in understanding of how the iodine treatment variables were defined. Table C.1: ISP Coverage Variation (from Field et al. (2009)) Region District Year 1 Coverage 1 Year 2 Coverage 2 Year 3 Coverage 3 Year 4 Coverage 4 Year 5 Coverage 5 Dodoma Mpwapwa 1990 0.65 1992 0.58 Arusha Monduli 1992 0.71 Arusha Arumera 1991 0.89 Kilimanjaro Rombo 1990 0.68 Mororgoro Ulanga 1988 0.73 1991 0.61 1992 0.34 Ruvuma Songea Rural 1987 0.91 1991 0.74 1995 0.85 Ruvuma Mbinga 1995 0.92 Iringa Mufundi 1986 0.41 1991 0.63 1995 0.54 Iringa Makete 1986 0.2 1991 0.62 1993 0.62 1996 0.49 Iringa Njombe 1989 0.76 1992 0.68 1995 0.64 Iringa Ludewa 1989 0.59 1992 0.62 1995 0.47 Mbeya Chunya 1990 0.49 Mbeya Mebya Rural 1986 0.44 1989 0.84 1990 0.9 1993 0.53 1997 0.53 Mbeya Kyela 1989 0.91 1993 0.57 Mbeya Rungwe 1986 0.35 1990 0.73 1993 0.49 Mbeya Ileja 1989 0.94 1992 0.71 Mbeya Mbozi 1989 0.67 1991 0.63 Rukwa Mpanda 1987 0.79 1991 0.6 1993 0.72 Rukwa Sumbawanga 1987 0.76 1990 0.89 1993 0.72 1996 0.51 Rukwa Nkansi 1987 0.89 1991 0.49 Kigoma Kibondo 1989 0.73 1992 0.75 1996 Kigoma Kasulu 1987 0.5 1990 0.66 1996 0.49 Kigoma Kigoma Rural 1991 0.91 Kagera Karagwe 1990 0.96 1994 0.85 Kagera Bukoba Rural 1994 0.78 Kagera Biharamulo 1990 0.96 1994 0.38 Kagera Ngara 1989 0.29 1994 0.51 169 Calculation of probability of protection: The treated mothers received and iodine dosage of 380 mg via the IOC [Peterson (2000); Peterson et al. (1999)]. However, as described in Field et al. (2009), Wolff (2001), Jun and Jianqun (1985) and Untoro et al. (1998) provide a review of literature that finds that majority of iodine stored in the fatty tissue is depleted rapidly within the first week and an hyperbolic rate thereafter. Following Field et al. (2009), we assume that 85 percent (323) of the 380 mg dose was extracted away immediately within the first month and the depletion followed the simple hyperbolic discounting formula V =A/(1 +kt) after that, where k −1 is the half life of iodine in months. Using the observation from Cao et al. (1994) and Eltom et al. (1985), which use similar dosages of IOC provides full protection for 24 months and that 6.5 mg is the minimum iodine requirement for one full month of protection, Field et al. (2009) calculate the half life to be 3 months. This implied half life is consistent with other studies of the approximate half lives of urine iodine excretion after oral iodine administration to human populations with iodine deficiency (See Wolff (2001)). The probability of protection in a month of the first trimester, therefore, is the probability that the program had started and reached the mother of the child by that month and the stocks of iodine had not depleted to levels insufficient for protection (< 4.2 mg as per Field et al. (2009)) in that month. 1 A child is protected in the first trimester if she is protected throughout weeks 1 to 12 (roughly three months) Based on the information and assumption above, probability of protection from in utero IDD if the child district of birth received the ISP in year t (by month of birth): 1 The 6.5 mg and 4.2 mg figures are calculated based in the recommended daily allowance (RDA) for pregnant women 170 Table C.2: Probability of Protection Year Jan Feb March April May June July Aug Sep Oct Nov Dec Birth year average t 0 0 0 0 0 0 0 0.028 0.083 0.167 0.250 0.333 0.072 t+1 0.417 0.5 0.583 0.667 0.75 0.833 0.917 1 1 1 1 1 0.806 t+2 1 1 1 1 1 1 1 1 1 0.998 0.991 0.977 0.997 t+3 0.955 0.927 0.891 0.849 0.802 0.749 0.69 0.627 0.559 0.488 0.419 0.353 0.668 t+4 0.292 0.237 0.189 0.148 0.112 0.082 0.057 0.037 0.022 0.011 0.004 0.001 0.099 C.2 Alternative Definitions of ISP Exposure Recall that our definition of ISP exposure probability used the variation in the coverage rate across districts and years and the probability of protection based on the availability of adequate amount of iodine in the mother’s body which depends on the relative timings of supplementation and conception. Since we did not have the exact date of supplementation and birth, we assumed that the probability of supplementation and birth are uniform across the year. This assumption can, however, bias our results. We check the robustness of our results to different definitions of ISP exposure in table C.3. The results from the most preferred specification (specification (8) in table 4.2) are reproduced in column (1) for comparison. In column (2), we use the district-year specific coverage rate as the probability of ISP exposure. This avoids biases due to differences in exact date of supplementation. In column (3), we use only the depletion formula for the exposure probability calculation assuming that if a district was treated in a particular year, all individuals from the district received the supplementation. This avoids biases due to measurement and reporting errors in coverage rate. This is the main specification used in Field et. al (2009). In column (4), we use a dummy indicator of whether or not the probability of exposure of an individual was non-zero. The results suggest our findings are robust to the alternative ways of defining ISP treatment. 171 Table C.3: Robustness of ISP Exposure Definition (1) (2) (3) (4) VARIABLES Years of Schooling ISP -0.71*** (0.15) ISP2: coverage only (no depletion) -0.52*** (0.14) ISP3: depletion only (no coverage) -0.55*** (0.13) ISP4: depletion dummy (= 1, if exposed at all) -0.40*** (0.10) Religion dummy YES YES YES YES Tribe dummy YES YES YES YES Livestock Value YES YES YES YES Mean of dependent variable 2.20 2.20 2.20 2.20 Mean ISP treatment probability 0.31 0.80 0.39 Observations 518 518 518 518 R-squared 0.3641 0.3624 0.3633 0.3627 Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. The standard errors are clustered at geoage level where geoage groups are district-year of birth groups. Other controls include a dummy each indicating whether the mother and the father of the child had some education, age, gender and primary enumeration area fixed effects. 172
Abstract (if available)
Abstract
This dissertation deals with two education programs and an urban development plan. Chapter 2 evaluates the education policy change from tracking to mixing system in secondary education in South Korea. In chapter 3, with the supervised machine learning approach, heterogeneity in apartment price premium caused by the new subway transit stations in Seoul are estimated. Chapter 4 explores the dynamics of human capital development, using two programs in Tanzania: Iodine Supplementation Program (ISP) and Primary Education Development Program (PEDP). The key thing that puts three essays into together is that all explicitly study heterogeneity in treatment effects. Especially, chapter 3 takes advantages of supervised machine learning approach based on a regression tree in order to understand multi-dimensional heterogeneity in subway stations’ capitalization effects. Three essays imply that public programs often vary across stakeholders and policymakers should take into account differential treatment effects.
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Chin, Seungwoo
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Three essays in education and urban economics
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College of Letters, Arts and Sciences
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Doctor of Philosophy
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Economics
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06/06/2018
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04/23/2018
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