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Estimation of an Education Production Function under Random Assignment with Selection

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  • Eleanor Jawon Choi
  • Hyungsik Roger Moon
  • Geert Ridder

Abstract

This paper estimates an education production function using data on the College Scholastic Ability Test (CSAT) score and high school characteristics from Seoul, Korea.1 A unique institutional feature of the high school system in Seoul is that on entering high school students are randomly assigned to schools within each school district. The main contribution of our study is to derive a school production function by aggregating the individuals’ potential outcome functions that depend on observed and unobserved school inputs interacted with heterogeneous and unobserved individual abilities. The school production function derived under random assignment and under the assumption that there are no cohort effects has three unique features that have not been considered in previous studies. First, its average (over students) coefficients on school inputs do not differ by school or over time, but by district. This is a consequence of the endogenous sorting of students between districts 2. combined with the random assignment to schools within districts. Second, it allows unobserved school effects to be potentially correlated with observed ones. Third, the weighted average of the district-specific school input effects with weights equal to the fraction of the population in the districts is equal to the average partial effect (APE) of school inputs on individual academic achievement. To estimate the school production function coefficients, we first obtain district-specific coefficients using the fixed effect estimation method in school level panel data for each district and compute the weighted average described above. The empirical findings are (i) the school production function coefficients do differ between districts, which may be due to potentially endogenous sorting of students or unobserved differences in district characteristics, (ii) our estimate of the single-sex school effect is much larger than that found in previous studies most of which assumed constant school input coefficients across districts and did not consider school fixed effects.

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  • Eleanor Jawon Choi & Hyungsik Roger Moon & Geert Ridder, 2014. "Estimation of an Education Production Function under Random Assignment with Selection," Working Paper 9240, USC Lusk Center for Real Estate.
    • Handle: RePEc:luk:wpaper:9240
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    References listed on IDEAS

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    1. Erik Hanushek & Stephen Machin & Ludger Woessmann (ed.), 2011. "Handbook of the Economics of Education," Handbook of the Economics of Education, Elsevier, edition 1, volume 4, number 4, June.
    2. Meghir, Costas & Rivkin, Steven, 2011. "Econometric Methods for Research in Education," Handbook of the Economics of Education, in: Erik Hanushek & Stephen Machin & Ludger Woessmann (ed.), Handbook of the Economics of Education, edition 1, volume 3, chapter 1, pages 1-87, Elsevier.
    3. Patrick Bayer & Fernando Ferreira & Robert McMillan, 2007. "A Unified Framework for Measuring Preferences for Schools and Neighborhoods," Journal of Political Economy, University of Chicago Press, vol. 115(4), pages 588-638, August.
    4. Hyunjoon Park & Jere Behrman & Jaesung Choi, 2013. "Causal Effects of Single-Sex Schools on College Entrance Exams and College Attendance: Random Assignment in Seoul High Schools," Demography, Springer;Population Association of America (PAA), vol. 50(2), pages 447-469, April.
    5. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    6. Kim, Taejong & Lee, Ju-Ho & Lee, Young, 2008. "Mixing versus sorting in schooling: Evidence from the equalization policy in South Korea," Economics of Education Review, Elsevier, vol. 27(6), pages 697-711, December.
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    Cited by:

    1. Cheng Maolin & Jiang Zedi, 2016. "A New Class of Production Function Model and Its Application," Journal of Systems Science and Information, De Gruyter, vol. 4(2), pages 177-185, April.
    2. Soohyung Lee & Lesley J. Turner & Seokjin Woo & Kyunghee Kim, 2014. "All or Nothing? The Impact of School and Classroom Gender Composition on Effort and Academic Achievement," NBER Working Papers 20722, National Bureau of Economic Research, Inc.
    3. Eleanor Jawon Choi & Hyungsik Roger Moon & Geert Ridder, 2019. "Within-District School Lotteries, District Selection, and the Average Partial Effects of School Inputs," Korean Economic Review, Korean Economic Association, vol. 35, pages 275-306.
    4. Dustmann, Christian & Ku, Hyejin & Kwak, Do Won, 2018. "Why Are Single-Sex Schools Successful?," Labour Economics, Elsevier, vol. 54(C), pages 79-99.
    5. Choi, Jaesung & Park, Hyunjoon & Behrman, Jere R., 2015. "Separating boys and girls and increasing weight? Assessing the impacts of single-sex schools through random assignment in Seoul," Social Science & Medicine, Elsevier, vol. 134(C), pages 1-11.
    6. Varughese, Aswathy Rachel & Bairagya, Indrajit, 2021. "Interstate variation in household spending on education in India: Does it influence educational status?," Structural Change and Economic Dynamics, Elsevier, vol. 59(C), pages 405-415.
    7. Seul-Ki Kim & Young-Chul Kim, 2021. "Coed vs Single-Sex Schooling: An Empirical Study on Mental Health Outcomes," Working Papers 2103, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy).

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    More about this item

    Keywords

    education;

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education
    • I23 - Health, Education, and Welfare - - Education - - - Higher Education; Research Institutions

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