IDEAS home Printed from https://ideas.repec.org/a/ucp/jpolec/doi10.1086-736768.html

Rationed Fertility: Treatment Effect Heterogeneity in the Child Quantity-Quality Trade-Off

Author

Listed:
  • Rufei Guo
  • Junjian Yi
  • Junsen Zhang
  • Ning Zhang

Abstract

We develop a generalized theory of rationed fertility to analyze treatment effect heterogeneity in the child quantity-quality trade-off. An exogenous increase in fertility can be either desired or undesired. We derive a positive rationing income effect on child quality for desired fertility increases but a negative rationing income effect for undesired fertility increases. We propose an econometric framework to identify treatment effects of desired and undesired fertility increases and estimate a structural model to gauge the quantitative importance of the novel rationing income effect. Our study highlights the importance of distinguishing between desired and undesired changes when evaluating social programs.

Suggested Citation

  • Rufei Guo & Junjian Yi & Junsen Zhang & Ning Zhang, 2025. "Rationed Fertility: Treatment Effect Heterogeneity in the Child Quantity-Quality Trade-Off," Journal of Political Economy, University of Chicago Press, vol. 133(10), pages 3349-3386.
  • Handle: RePEc:ucp:jpolec:doi:10.1086/736768
    DOI: 10.1086/736768
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1086/736768
    Download Restriction: Access to the online full text or PDF requires a subscription.

    File URL: http://dx.doi.org/10.1086/736768
    Download Restriction: Access to the online full text or PDF requires a subscription.

    File URL: https://libkey.io/10.1086/736768?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2008. "Instrumental Variables in Models with Multiple Outcomes: The General Unordered Case," Annals of Economics and Statistics, GENES, issue 91-92, pages 151-174.
    2. James Tobie & H. S. Houthakker, 1950. "The Effects of Rationing on Demand Elasticities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 18(3), pages 140-153.
    3. Rosenzweig, Mark R. & Paul Schultz, T., 1987. "Fertility and investments in human capital : Estimates of the consequence of imperfect fertility control in Malaysia," Journal of Econometrics, Elsevier, vol. 36(1-2), pages 163-184.
    4. Junsen Zhang, 2017. "The Evolution of China's One-Child Policy and Its Effects on Family Outcomes," Journal of Economic Perspectives, American Economic Association, vol. 31(1), pages 141-160, Winter.
    5. Sokbae Lee & Bernard Salanié, 2018. "Identifying Effects of Multivalued Treatments," Econometrica, Econometric Society, vol. 86(6), pages 1939-1963, November.
    6. Heckman, James J. & Urzúa, Sergio, 2010. "Comparing IV with structural models: What simple IV can and cannot identify," Journal of Econometrics, Elsevier, vol. 156(1), pages 27-37, May.
    7. James J. Heckman, 2010. "Building Bridges between Structural and Program Evaluation Approaches to Evaluating Policy," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 356-398, June.
    8. Jonathan Gruber & Phillip Levine & Douglas Staiger, 1999. "Abortion Legalization and Child Living Circumstances: Who is the "Marginal Child"?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(1), pages 263-291.
    9. J.J. Heckman & E.E. Leamer (ed.), 2007. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 6, number 6a.
    10. Sandra E. Black & Paul J. Devereux & Kjell G. Salvanes, 2005. "The More the Merrier? The Effect of Family Size and Birth Order on Children's Education," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(2), pages 669-700.
    11. Mark R. Rosenzweig & Junsen Zhang, 2009. "Do Population Control Policies Induce More Human Capital Investment? Twins, Birth Weight and China's "One-Child" Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 1149-1174.
    12. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    13. Gary S. Becker & H. Gregg Lewis, 1974. "Interaction between Quantity and Quality of Children," NBER Chapters, in: Economics of the Family: Marriage, Children, and Human Capital, pages 81-90, National Bureau of Economic Research, Inc.
    14. Sandra E. Black & Paul J. Devereux & Kjell G. Salvanes, 2010. "Small Family, Smart Family? Family Size and the IQ Scores of Young Men," Journal of Human Resources, University of Wisconsin Press, vol. 45(1).
    15. Christian N. Brinch & Magne Mogstad & Matthew Wiswall, 2017. "Beyond LATE with a Discrete Instrument," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 985-1039.
    16. David de la Croix & Matthias Doepke, 2003. "Inequality and Growth: Why Differential Fertility Matters," American Economic Review, American Economic Association, vol. 93(4), pages 1091-1113, September.
    17. Patrick Kline & Christopher R. Walters, 2016. "Evaluating Public Programs with Close Substitutes: The Case of HeadStart," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(4), pages 1795-1848.
    18. Heckman, James J & Walker, James R, 1990. "The Third Birth in Sweden," Journal of Population Economics, Springer;European Society for Population Economics, vol. 3(4), pages 235-275, December.
    19. Hongbin Li & Junsen Zhang & Yi Zhu, 2008. "The quantity-Quality trade-Off of children In a developing country: Identification using chinese twins," Demography, Springer;Population Association of America (PAA), vol. 45(1), pages 223-243, February.
    20. Wei Huang, 2017. "How does the one child policy impact social and economic outcomes?," World of Labour, LISER, pages 387-387, September.
    21. Elizabeth Oltmans Ananat & Daniel M. Hungerman, 2012. "The Power of the Pill for the Next Generation: Oral Contraception's Effects on Fertility, Abortion, and Maternal and Child Characteristics," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 37-51, February.
    22. J.J. Heckman & E.E. Leamer (ed.), 2007. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 6, number 6b.
    23. Seshadri, Ananth & Zhou, Anson, 2022. "Intergenerational mobility begins before birth," Journal of Monetary Economics, Elsevier, vol. 129(C), pages 1-20.
    24. Hai-Anh H. Dang & F. Halsey Rogers, 2016. "The Decision to Invest in Child Quality over Quantity: Household Size and Household Investment in Education in Vietnam," The World Bank Economic Review, World Bank, vol. 30(1), pages 104-142.
    25. David N. Weil & Oded Galor, 2000. "Population, Technology, and Growth: From Malthusian Stagnation to the Demographic Transition and Beyond," American Economic Review, American Economic Association, vol. 90(4), pages 806-828, September.
    26. Haoming Liu, 2014. "The quality–quantity trade-off: evidence from the relaxation of China’s one-child policy," Journal of Population Economics, Springer;European Society for Population Economics, vol. 27(2), pages 565-602, April.
    27. Jesper Bagger & Javier A Birchenall & Hani Mansour & Sergio Urzúa, 2021. "Education, Birth Order and Family Size [Family size and children’s education in Vietnam]," The Economic Journal, Royal Economic Society, vol. 131(633), pages 33-69.
    28. Elizabeth Oltmans Ananat & Jonathan Gruber & Phillip B. Levine & Douglas Staiger, 2009. "Abortion and Selection," The Review of Economics and Statistics, MIT Press, vol. 91(1), pages 124-136, February.
    29. Joshua Angrist & Victor Lavy & Analia Schlosser, 2010. "Multiple Experiments for the Causal Link between the Quantity and Quality of Children," Journal of Labor Economics, University of Chicago Press, vol. 28(4), pages 773-824, October.
    30. Wanchuan Lin & Juan Pantano & Shuqiao Sun, 2020. "Birth order and unwanted fertility," Journal of Population Economics, Springer;European Society for Population Economics, vol. 33(2), pages 413-440, April.
    31. Wei Huang & Xiaoyan Lei & Yaohui Zhao, 2016. "One-Child Policy and the Rise of Man-Made Twins," The Review of Economics and Statistics, MIT Press, vol. 98(3), pages 467-476, July.
    32. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    33. Neary, J. P. & Roberts, K. W. S., 1980. "The theory of household behaviour under rationing," European Economic Review, Elsevier, vol. 13(1), pages 25-42, January.
    34. James Heckman & Neil Hohmann & Jeffrey Smith & Michael Khoo, 2000. "Substitution and Dropout Bias in Social Experiments: A Study of an Influential Social Experiment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 115(2), pages 651-694.
    35. Tiago Cavalcanti & Georgi Kocharkov & Cezar Santos, 2021. "Family Planning and Development: Aggregate Effects of Contraceptive Use," The Economic Journal, Royal Economic Society, vol. 131(634), pages 624-657.
    36. Gary S. Becker & Robert J. Barro, 1988. "A Reformulation of the Economic Theory of Fertility," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(1), pages 1-25.
    37. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    38. Wei Huang & Xiaoyan Lei & Ang Sun, 2021. "Fertility Restrictions and Life Cycle Outcomes: Evidence from the One-Child Policy in China," The Review of Economics and Statistics, MIT Press, vol. 103(4), pages 694-710, October.
    39. Shareen Joshi & T. Schultz, 2013. "Family Planning and Women’s and Children’s Health: Long-Term Consequences of an Outreach Program in Matlab, Bangladesh," Demography, Springer;Population Association of America (PAA), vol. 50(1), pages 149-180, February.
    40. Nancy Qian, 2009. "Quantity-Quality and the One Child Policy:The Only-Child Disadvantage in School Enrollment in Rural China," NBER Working Papers 14973, National Bureau of Economic Research, Inc.
    41. Rosenzweig, Mark R & Wolpin, Kenneth I, 1980. "Testing the Quantity-Quality Fertility Model: The Use of Twins as a Natural Experiment," Econometrica, Econometric Society, vol. 48(1), pages 227-240, January.
    42. James J. Heckman, 1991. "Randomization and Social Policy Evaluation Revisited," NBER Technical Working Papers 0107, National Bureau of Economic Research, Inc.
    43. Yi Chen & Yingfei Huang, 2020. "The power of the government: China's Family Planning Leading Group and the fertility decline of the 1970s," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 42(35), pages 985-1038.
    44. repec:adr:anecst:y:2008:i:91-92:p:08 is not listed on IDEAS
    45. James J. Heckman & Rodrigo Pinto, 2018. "Unordered Monotonicity," Econometrica, Econometric Society, vol. 86(1), pages 1-35, January.
    46. Magne Mogstad & Matthew Wiswall, 2016. "Testing the quantity–quality model of fertility: Estimation using unrestricted family size models," Quantitative Economics, Econometric Society, vol. 7(1), pages 157-192, March.
    47. Hanushek, Eric A, 1992. "The Trade-Off between Child Quantity and Quality," Journal of Political Economy, University of Chicago Press, vol. 100(1), pages 84-117, February.
    48. Heckman, James J & Walker, James R, 1990. "The Relationship between Wages and Income and the Timing and Spacing of Births: Evidence from Swedish Longitudinal Data," Econometrica, Econometric Society, vol. 58(6), pages 1411-1441, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jin, Wenchao & Jin, Zhangfeng, 2026. "Migration Reform and Fertility: Evidence from Rural China," GLO Discussion Paper Series 1718, Global Labor Organization (GLO).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Damian Clarke, 2018. "Children And Their Parents: A Review Of Fertility And Causality," Journal of Economic Surveys, Wiley Blackwell, vol. 32(2), pages 518-540, April.
    2. Oliveira, Jaqueline, 2016. "The value of children: Inter-generational support, fertility, and human capital," Journal of Development Economics, Elsevier, vol. 120(C), pages 1-16.
    3. Ea Hoppe Blaabæk & Mads Meier Jæger & Joseph Molitoris, 2020. "Family Size and Educational Attainment: Cousins, Contexts, and Compensation," European Journal of Population, Springer;European Association for Population Studies, vol. 36(3), pages 575-600, July.
    4. Li, Honghui & Hiwatari, Masato, 2020. "Family Size and Educational Attainment : The Case of China," Discussion paper series. A 353, Graduate School of Economics and Business Administration, Hokkaido University.
    5. Mogstad, Magne & Torgovitsky, Alexander, 2024. "Instrumental variables with unobserved heterogeneity in treatment effects," Handbook of Labor Economics,, Elsevier.
    6. Jingdong Zhong & Jingjing Gao & Chengfang Liu & Jie Huang & Renfu Luo, 2019. "Quantity–Quality Trade-Off and Early Childhood Development in Rural Family: Evidence from China’s Guizhou Province," IJERPH, MDPI, vol. 16(7), pages 1-29, April.
    7. Guo, Rufei & Yi, Junjian & Zhang, Junsen, 2017. "Family size, birth order, and tests of the quantity–quality model," Journal of Comparative Economics, Elsevier, vol. 45(2), pages 219-224.
    8. Timothy J. Hatton, 2015. "Stature and Sibship: Historical Evidence," CEH Discussion Papers 039, Centre for Economic History, Research School of Economics, Australian National University.
    9. Shuxi Zeng & Fan Li & Peng Ding, 2020. "Is being an only child harmful to psychological health?: evidence from an instrumental variable analysis of China's one‐child policy," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1615-1635, October.
    10. Chen, Qihui, 2021. "Population policy, family size and child malnutrition in Vietnam – Testing the trade-off between child quantity and quality from a child nutrition perspective," Economics & Human Biology, Elsevier, vol. 41(C).
    11. Jaqueline Oliveira, 2019. "Birth order and the gender gap in educational attainment," Review of Economics of the Household, Springer, vol. 17(3), pages 775-803, September.
    12. Christian N. Brinch & Magne Mogstad & Matthew Wiswall, 2017. "Beyond LATE with a Discrete Instrument," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 985-1039.
    13. Wang, Xuebo & Zhang, Junsen, 2018. "Beyond the Quantity–Quality tradeoff: Population control policy and human capital investment," Journal of Development Economics, Elsevier, vol. 135(C), pages 222-234.
    14. Jia, Nan & Zhou, Ying & Yang, Tianchi, 2021. "“Selective two-child” policy and household resource allocation," China Economic Review, Elsevier, vol. 68(C).
    15. Christina J. Diaz & Jeremy E. Fiel, 2021. "When Size Matters: IV Estimates of Sibship Size on Educational Attainment in the U.S," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 40(6), pages 1195-1220, December.
    16. Claude Diebolt & Faustine Perrin, 2013. "From Stagnation to Sustained Growth: The Role of Female Empowerment," American Economic Review, American Economic Association, vol. 103(3), pages 545-549, May.
    17. Chinhui Juhn & Yona Rubinstein & C. Andrew Zuppann, 2015. "The Quantity-Quality Trade-off and the Formation of Cognitive and Non-cognitive Skills," NBER Working Papers 21824, National Bureau of Economic Research, Inc.
    18. Liang, Yun & Gibson, John, 2018. "Do siblings take your food away? Using China's one-child policy to test for child quantity-quality trade-offs," China Economic Review, Elsevier, vol. 48(C), pages 14-26.
    19. Dong, Xinwei, 2020. "Effect of birth interval on the first child’s nutrition status: Evidence from China," Labour Economics, Elsevier, vol. 67(C).
    20. Chen, Qihui, 2017. "Relaxed population policy, family size and parental investments in children’s education in rural Northwestern China," International Journal of Educational Development, Elsevier, vol. 54(C), pages 39-50.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ucp:jpolec:doi:10.1086/736768. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Journals Division (email available below). General contact details of provider: https://www.journals.uchicago.edu/JPE .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.