IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/17039.html
   My bibliography  Save this paper

Estimating and Testing Models with Many Treatment Levels and Limited Instruments

Author

Listed:
  • Lance Lochner
  • Enrico Moretti

Abstract

Many empirical microeconomic studies estimate econometric models that assume a single finite-valued discrete endogenous regressor (for example: different levels of schooling), exogenous regressors that are additively separable and enter the equation linearly; and coefficients (including per-unit treatment effects) that are homogeneous in the population. Empirical researchers interested in the causal effect of the endogenous regressor often use instrumental variables. When few valid instruments are available, researchers typically estimate restricted specifications that impose uniform per-unit treatment effects, even when these effects are likely to vary depending on the treatment level. In these cases, ordinary least squares (OLS) and instrumental variables (IV) estimators identify different weighted averages of all per-unit effects, so the traditional Hausman test (based on the restricted specification) is uninformative about endogeneity. Addressing this concern, we develop a new exogeneity test that compares the IV estimate from the restricted model with an appropriately weighted average of all per-unit effects estimated from the more general model using OLS. Notably, our test works even when the true model cannot be estimated using IV methods as long as a single valid instrument is available (e.g. a single binary instrument). We re-visit three recent empirical examples that examine the role of educational attainment on various outcomes to demonstrate the practical value of our test.

Suggested Citation

  • Lance Lochner & Enrico Moretti, 2011. "Estimating and Testing Models with Many Treatment Levels and Limited Instruments," NBER Working Papers 17039, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:17039
    Note: CH ED LS
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w17039.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Pedro Carneiro & James J. Heckman & Edward Vytlacil, 2010. "Evaluating Marginal Policy Changes and the Average Effect of Treatment for Individuals at the Margin," Econometrica, Econometric Society, vol. 78(1), pages 377-394, January.
    2. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    3. Kling, Jeffrey R, 2001. "Interpreting Instrumental Variables Estimates of the Returns to Schooling," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 358-364, July.
    4. James J. Heckman & Lance J. Lochner & Petra E. Todd, 2008. "Earnings Functions and Rates of Return," Journal of Human Capital, University of Chicago Press, vol. 2(1), pages 1-31.
    5. Magne Mogstad & Matthew Wiswall, 2009. "How Linear Models Can Mask Non-Linear Causal Relationships. An Application to Family Size and Children's Education," Discussion Papers 586, Statistics Norway, Research Department.
    6. 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.
    7. Card, David, 1999. "The causal effect of education on earnings," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 30, pages 1801-1863, Elsevier.
    8. Lance Lochner & Enrico Moretti, 2004. "The Effect of Education on Crime: Evidence from Prison Inmates, Arrests, and Self-Reports," American Economic Review, American Economic Association, vol. 94(1), pages 155-189, March.
    9. Yitzhaki, Shlomo, 1996. "On Using Linear Regressions in Welfare Economics," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 478-486, October.
    10. Daron Acemoglu & Joshua Angrist, 2001. "How Large Are Human Capital Externalities? Evidence from Compulsory Schooling Laws," NBER Chapters, in: NBER Macroeconomics Annual 2000, Volume 15, pages 9-74, National Bureau of Economic Research, Inc.
    11. Hungerford, Thomas & Solon, Gary, 1987. "Sheepskin Effects in the Returns to Education," The Review of Economics and Statistics, MIT Press, vol. 69(1), pages 175-177, February.
    12. O. Ashenfelter & D. Card (ed.), 1999. "Handbook of Labor Economics," Handbook of Labor Economics, Elsevier, edition 1, volume 3, number 3.
    13. Park, Jin Heum, 1999. "Estimation of sheepskin effects using the old and the new measures of educational attainment in the Current Population Survey," Economics Letters, Elsevier, vol. 62(2), pages 237-240, February.
    14. Jaeger, David A & Page, Marianne E, 1996. "Degrees Matter: New Evidence on Sheepskin Effects in the Returns to Education," The Review of Economics and Statistics, MIT Press, vol. 78(4), pages 733-740, 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. Hisham S. El-Osta, 2018. "Strategies to Manage Risk and their Role in Impacting Economic Performance among Farm Households," Applied Economics and Finance, Redfame publishing, vol. 5(2), pages 49-64, March.
    2. Blemings, Benjamin T. & Bock, Margaret & Scarcioffolo, Alexandre, 2022. "Hoggin' the Road: Negative Road Externalities of Pork Slaughterhouses," 2022 Annual Meeting, July 31-August 2, Anaheim, California 322466, Agricultural and Applied Economics Association.
    3. Lucija Muehlenbachs & Stefan Staubli & Mark A. Cohen, 2016. "The Impact of Team Inspections on Enforcement and Deterrence," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 3(1), pages 159-204.
    4. Shoya Ishimaru, 2024. "Empirical Decomposition of the IV-OLS Gap with Heterogeneous and Nonlinear Effects," The Review of Economics and Statistics, MIT Press, vol. 106(2), pages 505-520, March.
    5. Mario Fiorini & Katrien Stevens, 2021. "Scrutinizing the Monotonicity Assumption in IV and fuzzy RD designs," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(6), pages 1475-1526, December.
    6. Escanciano, Juan Carlos & Li, Wei, 2021. "Optimal Linear Instrumental Variables Approximations," Journal of Econometrics, Elsevier, vol. 221(1), pages 223-246.
    7. Tymon S{l}oczy'nski, 2018. "Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights," Papers 1810.01576, arXiv.org, revised May 2020.
    8. Tymon Sloczynski, 2018. "A General Weighted Average Representation of the Ordinary and Two-Stage Least Squares Estimands," Working Papers 125, Brandeis University, Department of Economics and International Business School.
    9. Tymon S{l}oczy'nski, 2020. "When Should We (Not) Interpret Linear IV Estimands as LATE?," Papers 2011.06695, arXiv.org, revised Oct 2024.
    10. Cygan-Rehm, Kamila & Wunder, Christoph, 2018. "Do working hours affect health? Evidence from statutory workweek regulations in Germany," Labour Economics, Elsevier, vol. 53(C), pages 162-171.
    11. Francesco Fasani & Tommaso Frattini & Luigi Minale, 2021. "Lift the Ban? Initial Employment Restrictions and Refugee Labour Market Outcomes," Journal of the European Economic Association, European Economic Association, vol. 19(5), pages 2803-2854.
    12. Firmin DOKO TCHATOKA & Jean-Marie DUFOUR, 2016. "Exogeneity Tests, Incomplete Models, Weak Identification and Non-Gaussian Distributions : Invariance and Finite-Sample Distributional Theory," Cahiers de recherche 14-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    13. Katrine V. Løken & Magne Mogstad & Matthew Wiswall, 2012. "What Linear Estimators Miss: The Effects of Family Income on Child Outcomes," American Economic Journal: Applied Economics, American Economic Association, vol. 4(2), pages 1-35, April.
    14. Javier Cano-Urbina & Lance Lochner, 2019. "The Effect of Education and School Quality on Female Crime," Journal of Human Capital, University of Chicago Press, vol. 13(2), pages 188-235.
    15. Gaurab Aryal & Manudeep Bhuller & Fabian Lange, 2022. "Signaling and Employer Learning with Instruments," American Economic Review, American Economic Association, vol. 112(5), pages 1669-1702, May.
    16. Loh, Isaac, 2023. "Nonparametric identification and estimation with discrete instruments and regressors," Journal of Econometrics, Elsevier, vol. 235(2), pages 1257-1279.
    17. Tymon Sloczynski, 2021. "When Should We (Not) Interpret Linear IV Estimands as LATE?," CESifo Working Paper Series 9064, CESifo.
    18. Firmin Doko Tchatoka & Jean-Marie Dufour, 2016. "Exogeneity tests, weak identification, incomplete models and non-Gaussian distributions: Invariance and finite-sample distributional theory," School of Economics and Public Policy Working Papers 2016-01, University of Adelaide, School of Economics and Public Policy.
    19. Kamila Cygam-Rehm & Christoph Wunder, 2018. "Do Working Hours Affect Health? Evidence from Statutory Workweek Regulations in Germany," SOEPpapers on Multidisciplinary Panel Data Research 967, DIW Berlin, The German Socio-Economic Panel (SOEP).
    20. Sergi Jiménez-Martín & Cristina Vilaplana Prieto, 2013. "Informal Care and intergenerational transfers in European Countries," Working Papers 2013-25, FEDEA.
    21. Wossen, Tesfamicheal & Abay, Kibrom A. & Abdoulaye, Tahirou, 2022. "Misperceiving and misreporting input quality: Implications for input use and productivity," Journal of Development Economics, Elsevier, vol. 157(C).
    22. Doko Tchatoka, Firmin & Dufour, Jean-Marie, 2020. "Exogeneity tests, incomplete models, weak identification and non-Gaussian distributions: Invariance and finite-sample distributional theory," Journal of Econometrics, Elsevier, vol. 218(2), pages 390-418.
    23. Shoya Ishimaru, 2021. "What Do We Get from Two-Way Fixed Effects Regressions? Implications from Numerical Equivalence," Papers 2103.12374, arXiv.org, revised Oct 2024.

    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. Lance Lochner & Enrico Moretti, 2011. "Estimating and Testing Non-Linear Models Using Instrumental Variables," University of Western Ontario, Centre for Human Capital and Productivity (CHCP) Working Papers 20112, University of Western Ontario, Centre for Human Capital and Productivity (CHCP).
    2. Pedro Carneiro & Michael Lokshin & Nithin Umapathi, 2017. "Average and Marginal Returns to Upper Secondary Schooling in Indonesia," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(1), pages 16-36, January.
    3. Pedro Carneiro & James J. Heckman & Edward J. Vytlacil, 2011. "Estimating Marginal Returns to Education," American Economic Review, American Economic Association, vol. 101(6), pages 2754-2781, October.
    4. Lance Lochner & Enrico Moretti, 2004. "The Effect of Education on Crime: Evidence from Prison Inmates, Arrests, and Self-Reports," American Economic Review, American Economic Association, vol. 94(1), pages 155-189, March.
    5. Dee, Thomas S., 2004. "Are there civic returns to education?," Journal of Public Economics, Elsevier, vol. 88(9-10), pages 1697-1720, August.
    6. Shoya Ishimaru, 2024. "Empirical Decomposition of the IV-OLS Gap with Heterogeneous and Nonlinear Effects," The Review of Economics and Statistics, MIT Press, vol. 106(2), pages 505-520, March.
    7. Ana Ferrer & W. Craig Riddell, 2008. "Education, credentials, and immigrant earnings," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 41(1), pages 186-216, February.
    8. Hofmarcher, Thomas, 2021. "The effect of education on poverty: A European perspective," Economics of Education Review, Elsevier, vol. 83(C).
    9. Jörn-Steffen Pischke & Till von Wachter, 2008. "Zero Returns to Compulsory Schooling in Germany: Evidence and Interpretation," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 592-598, August.
    10. Gaurab Aryal & Manudeep Bhuller & Fabian Lange, 2022. "Signaling and Employer Learning with Instruments," American Economic Review, American Economic Association, vol. 112(5), pages 1669-1702, May.
    11. Polachek, Solomon W., 2008. "Earnings Over the Life Cycle: The Mincer Earnings Function and Its Applications," Foundations and Trends(R) in Microeconomics, now publishers, vol. 4(3), pages 165-272, April.
    12. Dickson, Matt & Harmon, Colm, 2011. "Economic returns to education: What We Know, What We Don’t Know, and Where We Are Going—Some brief pointers," Economics of Education Review, Elsevier, vol. 30(6), pages 1118-1122.
    13. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
    14. Takahide Yanagi, 2019. "Inference on local average treatment effects for misclassified treatment," Econometric Reviews, Taylor & Francis Journals, vol. 38(8), pages 938-960, September.
    15. Huebener, Mathias & Marcus, Jan, 2017. "Compressing instruction time into fewer years of schooling and the impact on student performance," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 58, pages 1-14.
    16. Katrine V. Løken & Magne Mogstad & Matthew Wiswall, 2012. "What Linear Estimators Miss: The Effects of Family Income on Child Outcomes," American Economic Journal: Applied Economics, American Economic Association, vol. 4(2), pages 1-35, April.
    17. James J. Heckman & Lance J. Lochner & Petra E. Todd, 2008. "Earnings Functions and Rates of Return," Journal of Human Capital, University of Chicago Press, vol. 2(1), pages 1-31.
    18. Heckman, James J. & Humphries, John Eric & Veramendi, Gregory, 2016. "Dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 191(2), pages 276-292.
    19. Domenico Depalo, 2020. "Explaining the causal effect of adherence to medication on cholesterol through the marginal patient," Health Economics, John Wiley & Sons, Ltd., vol. 29(S1), pages 110-126, October.
    20. Pedro Carneiro & Sokbae (Simon) Lee, 2005. "Ability, sorting and wage inequality," CeMMAP working papers CWP16/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • J0 - Labor and Demographic Economics - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:nbr:nberwo:17039. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    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.