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Estimating and Testing Models with Many Treatment Levels and Limited Instruments

Author

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  • Lance Lochner

    () (University of Western Ontario and NBER)

  • Enrico Moretti

    (University of California-Berkeley, NBER, CEPR, and IZA)

Abstract

Empirical researchers interested in the causal effect of the endogenous regressor often use instrumental variables. When few valid instruments are available, they typically estimate restricted specifications that impose uniform per unit treatment effects, even when these effects are likely to vary. We show that in these cases, ordinary least squares and instrumental variables estimators identify different weighted averages of all per unit effects, so the traditional Hausman test is uninformative about endogeneity. We develop a new exogeneity test that works even when the true model cannot be estimated using IV methods as long as a single valid instrument is available. We revisit three recent empirical examples to demonstrate the practical value of our test. © 2015 The President and Fellows of Harvard College and the Massachusetts Institute of Technology

Suggested Citation

  • Lance Lochner & Enrico Moretti, 2015. "Estimating and Testing Models with Many Treatment Levels and Limited Instruments," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 387-397, May.
  • Handle: RePEc:tpr:restat:v:97:y:2015:i:2:p:387-397
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    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. Mogstad, Magne & Wiswall, Matthew, 2009. "How Much Should We Trust Linear Instrumental Variables Estimators? An Application to Family Size and Children's Education," IZA Discussion Papers 4562, Institute of Labor Economics (IZA).
    6. Mogstad, Magne & Wiswall, Matthew, 2009. "How Much Should We Trust Linear Instrumental Variables Estimators? An Application to Family Size and Children's Education," IZA Discussion Papers 4562, Institute of Labor Economics (IZA).
    7. 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.
    8. 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.
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    Citations

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    Cited by:

    1. Kamila Cygan-Rehm & Christoph Wunder, 2018. "Do Working Hours Affect Health? Evidence from Statutory Workweek Regulations in Germany," CESifo Working Paper Series 7098, CESifo Group Munich.
    2. 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.
    3. 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).
    4. repec:eee:labeco:v:53:y:2018:i:c:p:162-171 is not listed on IDEAS
    5. 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 Working Papers 2016-01, University of Adelaide, School of Economics.
    6. Javier Cano-Urbina & Lance Lochner, 2016. "The Effect of Education and School Quality on Female Crime," University of Western Ontario, Centre for Human Capital and Productivity (CHCP) Working Papers 20163, University of Western Ontario, Centre for Human Capital and Productivity (CHCP).
    7. 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.
    8. Sergi Jiménez-Martín & Cristina Vilaplana Prieto, 2013. "Informal Care and intergenerational transfers in European Countries," Working Papers 2013-25, FEDEA.

    More about this item

    Keywords

    empirical; causal effect; endogenous regressor; per unit effects; endogeneity;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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