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Estimating and Testing Non-Linear Models Using Instrumental Variables

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Abstract
In many empirical studies, researchers seek to estimate causal relationships using instrumental variables. When only one valid instrumental variable is available, researchers are limited to estimating linear models, even when the true model may be non-linear. In this case, ordinary least squares and instrumental variable estimators will identify different weighted averages of the underlying marginal causal effects even in the absence of endogeneity. As such, the traditional Hausman test for endogeneity is uninformative. We build on this insight to develop a new test for endogeneity that is robust to any form of non-linearity. Notably, our test works well even when only a single valid instrument is available. This has important practical applications, since it implies that researchers can estimate a completely unrestricted non-linear model by OLS, and then use our test to establish whether those OLS estimates are consistent. We re-visit a few recent empirical examples to show how the test can be used to shed new light on the role of non-linearity.

Suggested Citation

  • 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).
    • Handle: RePEc:uwo:hcuwoc:20112
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    File URL: https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=1064&context=economicscibc
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    Cited by:

    1. Johnston, David W. & Lordan, Grace & Shields, Michael A. & Suziedelyte, Agne, 2015. "Education and health knowledge: Evidence from UK compulsory schooling reform," Social Science & Medicine, Elsevier, vol. 127(C), pages 92-100.
    2. Sergi Jiménez-Martín & Cristina Vilaplana Prieto, 2013. "Informal Care and intergenerational transfers in European Countries," Working Papers 2013-25, FEDEA.
    3. Gibbons Charles E. & Suárez Serrato Juan Carlos & Urbancic Michael B., 2019. "Broken or Fixed Effects?," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-12, January.
    4. 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.
    5. Dieterle, Steven G. & Snell, Andy, 2016. "A simple diagnostic to investigate instrument validity and heterogeneous effects when using a single instrument," Labour Economics, Elsevier, vol. 42(C), pages 76-86.

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