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Estimating and Testing Non-Linear Models Using Instrumental Variables

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.

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File URL: http://economics.uwo.ca/cibc/workingpapers_docs/wp2011/Lochner_Moretti02.pdf
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Paper provided by University of Western Ontario, CIBC Centre for Human Capital and Productivity in its series University of Western Ontario, CIBC Centre for Human Capital and Productivity Working Papers with number 20112.

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Date of creation: 2011
Date of revision:
Handle: RePEc:uwo:hcuwoc:20112
Contact details of provider: Postal: CIBC Centre for Human Capital and Productivity, Social Science Centre, University of Western Ontario, London, Ontario, Canada N6A 5C2
Phone: 519-661-2111 Ext.85244
Web page: http://economics.uwo.ca/research/research_papers/cibc_workingpapers.html

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  1. Carneiro, Pedro & Heckman, James J. & Vytlacil, Edward, 2009. "Evaluating Marginal Policy Changes and the Average Effect of Treatment for Individuals at the Margin," IZA Discussion Papers 4324, Institute for the Study of Labor (IZA).
  2. 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.
  3. Mogstad, Magne & Wiswall, Matthew, 2010. "Linearity in Instrumental Variables Estimation: Problems and Solutions," IZA Discussion Papers 5216, Institute for the Study of Labor (IZA).
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