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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.

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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
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Handle: RePEc:uwo:hcuwoc:20112

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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. Lance Lochner & Enrico Moretti, 2001. "The Effect of Education on Crime: Evidence from Prison Inmates, Arrests, and Self-Reports," NBER Working Papers 8605, National Bureau of Economic Research, Inc.
  2. Heckman, James J. & Lochner, Lance & Todd, Petra E., 2008. "Earnings Functions and Rates of Return," IZA Discussion Papers 3310, Institute for the Study of Labor (IZA).
  3. 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, 01.
  4. Mogstad, Magne & Wiswall, Matthew, 2010. "Linearity in Instrumental Variables Estimation: Problems and Solutions," IZA Discussion Papers 5216, Institute for the Study of Labor (IZA).
  5. Yitzhaki, Shlomo, 1996. "On Using Linear Regressions in Welfare Economics," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 478-86, October.
  6. 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 733-40, November.
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Cited by:
  1. Katrine V. L�ken & 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.
  2. Sergi Jiménez-Martín & Cristina Vilaplana Prieto, 2013. "Informal Care and intergenerational transfers in European Countries," Working Papers 2013-25, FEDEA.

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