This article corresponds to a revised version of the first chapter of my doctoral dissertation, which circulated under the title “Semiparametric estimation of microeconometric models with endogenous regressors and sorting.” I am highly indebted to David Card and Jim Powell for their continuous guidance and support. I would like to thank Ken Chay, Frank Vella, and Juan Pablo Torres-Martínez for helpful discussions and suggestions. This paper has benefited from the comments of Matias Cattaneo, Bryan Graham, Michael Greenstone, Michael Jansson, David Lee, Rob McMillan, Enrico Moretti, Franco Peracchi, Marina Halac, Richard Crump, and seminar participants at UC Berkeley, Concordia University, Universidad de Chile, University of Minnesota, University of Texas-Austin, University of Washington-Seattle, University of Western Ontario, the 2006 North American Summer Meeting of the Econometric Society, and the Sixth Villa Mondragone Workshop in Economic Theory and Econometrics. I gratefully acknowledge financial support from the Institute of Business and Economic Research at the University of California–Berkeley and from the Millennium Science Initiative from the Ministry of Economy, Development and Tourism to Microdata Center, Project NS100041. All errors, however, are my own.
Modeling structural equations with endogenous regressors and heterogeneity through derivative constraints
Article first published online: 12 MAR 2013
Copyright © 2013 Tomás Rau
Volume 4, Issue 1, pages 125–148, March 2013
How to Cite
Rau, T. (2013), Modeling structural equations with endogenous regressors and heterogeneity through derivative constraints. Quantitative Economics, 4: 125–148. doi: 10.3982/QE123
- Issue published online: 12 MAR 2013
- Article first published online: 12 MAR 2013
- Submitted December, 2010. Final version accepted October, 2012.
- Nonparametric regression;
- endogenous regressors;
- control function;
- endogenous treatment;
- returns to schooling
In this paper, I present a general modeling framework for nonparametric models with endogenous regressors and heterogeneity. I show that many existing models in the literature can be derived from a structural equation with unobserved heterogeneity by imposing constancy assumptions on the first and second derivatives. I consider a less restrictive model that imposes constancy assumptions on the second partial derivative of the structural equation. Assuming the existence of suitable instrumental variables, I provide identification results and show that the model can be estimated using a generalized control function approach. I consider an application to the estimation of the returns to education in Chile, exploiting variation across regions and cohorts in educational infrastructure and compulsory schooling laws. Using penalized spline functions to approximate the components of the average structural function, I find that the local average returns to schooling are highly nonlinear and typically underestimated by flexible models that ignore the endogeneity of schooling. I also find evidence of credential effects for high school and college graduates, and limited evidence of comparative advantage bias in the returns to certain levels of education.