Abstract
The control function approach is an econometric method used to correct for biases that arise as a consequence of selection and/or endogeneity. It is the leading approach for dealing with selection bias in the correlated random coefficients model (see Heckman and Robb, 1985; 1986; Heckman and Vytlacil, 1998; Wooldridge, 1997; 2003; Heckman and Navarro, 2004), but it can be applied in more general semiparametric settings (see Newey, Powell and Vella, 1999; Altonji and Matzkin, 2005; Chesher, 2003; Imbens and Newey, 2006; Florens et al, 2007).
Keywords
- Instrumental Variable
- Control Function
- Endogeneity Problem
- Average Treatment Effect
- Semiparametric Regression
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Altonji, J.G. and Matzkin, R.L. 2005. Cross section and panel data estimators for nonseparable models with endogenous regressors. Econometrica 73, 1053–102.
Basu, A., Heckman, J.J., Navarro, S. and Urzua, S. 2006. Use of instrumental variables in the presence of heterogeneity and self-selection: an application in breast cancer patients. Unpublished manuscript, Department of Medicine, University of Chicago.
Blundell, R. and Powell, J. 2003. Endogeneity in nonparametric and semiparametric regression models. In Advances in Economics and Econometrics: Theory and Applications, Eighth World Congress, vol. 2, ed. L.P. Hansen, M. Dewatripont and S.J. Turnovsky. Cambridge: Cambridge University Press.
Chesher, A. 2003. Identification in nonseparable models. Econometrica 71, 1405–41.
Cunha, E, Heckman, J.J. and Navarro, S. 2005. Separating uncertainty from heterogeneity in life cycle earnings. Oxford Economic Papers 57, 191–261.
Florens, J.-P., Heckman, J.J., Meghir, C. and Vytlacil, E.J. 2007. Identification of treatment effects using control functions in models with continuous, endogenous treatment and heterogeneous effects. Unpublished manuscript, Columbia University.
Florens, J.-P., Mouchart, M. and Rolin, J.M. 1990. Elements of Bayesian Statistics. New York: M. Dekker.
Heckman, J.J. 1979. Sample selection bias as a specification error. Econometrica 47, 153–62.
Heckman, J.J. 1997. Instrumental variables: a study of implicit behavioral assumptions used in making program evaluations. Journal of Human Resources 32, 441–62. Addendum published in 33(1) (1998).
Heckman, J.J., Lochner, L.J. and Todd, P.E. 2003. Fifty years of Mincer earnings regressions. Technical Report No. 9732. Cambridge, MA: NBER.
Heckman, J.J. and Navarro, S. 2004. Using matching, instrumental variables, and control functions to estimate economic choice models. Review of Economics and Statistics 86, 30–57.
Heckman, J.J. and Robb, R. 1985. Alternative methods for evaluating the impact of interventions: an overview. Journal of Econometrics 30, 239–67.
Heckman, J.J. and Robb, R. 1986. Alternative methods for solving the problem of selection bias in evaluating the impact of treatments on outcomes. In Drawing Inferences from Self-Selected Samples, ed. H. Wainer. New York: Springer. Repr. Mahwah, NJ: Lawrence Erlbaum Associates, 2000.
Heckman, J.J. and Sedlacek, G.L. 1985. Heterogeneity, aggregation, and market wage functions: an empirical model of self-selection in the labor market. Journal of Political Economy 93, 1077–125.
Heckman, J.J. and Smith, J.A. 1998. Evaluating the welfare state. In Econometrics and Economic Theory in the Twentieth Century: The Ragnar Frisch Centennial Symposium, ed. S. Strom. New York: Cambridge University Press.
Heckman, J.J., Urzua, S. and Vytlacil, E.J. 2006. Understanding instrumental variables in models with essential heterogeneity. Review of Economics and Statistics 88, 389–132.
Heckman, J.J. and Vytlacil, E.J. 1998. Instrumental variables methods for the correlated random coefficient model: estimating the average rate of return to schooling when the return is correlated with schooling. Journal of Human Resources 33, 974–87.
Imbens, G.W. and Newey, W.K. 2006. Identification and estimation of triangular simultaneous equations models without additivity Unpublished manuscript, Department of Economics, MIT.
Manski, CF. 1988. Identification of binary response models. Journal of the American Statistical Association 83, 729–38.
Matzkin, R.L. 1992. Nonparametric and distribution-free estimation of the binary threshold crossing and the binary choice models. Econometrica 60, 239–70.
Matzkin, R.L. 2003. Nonparametric estimation of nonadditive random functions. Econometrica 71, 1393–75.
Newey, W.K., Powell, J.L. and Vella, F. 1999. Nonparametric estimation of triangular simultaneous equations models. Econometrica 67, 565–603.
Olley, G.S. and Pakes, A. 1996. The dynamics of productivity in the telecommunications equipment industry. Econometrica 64, 1263–97.
Robinson, P.M. 1988. Root-n-consistent semiparametric regression. Econometrica 56, 931–54.
Roy, A.D. 1951. Some thoughts on the distribution of earnings. Oxford Economic Papers 3, 135–46.
Telser, L.G. 1964. Iterative estimation of a set of linear regression equations. Journal of the American Statistical Association 59, 845–62.
Willis, R.J. and Rosen, S. 1979. Education and self-selection. Journal of Political Economy 87(5, Par 2), S7–S36.
Wooldridge, J.M. 1997. On two stage least squares estimation of the average treatment effect in a random coefficient model. Economics Letters 56, 129–33.
Wooldridge, J.M. 2003. Further results on instrumental variables estimation of average treatment effects in the correlated random coefficient model. Economics Letters 79, 185–91.
Editor information
Editors and Affiliations
Copyright information
© 2010 Palgrave Macmillan, a division of Macmillan Publishers Limited
About this chapter
Cite this chapter
Navarro, S. (2010). Control Functions. In: Durlauf, S.N., Blume, L.E. (eds) Microeconometrics. The New Palgrave Economics Collection. Palgrave Macmillan, London. https://doi.org/10.1057/9780230280816_4
Download citation
DOI: https://doi.org/10.1057/9780230280816_4
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-0-230-23881-7
Online ISBN: 978-0-230-28081-6
eBook Packages: Palgrave Media & Culture CollectionLiterature, Cultural and Media Studies (R0)