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. The basic idea of the method is to model the dependence between the variables not observed by the analyst on the observables in a way that allows us to construct a function K such that, conditional on the function, the endogeneity problem (relative to the object of interest) disappears.
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Bibliography
Altonji, J.G., and R.L. Matzkin. 2005. Cross section and panel data estimators for nonseparable models with endogenous regressors. Econometrica 73: 1053–1102.
Basu, A., J.J. Heckman, S. Navarro, and S. Urzua. 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 Unpublished manuscript, Department of Medicine, University of Chicago.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 J. Powell. 2003. Endogeneity in nonparametric and semiparametric regression models. In Advances in economics and econometrics: Theory and applications, eighth world congress, ed. L.P. Hansen, M. Dewatripont, and S.J. Turnovsky, Vol. 2. Cambridge: Cambridge University Press.
Chesher, A. 2003. Identification in nonseparable models. Econometrica 71: 1405–1441.
Cunha, F., J.J. Heckman, and S. Navarro. 2005. Separating uncertainty from heterogeneity in life cycle earnings. Oxford Economic Papers 57: 191–261.
Florens, J.-P., M. Mouchart, and J.M. Rolin. 1990. Elements of Bayesian statistics. New York: M. Dekker.
Florens, J.-P., J.J. Heckman, C. Meghir, and E.J. Vytlacil. 2007. Identification of treatment effects using control functions in models with continuous, endogenous treatment and heterogeneous effects. Unpublished manuscript, Columbia University.
Heckman, J.J. 1979. Sample selection bias as a specification error. Econometrica 47: 153–162.
Heckman, J.J. 1997. Instrumental variables: A study of implicit behavioral assumptions used in making program evaluations. Journal of Human Resources 32: 441–462. Addendum published in 33(1) (1998).
Heckman, J.J., and S. Navarro. 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 R. Robb. 1985. Alternative methods for evaluating the impact of interventions: An overview. Journal of Econometrics 30: 239–267.
Heckman, J.J., and R. Robb. 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: Lawrence Erlbaum Associates, 2000.
Heckman, J.J., and G.L. Sedlacek. 1985. Heterogeneity, aggregation, and market wage functions: An empirical model of self-selection in the labor market. Journal of Political Economy 93: 1077–1125.
Heckman, J.J., and J.A. Smith. 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., and E.J. Vytlacil. 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: 974–987.
Heckman, J.J., L.J. Lochner, and P.E. Todd. 2003. Fifty years of mincer earnings regressions. Technical Report No. 9732. Cambridge, MA: NBER.
Heckman, J.J., S. Urzua, and E.J. Vytlacil. 2006. Understanding instrumental variables in models with essential heterogeneity. Review of Economics and Statistics 88: 389–432.
Imbens, G.W., and W.K. Newey. 2006. Identification and estimation of triangular simultaneous equations models without additivity. Unpublished manuscript, Department of Economics, MIT.
Manski, C.F. 1988. Identification of binary response models. Journal of the American Statistical Association 83: 729–738.
Matzkin, R.L. 1992. Nonparametric and distribution-free estimation of the binary threshold crossing and the binary choice models. Econometrica 60: 239–270.
Matzkin, R.L. 2003. Nonparametric estimation of nonadditive random functions. Econometrica 71: 1393–1375.
Newey, W.K., J.L. Powell, and F. Vella. 1999. Nonparametric estimation of triangular simultaneous equations models. Econometrica 67: 565–603.
Olley, G.S., and A. Pakes. 1996. The dynamics of productivity in the telecommunications equipment industry. Econometrica 64: 1263–1297.
Robinson, P.M. 1988. Root-n-consistent semiparametric regression. Econometrica 56: 931–954.
Roy, A.D. 1951. Some thoughts on the distribution of earnings. Oxford Economic Papers 3: 135–146.
Telser, L.G. 1964. Iterative estimation of a set of linear regression equations. Journal of the American Statistical Association 59: 845–862.
Willis, R.J., and S. Rosen. 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: 129–133.
Wooldridge, J.M. 2003. Further results on instrumental variables estimation of average treatment effects in the correlated random coefficient model. Economics Letters 79: 185–191.
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Navarro, S. (2018). Control Functions. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2262
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DOI: https://doi.org/10.1057/978-1-349-95189-5_2262
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