We consider a semiparametric transformation model, in which the regression func- tion has an additive nonparametric structure and the transformation of the response is assumed to belong to some parametric family. We suppose that endogeneity is present in the explanatory variables. Using a control function approach, we show that the pro- posed model is identified under suitable assumptions, and propose a profile estimation method for the transformation. The proposed estimator is shown to be asymptotically normal under certain regularity conditions. A simulation study shows that the esti- mator behaves well in practice. Finally, we give an empirical example using the U.K. Family Expenditure Survey.
Causal inference; Semiparametric regression; Transformation models; Profiling; Endogeneity; Instrumental variable; Control function; Additive models;
Ingrid Van Keilegom, and Anne Vanhems, “Semiparametric transformation model with endogeneity: a control function approach”, TSE Working Paper, n. 11-243, May 13, 2011.
Ingrid Van Keilegom, and Anne Vanhems, “Estimation of a semiparametric transformation model in the presence of endogeneity”, TSE Working Paper, n. 16-654, May 2016.
Ingrid Van Keilegom, and Anne Vanhems, “Estimation of a semiparametric transformation model in the presence of endogenety”, Econometric Theory, vol. 35, n. 1, February 2019, pp. 73–110.
Econometric Theory, vol. 35, n. 1, February 2019, pp. 73–110