Identification and estimation of nonlinear regression models using control functions
Daniel Gutknecht · Warwick Research Archive Portal (University of Warwick) · 2012
According to Blundell and Powell (2003), the development of strategies to identify and estimate certain parameters or even entire functions of regression models under endogeneity has arguably been one of the main contributions of microeconometrics to the statistical literature. The term endogeneity, in this context, refers to a correlation between observable regressor(s) and model unobservable(s), which can arise for multiple reasons such as, among others, omitted variables, measurement error, unobserved heterogeneity, or simultaneous causality. Whereas linear identification and estimation techniques to address endogeneity date back as far as 1928 (Stock and Trebbi, 2003), advances in the field of nonlinear models are much more recent: nonlinear parametric models under endogeneity only came under investigation during the 1970s and 1980s (e.g. Ameniya, 1974; Hansen, 1982), and it was not until the mid 1990s that models of (partially) unknown functional form were considered.