Control variables, discrete instruments, and identification of structural functions - Whitney K. Newey; Sami Stouli (Centre for Microdata Methods and Practice (cemmap), 2018)
Control variables provide an important means of controlling for endogeneity in econometric models with nonseparable and/or multidimensional heterogeneity. We allow for discrete instruments, giving identi cation results under a variety of restrictions on the way the endogenous variable and the control variables affect the outcome. We consider many structural objects of interest, such as average or quantile treatment effects. We illustrate our results with an empirical application to Engel curve estimation.
Keywords: C14; C31; C35; 330; Control variables; discrete instruments; structural functions; endogeneity; partially parametric; nonseparable models; identification