Included and Excluded Instruments in Structural Estimation
Paper joint with Nano Barahona, Matthew Gentzkow, Ashesh Rambachan, and Jesse M. Shapiro
Abstract: We consider the choice of instrumental variables when a researcher’s structural model may be misspecified. We contrast included instruments, which have a direct causal effect on the outcome holding constant the endogenous variable of interest, with excluded instruments, which do not. We show conditions under which the researcher’s estimand maintains an interpretation in terms of causal effects of the endogenous variable under excluded instruments but not under included instruments. We apply our framework to estimation of a linear instrumental variables model, and of differentiated goods demand models under price endogeneity. We show that the distinction between included and excluded instruments is quantitatively important in simulations based on an application. We extend our results to a dynamic setting by studying estimation of production function parameters under input endogeneity.