Identification without exogeneity under equiconfounding in linear recursive structural systems

Abstract

This chapter obtains identification of structural coefficients in linear recursive systems of structural equations without requiring that observable variables are exogenous or conditionally exogenous. In particular, standard instrumental variables and control variables need not be available in these systems. Instead, we demonstrate that the availability of one or two variables that are equally affected by the unobserved confounder as is the response of interest, along with exclusion restrictions, permits the identification of all the system's structural coefficients. We provide conditions under which equiconfounding supports either full identification of structural coefficients or partial identification in a set consisting of two points.