On solving endogeneity with invalid instruments: an application to investment equations

Regression models relating investment demand with firms'Tobin's q and cash flow are fraught with measurement errors which, in turn, cause endogeneity bias. We propose an alternative solution to this problem based on modelling the interaction between the endogenous Tobin's q and the error term in the investment equation as a function of lagged values of Tobin's q. We then study the identification conditions and asymptotic properties of the resulting estimator. Our analysis of a panel of US firms reveals a larger effect of Tobin's q on firms' investment demand than that obtained by using available estimators in the literature. Moreover, the estimates highlight the importance of cash flow. We find mixed evidence on the relationship between investment demand and firms' cash flow with respect to different measures of financial constraints. Nevertheless, this evidence is more supportive of the view that firms' cash flows have a weaker correlation to investment demand when financial conditions tighten.