Measurement error in multiple equations: Tobin’s q and corporate investment, saving, and debt

Abstract

We characterize the sharp identification regions for the coefficients in a system of linear equations that share an explanatory variable measured with classical error. We demonstrate the identification gain from analyzing the equations jointly. We derive the sharp identification regions under any configuration of three auxiliary assumptions. These restrict the “noise-to-signal” ratio, the coefficients of determination, and the signs of the correlations among the cross-equation disturbances. For inference, we implement results on intersection bounds. The application studies the effects of cash flow on the investment, saving, and debt of firms when Tobin’s q serves as a proxy for marginal q.