Linear Panel Regression Models with Non-Classical Measurement Errors: An Application to Investment Equations

This paper proposes a new minimum distance estimator for linear panel regression models with measurement error and analyzes its theoretical properties. The model considered is more general than examined in the literature in that (i) measurement error is non-classical in the sense it is allowed to be correlated with true regressors, and (ii) measurement error and idiosyncratic error can be serially correlated. Notably, the proposed estimator does not require any instrumental variables to deal with the endogeneity. The finite sample evidence confirms that the proposed estimator has desirable performance. We revisit the investment model and theoretically illustrate that measurement error is negatively correlated with Tobin's marginal $q$, which is empirically supported by applying the proposed method to US manufacturing firm data for the period 2002-2016. Furthermore, we find that there is a structural break in 2008 and cash flow is insignificant before 2007 but becomes significant after 2009.