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

This paper proposes a minimum distance (MD) estimator to estimate panel regression models with measurement error. The model considered is more general than examined in the literature in that (i) measurement error can be non-classical in the sense that they are allowed to be correlated with the true regressors, and (ii) serially correlated measurement error and idiosyncratic error are allowed. We estimate such a model by applying the covariance structure analysis, which does not require any instrumental variables to deal with the endogeneity caused by measurement error. The asymptotic properties of our MD estimator are established, which is non-trivial because an identification issue must be solved. Since our approach estimates the variances and covariances of latent variables as well as the coefficient of regressors, we can directly test, for instance, whether the measurement error are correlated with the true regressors. Monte Carlo simulation is conducted to investigate the finite sample performance and confirm that the proposed estimator has desirable performance. We apply the proposed method to estimate an investment equation for 2002-2016 and find that (i) there is a structural break between 2007 and 2008, (ii) Tobin's marginal $q$ is strongly significant, and (iii) cash flow is not significant before 2007, but tends to be significant after 2009 indicating increased investment-cash flow sensitivity, (iv) measurement error and idiosyncratic error are serially correlated, (v) measurement error is significantly negatively correlated with the marginal $q$, and hence non-classical measurement error