Assessing the performance of estimators dealing with measurement errors

We describe different procedures to deal with measurement error in linear models and assess their performance in finite samples using Monte Carlo simulations and data on corporate investment. We consider the standard instrumental variable approach proposed by Griliches and Hausman (Journal of Econometrics 31:93–118, 1986) as extended by Biorn (Econometric Reviews 19:391–424, 2000) [OLS-IV], the Arellano and Bond (Review of Economic Studies 58:277–297, 1991) instrumental variable estimator, and the higher-order moment estimator proposed by Erickson and Whited (Journal of Political Economy 108:1027–1057, 2000, Econometric Theory 18:776–799, 2002). Our analysis focuses on characterizing the conditions under which each of these estimators produce unbiased and efficient estimates in a standard “errors-invariables” setting. In the presence of fixed effects, under heteroscedasticity, or in the absence of a very high degree of skewness in the data, the EW estimator is inefficient and returns biased estimates for mismeasured and perfectly measured regressors. In contrast to the EW estimator, IV–type estimators (OLS–IV and AB-GMM) easily handle individual effects, heteroscedastic errors, and different degrees of data skewness. The IV approach, however, requires assumptions about the autocorrelation structure of the mismeasured regressor and the measurement error. We illustrate the application of the different estimators using empirical investment models. Our results show that the EW estimator produces inconsistent results when applied to real-world investment data, while the IV estimators tend to return results that are consistent with theoretical priors.​