Estimation of error correction model with measurement errors

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Effects of measurement errors on the analysis of error correction models (ECMs) of vector processes observed with measurement errors were studied in Hong et al. (2016. Analysis of cointegrated models with measurement errors. Journal of Statistical Computation and Simulation. 2016;86:623–639). It was found that statistically undesirable effects on the analysis attributable to endogeneity in the ECM induced by measurement errors, even in their simplest form. Therefore, we first propose a method using instrumental variables (IV) and derive the asymptotic distributions of the reduced rank estimator that eliminate the undesirable effect of endogeneity. Then, we propose a reduced rank maximum likelihood (ML) estimation using a moving-average term to deal with endogeneity. These methods yield estimators that are consistent and asymptotically unbiased. The first method with IV is simple to use computationally and yields good initial estimate for the second ML method. We investigate the effects of the measurement errors on the proposed methods through a Monte Carlo simulation study.