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Title: An approach to the errors-in-variables regression model Authors:  Taku Yamamoto - Institute of Statistical Research (Japan) [presenting]
Makoto Muto - Hitotsubashi University (Japan)
Teruo Nakatsuma - Keio University (Japan)
Abstract: Various methods have been proposed in order to handle the errors-in-variables regression model where its explanatory variable contains a measurement error. A relatively mild condition will be assumed. Namely, the explanatory variable is assumed to be positively auto-correlated. This condition is satisfied in most economic time series. It is well known that the ordinary least squares estimator of the errors-in-variables model is asymptotically biased (inconsistent). The first purpose is to show that, when the (latent) explanatory variable is positively auto-correlated, the temporal aggregation of the model decreases the asymptotic bias and the mean squared error of the ordinary least squares estimator. However, the temporal aggregation cannot completely eliminate the asymptotic bias. The second purpose is to propose a convenient consistent estimator which suitably combines two biased estimators. It can be regarded as an alternative instrumental variable estimator. The suitably designed Monte Carlo experiments show the effectiveness of temporal aggregation in small samples, and that the proposed combined estimator is superior to the previously proposed consistent estimators. Finally, the proposed method is applied for testing the Fisher equation in Japanese economy.