Measurement Error

# Measurement Error - Measurement Error Consistent Estimators...

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Measurement Error Consistent Estimators Y t = t + U t ; where 2 R 1 , EU 2 t = ± 2 U . We observe Y t and the contaminated regressor X c;t = X t + V t ; where EV t = 0 , EV 2 t = ± 2 V and U t is independent of V t . 1 The OLS estimator of Y t = c;t + U t t ; (0.1) equals B = P n t =1 Y t X c;t P n t =1 X 2 c;t : To keep within the familiar framework in cross-section econometrics, assume that Y t and X t are stationary random variables, so that we could put an i in place of t . As is easily shown, B is: biased, with the absolute value of the bias an increasing function of ± 2 V ; and inconsistent. To see why B is inconsistent, multiply both sides of (0.1) by X c;t and take expectations Cov ( Y t ; X c;t ) = ( X c;t ) + Cov ( U t ; X c;t ) ( V t ; X c;t ) : (0.2) Both Cov ( Y t ; X c;t ) and V ar ( X c;t ) are estimable from observed data and Cov ( U t ; X c;t ) equals 0 . Unfortunately,

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## This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.

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Measurement Error - Measurement Error Consistent Estimators...

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