Transcription of Lecture Notes on Measurement Error
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Lecture Notes on Measurement Error
Steve PischkeSpring 2007 Lecture Notes on Measurement ErrorThese Notes summarize a variety of simple results on Measurement errorwhich I nd useful. They also provide some references where more completeresults and applications can be Measurement ErrorWe will start with the simplest regressionmodels with one independent variable. For expositional ease we also assumethat both the dependent and the explanatory variable have mean zero. Supposewe wish to estimate the population relationshipy= x+ (1)Unfortunately, we only have data onex=x+u(2)ey=y+v(3) our observed variables are measured with an additive Error . Let s make thefollowing simplifying assumptionsE(u) = 0(4)plim1n(y0u) = 0(5)plim1n(x0u) = 0(6)plim1n( 0u) = 0(7)The Measurement Error in the explanatory variable has mean zero, is uncorre-lated with the true dependent and independent variables and with the equationerror.
by the i.i.d. assumption for u it.The long and short di⁄erences for x it will be correlated, on the other hand, since the x™s are correlated over time.
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