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Unformatted text preview: ifferent from that in X’s. Measurement Error in a Dependent Variable With measurement error in a dependent variable, OLS may still be ok. 1 •
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• Let’s define Y as the observed mismeasured variable, and Y* as the true (unobserved) variable. Y = Y*+ e, where e is the measurement error. Assume that the model of interest is Y * = α + β1 X 1 + ... + β k X k + u , where we assume all the assumptions hold. In particular, E(uX1,…,Xk)=0. Really estimating Y = α + β1 X 1 + ... + β k X k + (u + e). When will OLS produce unbiased results? • If the measurement error e is uncorrelated with X’s, then OLS is unbiased. o Example: Y = α + β X + u , where Y= alcohol consumption, X=education. If reported alcohol drinking has random errors due to people misremembering the accurate amount, so the reporting error has nothing to do with education. o While unbiased in this case, OLS estimators tend to have larger variances than without measurement error. • If the measurement error e is correlated with X’s, then OLS is biased. o Example: if individuals with low education are more likely to lie about /misreport their alcohol consumption—measurement error is correlated with education, then OLS is biased. Measurement Error in an Explanatory Variable Measurement error in an independent variable tends to lead to biased estimates. • • Define X * as...
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This document was uploaded on 03/11/2014.
 Spring '14

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