Consider the regression model, Yi = 1Xi + 2Wi + ui, where for simplicity the intercept is

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Consider the regression model, Yi = β1Xi + β2Wi + ui, where for simplicity the intercept is omitted and all variables are assumed to have a mean of zero. Suppose that Xi is distributed independently of (Wi, ui) but Wi and ui might be correlated and let β1 and β2 be the OLS estimators for this model. Show that
a. Whether or not Wi and ui are correlated,
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b. If Wi and ui are correlated, then β2 is inconsistent.
c. Let β1r be the OLS estimator from the regression of Y on X (the restricted regression that excludes W). Provide conditions under which β1 has a smaller asymptotic variance than β1r, allowing for the possibility that Wi and ui are correlated.

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Introduction to Econometrics

ISBN: 978-0133595420

3rd edition

Authors: James H. Stock, Mark W. Watson

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