In the model, show that OLS consistently estimates a and β if a. is uncorrelated with x. and b. is uncorrelated with x. and x2 , which are weaker assumptions than (9.19). [Hint: Write the equation as in and recall from Chapter 5 that sufficient for consistency of OLS for the intercept and slope is E(ui) = 0 and Cov(xi, ui) = 0.]
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