1. Consider the following population regression model relating the dependent variable Yi and regressor Xi, where Z is a valid instrument for X. (a) Explain why you should not use OLS to estimate . [5 marks] (b) In order to generate a consistent estimator for what should you do? [5 marks]
Added by Laura M.
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This violates the key assumption of OLS, which is that the regressors should be uncorrelated with the error term. If this assumption is violated, the OLS estimator will be biased and inconsistent. Show more…
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1A. With reference to the two-variable linear regression model: Population model: Yi = ̠0 + ̠1Xi + ui Sample model: Yi = ̠̂0 + ̠̂1Xi + ûi Show the expressions for the ordinary least squares estimators of ̠̂0 and ̠̂1 are: ̠̂0 = Ȳ - ̠̂1X̄ ̠̂1 = (ṇXiYi - ̣XịYi) / (ṇXi^2 - (̣Xi)^2) where Ȳ = ̣Yi/n and X̄ = ̣Xi/n ; n is the number of observations. 1B. Explain what is meant by the regression 'residual'. 1C. Why do the OLS estimators minimize the sum of squared residuals?
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