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2 assume the structural equation is where e uixi ...

Question: 2 assume the structural equation is where e uixi ...

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2. Assume the structural equation is where E [ui|Xi] = 0. It was discovered that we observe ri with a measurement error wi instead of the real value X X-Xi + w It is known that E [wi-0, V (wi) %-cou (Xi, wi)-cov is based on regressing Y, on a constant and X. (u,,wi) 0. The OLS estimator (i) Find the value to which the OLS estimator of β¡ is consistent for. (ii) Is the value equal to the true value β? If not, how is the bias related to the true value? (iii) Assume we have a consistent estimator for σ. How would you make a correction to consistently estimate β? (iv) Discuss other potential solutions when such estimator in (ii) is not available 3, Exercise #9.7 (Stock and Watson)

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