Question

Model: Y = β0 + β1X + u If E(u|X) 6= 0, then we know the OLS estimator will be biased and all further inference like Hypothesis test and Confidence interval will be invalid. In presence of such violation, we can go to Instrument variable estimation/regression method to rebuild the valid empirical study. Assume there is a “good” instrument variable Z for X. (1) How would you argue this is a valid instrument variable?(Hint: validity condition and relevance condition) (2) Given the “good” instrument variable Z for X, what are the two steps to get the estimator of β1. (2SLS: two stage least square, just write out the two regression models)

Answer 1

Solution :

Given that

The model is   Y = β0 + β1X + u If E(u|X) 6= 0,  then we know the OLS estimator will be biased and all further inference like Hypothesis test and Confidence interval will be invalid.

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