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IVEstimation

# IVEstimation - IV Estimation Instrumental Variables Yt = 1...

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IV Estimation Instrumental Variables

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Y = X + u β t 1 2 2,t k k,t t Y = + X + X + u t = 1,...,T β β β ... +
Y = X + u β Y X ) X X ( = β ˆ -1 OLS ) u β X ( X ) X (X = β ˆ / 1 - / OLS + u X ) X X ( + β = β ˆ -1 OLS ) u X ) X (X β X X ) X (X = β ˆ / 1 - / / 1 - / OLS + β ) β ˆ ( E then , 0 ) u , X ( Cor If OLS

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estimates t inefficien and consistent IV while estimates efficient and consistent OLS then 0 ) u , X ( Cor If = T 1,..., = t u + X + = Y t t 2 1 t β β
estimates consistent IV while estimates nt inconsiste OLS then 0 ) u , X ( Cor If T 1,..., = t u + X + = Y t t 2 1 t β β

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Implication Estimate model by OLS and by IV, and compare estimates If If But test INDIRECTLY using Wu-Hausman test. OLS use β ˆ β ˆ IV OLS IV use β ˆ β ˆ IV OLS
THE INSTRUMENTAL VARIABLES (IV) ESTIMATOR Suppose that one or more of the regressors in X is not independent of the equation error term, even in the limit as the sample size goes to infinity. That is, X is correlated with u, the equation disturbance.

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IVEstimation - IV Estimation Instrumental Variables Yt = 1...

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