Econometrics-I-13

Strategy n(1 purge ed of the influence of everything

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Unformatted text preview: Strategy n (1) Purge ED of the influence of everything but MS, FEM, BLK (and the other variables). Predict ED using all exogenous information in the sample ( X and Z ). n (2) Regress LWAGE on this prediction of ED and everything else. n Standard errors must be adjusted for the predicted ED ˜™™™™™™ ™ 8/61 Part 13: Endogeneity OLS ˜™™™™™™ ™ 9/61 Part 13: Endogeneity The weird results for the coefficient on ED happened because the instruments, MS,FEM,BLK are all dummy variables. There is not enough variation in these variables. ˜˜™™™™™ ™ 10/61 Part 13: Endogeneity Source of Endogeneity n LWAGE = f( ED, EXP,EXPSQ,WKS,OCC, SOUTH,SMSA,UNION ) + n ED = f( MS,FEM,BLK, EXP,EXPSQ,WKS,OCC, SOUTH,SMSA,UNION ) + u ˜˜™™™™™ ™ 11/61 Part 13: Endogeneity Remove the Endogeneity n LWAGE = f( ED, EXP,EXPSQ,WKS,OCC, SOUTH,SMSA,UNION ) + u + n Strategy p Estimate u p Add u to the equation. ED is uncorrelated with when u is in the equation. ˜˜™™™™™ ™ 12/61 Part 13: Endogeneity Auxiliary Regression for ED to Obtain Residuals ˜˜™™™™™ ™ 13/61 Part 13: Endogeneity OLS with Residual (Control Function) Added 2SLS ˜˜™™™™™ ™ 14/61 Part 13: Endogeneity A Warning About Control Function ˜˜™™™™™ ™ 15/61 Part 13: Endogeneity The Problem ˜˜™™™™™ ™ 16/61 1 2 Cov( , ) , K variables Cov( , ) , K variables is OLS regression of y on ( , ) cannot estimate ( , ) consistently. Some other estimator is needed. Additional structure: = + wh = + + = ≠ endogenous y X Y X Y Y X Y Y Z V β δ ε ε ε β δ Π ere Cov( , )= . An estimator based on ( , ) may be able to estimate ( , ) consistently. instrumental variable ( Z X IV) Z ε β δ Part 13: Endogeneity Instrumental Variables p Framework: y = X + , K variables in X . p There exists a set of K variables, Z such that plim( Z’X/n ) but plim( Z’ /n) = The variables in Z are called instrumental variables. p An alternative (to least squares) estimator of is b IV = ( Z’X )-1 Z’y p We consider the following: n Why use this estimator? n What are its properties compared to least squares? p We will also examine an important application ˜˜™™™™™ ™ 17/61 Part 13: Endogeneity IV Estimators Consistent b IV = ( Z’X )-1 Z’y = ( Z’X /n)-1 ( Z’X /n) β + ( Z’X /n)-1 Z’ε /n = β + ( Z’X /n)-1 Z’ε /n β Asymptotically normal (same approach to proof as for OLS) Inefficient – to be shown. ˜˜™™™™™ ™ 18/61 Part 13: Endogeneity The General Result By construction, the IV estimator is consistent. So, we have an estimator that is consistent when least squares is not....
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Strategy n(1 Purge ED of the influence of everything but MS...

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