Fall 2008 under econometrics prof keunkwan ryu 4

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Fall 2008 under Econometrics Prof. Keunkwan Ryu 4 Fixed Effects or First Differencing? First Differences and Fixed Effects will be exactly the same when T = 2 For T > 2, the two methods are different Probably see fixed effects estimation more often than differences – probably more because it’s easier than that it’s better Fixed effects easily implemented for unbalanced panels, not just balanced panels
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Fall 2008 under Econometrics Prof. Keunkwan Ryu 5 2. Random Effects Models Start with the same basic model with a composite error, y it = β 0 + β 1 x it1 + . . . β k x itk + a i + u it Assume cov(x itj ,a i )=0 , t=1,2,…,T ; j=1,2,..k Previously we’ve assumed that a i was correlated with the x ’s, but what if it’s not? OLS would be consistent in that case, but composite error will be serially correlated
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Fall 2008 under Econometrics Prof. Keunkwan Ryu 6 2. Random Effects (continued) Need to transform the model and do GLS to solve the problem and make correct inferences Need to transform the model and do GLS to solve the problem and make correct inferences
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Fall 2008 under Econometrics Prof. Keunkwan Ryu 7 2. Random Effects (continued) End up with a sort of weighted average of OLS and Fixed Effects – use quasi-demeaned data ( 29 [ ] ( 29 ( 29 ( 29 ( 29 i it ik itk k i it i it a u u x x x x y y T ν λ ν λ β λ β λ β λ σ σ σ λ - + - + + - + - = - + - = ... 1 1 1 1 1 0 2 1 2 2 2
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Fall 2008 under Econometrics Prof. Keunkwan Ryu 8 2.Random Effects (continued) If λ
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