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Unformatted text preview: 1 Econometrics Lecture #10: Further Issues in Dummy Variables Outline Combining Ftests and dummy interactions: the “Chow Test” Dummies for time periods Differenceindifferences Did the Mariel Boatlift lower the wages of Miami’s workers? Maybe briefly: Dummy Dependent Variable 2 “Chow Test” Special case of Ftest Chow test asks if separate models should be estimated for different groups? Ex: men & women Recall from last time: β represents the intercept from the excluded group – men β 1 is how much different the intercept is for women then men, So β 1 ≠ 0 says women have a different intercept i i i i i u female yrsed yrsed female wg + ⋅ + + + = 3 2 1 ) ln( β β β β “Chow Test” Recall from last time: β 2 represents the slope for the excluded group – the returns to education for men β 3 is how much different the slope is for women then men, So β 3 ≠ 0 says women have a different slope Therefore the hypothesis that women & men have the same wageeducation relationship can be tested with H : β 1 = β 3 = 0 An Ftest! i i i i i u female yrsed yrsed female wg + ⋅ + + + = 3 2 1 ) ln( β β β β Chow Test Example 1. Estimate “fully interacted model” = all variables interacted w/female R 2 unrestricted Equivalent to estimating separate m/f models 1. Estimate “pooled model” R 2 restricted 1. Compute Fstat, decide… i i i i i i i i u female etc etc female female yrsed yrsed female wg + ⋅ + + ⋅ + + ⋅ + + + = ...) . ... exp exp ( ) ln( 4 3 3 2 1 β β β β β β i i u yrsed wg + ′ + ′ + ′ = ... exp ) ln( 3 2 β β β Chow Test Example R 2 unrestricted R 2 restricted Regression 1 Regression 2 Regression 3 female0.5940.190*** (0.471) (0.0645) yrsed 0.0799*** 0.0965*** 0.0905*** (0.0258) (0.0173) (0.0175) yrsed_fem 0.0301 (0.0348) Constant 1.603*** 1.383*** 1.362*** (0.345) (0.233) (0.237) Observations 220 220 220 Rsquared 0.147 0.144 0.110 Regressions of Ln(wage) on Education, Female *** p<0.01, ** p<0.05, * p<0.1 Standard errors in parentheses Chow Test What are R 2 unres. , R 2 res , q, N and K? R 2 unres. = 0.147, R 2 res. = 0.110 q = 2, N = 220, K = 3 5% level critical value for F 2,216 ≈ 3 Fstat = 4.68 > 3 reject H at 5% level Test says wage regressions should be run separately for men and women ( 29 ( 29 ( 29 1 1 2 2 2 = K N R q R R stat F ed unrestrict restricted ed unrestrict ( 29 ( 29 ( 29 68 . 4 1 3 220 147 . 1 2 110 . 147 ....
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 Spring '09
 Econometrics, Regression Analysis, Miami, chow test

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