14B_Dummies_handout

14B_Dummies_handout - Dummy variables& more 73-261...

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Unformatted text preview: Dummy variables & more 73-261 Econometrics October 6 Reading: Wooldridge 7.1-7.4 p. 2 © CMU / Y. Kryukov 73-261 1.4 Dummies Overview: using OLS Finishing nonlinear terms: Transformed y and goodness-of-fit Quadratic & other power terms Interaction terms Today: Qualitative data (dummy variables) Single dummy – effect on constant Multiple-category dummy Interaction dummy – slope effect General issues Correlation vs. causation Selection issues p. 3 © CMU / Y. Kryukov 73-261 1.4 Dummies Transformed y : Goodness of fit Comparing two regressions: a. y = x β + u b. log y = x γ + v Want R 2 = 1 – RSS/TSS, comparable between a. & b. Must use same scale of y (= same TSS): GRETL’s R 2 for b . uses: ( ) 2 1 a ˆ RSS ∑ = − = N i i i X Y β ( ) 2 1 b ] ˆ exp[ RSS ∑ = − = N i i i X Y γ ( ) 2 1 log ˆ log RSS ∑ = − = N i i i X Y γ ( ) 2 1 TSS ∑ = − = N i i Y Y ( ) 2 1 log log log TSS ∑ = − = N i i Y Y p. 4 © CMU / Y. Kryukov 73-261 1.4 Dummies Example A. Scott and C. Wild, “Transformations and R 2 ” The American Statistician, May 1991, Vol. 45, No. 2 p. 5 © CMU / Y. Kryukov 73-261 1.4 Dummies Example - continued Similar lines, very different R 2 ’s p. 6 © CMU / Y. Kryukov 73-261 1.4 Dummies Quadratic term y = β + β 1 x + β 2 x 2 + u Effect (approximate): ∆ y = [ β 1 + 2 β 2 x ] ∆ x Marginal effect ( x > 0 ): β 1 and β 2 have __________ sign = increasing marginal effect y = maximum ( β 0 ) or min ( β 0 ) at: x * = −β 1 / (2 β 2 ) Make sure x * is in-sample before discussing it , and vice versa p. 7 © CMU / Y. Kryukov 73-261 1.4 Dummies Other power terms Can also use x 3 , x 4 , x 0.5 , x − 1 , etc....
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This note was uploaded on 01/21/2011 for the course ECON 73-261 taught by Professor Kyrkv during the Fall '09 term at Carnegie Mellon.

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14B_Dummies_handout - Dummy variables& more 73-261...

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