Lecture 14 Prof. Arkonac's Slides (Ch 8.3 - Ch 9) for ECO 4000_1

# Lecture 14 Prof. Arkonac's Slides (Ch 8.3 - Ch 9) for ECO 4000_1

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Nonlinear Regression III (cont’) Assessing Regression Studies I, ECO 4000 Lecture 14 by Seyhan Erden Arkonac, PhD 1

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2 (c) Interactions between two continuous variables Y i = 0 + 1 X 1 i + 2 X 2 i + u i X 1 , X 2 are continuous As specified, the effect of X 1 doesn’t depend on X 2 As specified, the effect of X 2 doesn’t depend on X 1 To allow the effect of X 1 to depend on X 2 , include the “interaction term” X 1 i X 2 i as a regressor: Y i = 0 + 1 X 1 i + 2 X 2 i + 3 ( X 1 i X 2 i ) + u i
3 Interpreting the coefficients: Y i = 0 + 1 X 1 i + 2 X 2 i + 3 ( X 1 i X 2 i ) + u i General rule: compare the various cases Y = 0 + 1 X 1 + 2 X 2 + 3 ( X 1 X 2 ) (b) Now change X 1 : Y + Y = 0 + 1 ( X 1 + X 1 ) + 2 X 2 + 3 [( X 1 + X 1 ) X 2 ] (a) subtract (a) – (b): Y = 1 X 1 + 3 X 2 X 1 or 1 Y X = 1 + 3 X 2 The effect of X 1 depends on X 2 (what we wanted) 3 = increment to the effect of X 1 from a unit change in X 2

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4 Example : TestScore, STR, PctEL TestScore = 686.3 – 1.12 STR – 0.67 PctEL + .0012( STR PctEL ), (11.8) (0.59) (0.37) (0.019) The estimated effect of class size reduction is nonlinear because the size of the effect itself depends on PctEL : TestScore STR = –1.12 + .0012 PctEL PctEL TestScore STR 0 –1.12 20% –1.12+.0012 20 = –1.10
5 Example, ctd: hypothesis tests TestScore = 686.3 – 1.12 STR – 0.67 PctEL + .0012( STR PctEL ), (11.8) (0.59) (0.37) (0.019) Does population coefficient on STR PctEL = 0? t = .0012/.019 = .06 can’t reject null at 5% level Does population coefficient on STR = 0? t = –1.12/0.59 = –1.90 can’t reject null at 5% level Do the coefficients on both STR and STR PctEL = 0? F = 3.89 ( p -value = .021) reject null at 5% level( !! ) (Why? high but imperfect multicollinearity)

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. reg wage educ exper tenure educxten female married, r Linear regression Number of obs = 526 F( 6, 519) = 35.69 Prob > F = 0.0000 R-squared = 0.3890 Root MSE = 2.9033 ------------------------------------------------------------------------------ | Robust wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .4036199 .0689833 5.85 0.000 .2680992 .5391406 exper | .0176922 .0101752 1.74 0.083 -.0022974 .0376818 tenure | -.1468756 .083224 -1.76 0.078 -.3103728 .0166217 educxten | .0237101 .0074023 3.20 0.001 .009168 .0382522 female | -1.793848 .2497369 -7.18 0.000 -2.284467 -1.303229 married | .5295801 .2557498 2.07 0.039 .0271479 1.032012 _cons | .317556 .8808376 0.36 0.719 -1.412889 2.048001 ------------------------------------------------------------------------------ How do you interpret educxtenure coefficient? 4 more years of education will increase wage by [(.404)+(.024)]x4=\$1.72 assuming
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## This note was uploaded on 05/05/2011 for the course ECON 4000 taught by Professor Arkonac during the Spring '11 term at CUNY Baruch.

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Lecture 14 Prof. Arkonac's Slides (Ch 8.3 - Ch 9) for ECO 4000_1

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