1. Christopher Dougherty EC220 - Introduction to econometrics (chapter 5) Slideshow: exercise 5.2 Original citation: Dougherty, C. (2012) EC220 - Introduction to econometrics (chapter 5). [Teaching Resource] © 2012 The Author This version available at: http://learningresources.lse.ac.uk/131/http://learningresources.lse.ac.uk/131/ Available in LSE Learning Resources Online: May 2012 This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 License. This license allows the user to remix, tweak, and build upon the work even for commercial purposes, as long as the user credits the author and licenses their new creations under the identical terms. http://creativecommons.org/licenses/by-sa/3.0/ http://creativecommons.org/licenses/by-sa/3.0/ http://learningresources.lse.ac.uk/

2. 1 The Stata output shows the result of regressing weight on height, first with a linear specification, then with a logarithmic one, including a dummy variable MALE, defined as in Exercise 5.1, in both cases. Give an interpretation of the equations and perform appropriate statistical tests. See Box 5.1 for a guide to the interpretation of dummy variable coefficients in logarithmic regressions. EXERCISE 5.2

3. 2. reg WEIGHT85 HEIGHT MALE Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 2, 537) = 191.56 Model | 273040.775 2 136520.388 Prob > F = 0.0000 Residual | 382702.973 537 712.668479 R-squared = 0.4164 -------------+------------------------------ Adj R-squared = 0.4142 Total | 655743.748 539 1216.59322 Root MSE = 26.696 ------------------------------------------------------------------------------ WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- HEIGHT | 4.006225.3971644 10.09 0.000 3.226039 4.786412 MALE | 13.7615 3.363568 4.09 0.000 7.154131 20.36886 _cons | -121.2502 25.70087 -4.72 0.000 -171.7367 -70.76363 ------------------------------------------------------------------------------ The regression output will first be presented without comment so that you can think about the interpretation. Further slides then give the interpretation. First, the linear specification. EXERCISE 5.2

4. 3. reg LGWEIGHT LGHEIGHT MALE Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 2, 537) = 224.03 Model | 11.3390838 2 5.66954189 Prob > F = 0.0000 Residual | 13.5897932 537.025306877 R-squared = 0.4549 -------------+------------------------------ Adj R-squared = 0.4528 Total | 24.928877 539.046250236 Root MSE =.15908 ------------------------------------------------------------------------------ LGWEIGHT | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- LGHEIGHT | 1.675851.1581459 10.60 0.000 1.36519 1.986511 MALE |.0975722.0199191 4.90 0.000.0584432.1367012 _cons | -2.077515.6590635 -3.15 0.002 -3.372173 -.782856 ------------------------------------------------------------------------------ The logarithmic specification. EXERCISE 5.2

5. 4. reg WEIGHT85 HEIGHT MALE Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 2, 537) = 191.56 Model | 273040.775 2 136520.388 Prob > F = 0.0000 Residual | 382702.973 537 712.668479 R-squared = 0.4164 -------------+------------------------------ Adj R-squared = 0.4142 Total | 655743.748 539 1216.59322 Root MSE = 26.696 ------------------------------------------------------------------------------ WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- HEIGHT | 4.006225.3971644 10.09 0.000 3.226039 4.786412 MALE | 13.7615 3.363568 4.09 0.000 7.154131 20.36886 _cons | -121.2502 25.70087 -4.72 0.000 -171.7367 -70.76363 ------------------------------------------------------------------------------ The linear regression indicates that weight tends to increase by 4.0 pounds for each inch of height and that, controlling for height, males tend to weigh 13.8 pounds more than females. The intercept has no sensible interpretation. EXERCISE 5.2

6. 5. reg LGWEIGHT LGHEIGHT MALE Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 2, 537) = 224.03 Model | 11.3390838 2 5.66954189 Prob > F = 0.0000 Residual | 13.5897932 537.025306877 R-squared = 0.4549 -------------+------------------------------ Adj R-squared = 0.4528 Total | 24.928877 539.046250236 Root MSE =.15908 ------------------------------------------------------------------------------ LGWEIGHT | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- LGHEIGHT | 1.675851.1581459 10.60 0.000 1.36519 1.986511 MALE |.0975722.0199191 4.90 0.000.0584432.1367012 _cons | -2.077515.6590635 -3.15 0.002 -3.372173 -.782856 ------------------------------------------------------------------------------ The logarithmic specification. Here you have to be a little careful since the height variable is logarithmic but the dummy variable is not. (The dummy variable cannot be logarithmic since the logarithm of zero is not defined.) EXERCISE 5.2

7. 6. reg LGWEIGHT LGHEIGHT MALE Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 2, 537) = 224.03 Model | 11.3390838 2 5.66954189 Prob > F = 0.0000 Residual | 13.5897932 537.025306877 R-squared = 0.4549 -------------+------------------------------ Adj R-squared = 0.4528 Total | 24.928877 539.046250236 Root MSE =.15908 ------------------------------------------------------------------------------ LGWEIGHT | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- LGHEIGHT | 1.675851.1581459 10.60 0.000 1.36519 1.986511 MALE |.0975722.0199191 4.90 0.000.0584432.1367012 _cons | -2.077515.6590635 -3.15 0.002 -3.372173 -.782856 ------------------------------------------------------------------------------ The coefficient of LGHEIGHT should be interpreted as an elasticity. A 1 percent increase in height tends to increase weight by 1.68 percent, controlling for sex. EXERCISE 5.2

8. 7. reg LGWEIGHT LGHEIGHT MALE Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 2, 537) = 224.03 Model | 11.3390838 2 5.66954189 Prob > F = 0.0000 Residual | 13.5897932 537.025306877 R-squared = 0.4549 -------------+------------------------------ Adj R-squared = 0.4528 Total | 24.928877 539.046250236 Root MSE =.15908 ------------------------------------------------------------------------------ LGWEIGHT | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- LGHEIGHT | 1.675851.1581459 10.60 0.000 1.36519 1.986511 MALE |.0975722.0199191 4.90 0.000.0584432.1367012 _cons | -2.077515.6590635 -3.15 0.002 -3.372173 -.782856 ------------------------------------------------------------------------------ The relationship between weight and the MALE dummy variable is effectively semilogarithmic. Being male increases weight by a proportion 0.098, that is, by 9.8 percent, controlling for height. The constant has no direct economic interpretation. EXERCISE 5.2

9. Copyright Christopher Dougherty 2000–2007. This slideshow may be freely copied for personal use. 14.11.07