LN3+Regression+with+Dummy+Variables

LN3+Regression+with+Dummy+Variables - Empirical Methods II...

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Empirical Methods II (API-202) Kennedy School of Government Harvard University 1 LECTURE NOTES 3 - REGRESSION WITH DUMMY VARIABLES I - INTRODUCTION Qualitative information can sometimes be captured by defining a binary variable (i.e. a zero-one variable), commonly called a dummy variable . Examples: female = 1 if person is female 0 if person is male male = 1 if person is male 0 if person is female In these lecture notes, we will study SRs with dummy variable among the RHS variables . In future classes, we will study SRs with a dummy variable as LHS variable . To illustrate the use of dummies in RA we are going to think about the following question: Do women earn less than men? How much less? Data: person Wage per hour educ exper female married 1 5.25 9 2 0 1 2 6.20 12 4 1 1 3 5.85 10 2 0 0 . . . . . . . . . . . . 526 6.15 12 3 1 0
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Empirical Methods II (API-202) Kennedy School of Government Harvard University 2 II - EXAMPLE: GENDER DIFFERENCES IN WAGES Question of interest: Do women earn less than men? How much less? Let’s first see what the data tell us and do a test of the difference in means (API-201). . ttest wage, by (female) unequal Two-sample t test with unequal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- 0 | 274 7.099489 .2513666 4.160858 6.604626 7.594352 1 | 252 4.587659 .1593349 2.529363 4.273855 4.901462 ---------+-------------------------------------------------------------------- combined | 526 5.896103 .1610262 3.693086 5.579768 6.212437 ---------+-------------------------------------------------------------------- diff | 2.51183 .2976118 1.926971 3.09669 ------------------------------------------------------------------------------ Satterthwaite's degrees of freedom: 456.327 Ho: mean(0) - mean(1) = diff = 0 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 t = 8.4400 t = 8.4400 t = 8.4400 P < t = 1.0000 P > |t| = 0.0000 P > t = 0.0000 QUESTION 1 : From this Stata output, what is: The sample average wage for males: The sample average wage for females: The difference in the sample average wages for males vs. females: Stata tests the null hypothesis that there is no difference between average wages for males and females in the population. The reported t-statistic for the test is:
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Kennedy School of Government Harvard University 3 Test using OLS You can also calculate this difference in means and perform a test for statistical significance of the difference using an OLS regression in which you estimate the SR: wage = 0 ˆ + 1 ˆ female + ˆ QUESTION 2 : Write out using the SR: -the predicted wage for males: -the predicted wage for females: QUESTION 3 : What is the interpretation of 0 ˆ and 1 ˆ ˆ to be positive or negative if males earn, on average, higher wages than females?
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This note was uploaded on 04/12/2009 for the course HKS API202A taught by Professor Levy during the Spring '09 term at Harvard.

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LN3+Regression+with+Dummy+Variables - Empirical Methods II...

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