Lecture+5+Regression+with+dummy+variables

Isexpectedwagewhenfemale0andblack0thatisforwhitemale

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Unformatted text preview: fficient represents the mean wage difference between male college grads and male non‐college grads. 4 o Keep in mind that the coefficients for simple dummies indicate difference from the base group. Quiz: What does δ 3 mean? Specifically: 1) Wage for male non‐college grads wage = α + β X + u. female = 0, colgrad = 0, 2) Wage for female non‐college grads wage = α + δ 1 + β X + u. female = 1, colgrad = 0, So δ1 is the mean wage difference between female non‐college grads and male non‐college grads. 3) Wage for male college graduates wage = α + δ 2 + β X + u. female = 0, hsgrad = 0 and colgrad = 1, So δ 2 is the mean wage difference between male college grads and male non‐ college grads. 4) Wage for female college graduates female = 1, hsgrad = 0 and colgrad = 1, wage = α + δ1 + δ 2 + δ 3 + β X + u. So δ1 + δ 2 + δ 3 is the mean wage difference between female college grads and male non‐college grads. Example2: How to interpret the intercept and slopes in the following model? wage = α + β1 female + β 2black + β3 female * black + u. α is expected wage when female=0 and black=0, that is for white male. What does β1 mean? What does β 2 mean? What does β 3 mean? 5 Example3 (Difference in differences, aka, DID estimation): Suppose that CA has passed a law requiring employers to pay for career‐related depression consultation for women. You are concerned that employers will decrease women’s wages in order to pay for this new benefit. You find a data set that has data on wages from the year before the law took effect and the year after. The mean hourly wages for various groups are as follows: men women before $10 $8 after $12 $9 Suppose you estimate the following model: wage = α + β1after + β 2 women + β3after ∗ women + u, where after and women are dummies indicating the year after the law took effect and a woman respectively. What are your estimates of α , β1 , β2 , and β3 in the above model? A Dummy Interacted with a Continuous Variable Can also consider interacting a dummy variable, d, with a continuous variable, X; i.e., the impact of X on Y depends on d. Y=α +δ 0 d + β1 X + δ1d * X + u If d = 0, then Y = α + β X + u If d = 1, then Y = (α + δ 0 ) + (...
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