chapter 5 [article]

chapter 5 [article] - Contents 1 Intro 1 1.1 Categorical...

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Unformatted text preview: Contents 1 Intro 1 1.1 Categorical variables . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Shift dummies 3 2.1 Two categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 More than two categories . . . . . . . . . . . . . . . . . . . . . . 6 3 Slope dummies 9 3.1 Slope dummies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Chow test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1 Intro Contents 1.1 Categorical variables Contents We are often interested in the effect on Y of categorical or qualitative variables e.g. gender For example, we might wish to know the effect of gender on earnings, etc We could investigate this by including as a regressor a dummy variable FEMALE that is equal to 0 when the observed individual is male and equal to 1 when the individual is female Dummies can enter regression models as shift dummies or as slope dum- mies In a regression of earnings on education, a shift dummy for gender would merely shift the fitted line up or down i.e. there would be two fitted lines with the same slope, one for each gender the marginal effect of S on EARNINGS would be identical for males and females A slope dummy would allow the slope of the fitted line to differ by gender e.g. perhaps another year of school raises female earnings by more than male EARNINGS S A 1 B 1 Model with shift dummy EARNINGS S 1 Model with slope dummy Why use dummy variables? Why not just run two separate regressions for males and females? Using dummies allows us to restrict the effects of other variables to be the same for both genders Again, in the shift dummy example above we are implicitly assuming the marginal effect of education is the same for males and females Benefit: using whole sample in one single regression reduces the variance of 2 , our estimator of this marginal effect 2 2 Shift dummies Contents 2.1 Two categories Contents Start with shift dummies Textbooks example of how cost of running a secondary school varies with the number of students and the type of school 74 schools in Shanghai in 1980s, occupational and regular Hypothesise that the true models for the types of school are: COST = 1 + 2 N + u (regular) (5.3) COST = 1 + 2 N + u (occupational) (5.4) Same 2 and error process u , but different intercept perhaps higher fixed costs for occupational schools, so 1 = 1 + COST N 1 regular 1 + occupational School costs We would estimate these two lines simultaneously by constructing a dummy variable that indexes whether a school is regular or occupational Follow the book and let the dummy variable be OCC , where OCC = 1 if its an occupational school, and OCC = 0 if its a regular school 3 We would use the whole sample (both types of school) to do OLS on the following model: COST = 1 + OCC + 2...
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This note was uploaded on 01/14/2012 for the course ECON 201 taught by Professor Witte during the Spring '08 term at Northwestern.

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chapter 5 [article] - Contents 1 Intro 1 1.1 Categorical...

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