Alcoholt 1 female 2 alcoholt 1 3 female alcoholt

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Unformatted text preview: 1 + δ1 ) X + u. So in this case, the dummy shifts both the intercept (by δ 0 ) and the slope (by δ1 ), so the effects of X on Y are different across the two groups (d=1, d=0). The regression function can be represented by two straight lines with different intercepts and slopes. Figure: assuming δ 0 > 0 and δ1 < 0 6 Testing for Differences across Groups • Running two separate regressions are the same as running one big regression with a dummy (indicating one group vs. the other) and the dummy interacted with all k covariates. Example: log( wage) = α + β1 female + β 2educ + β3 female * educ + u is the same as running two linear regressions of log(wage) on educ for femals and males separately. • Testing whether the effects of education on log(wage) depends on gender, or whether the effects of education on log(wage) differ across gender means ˆ testing the significance of β . 3 • Testing whether education affects wage at all means testing the joint ˆ ˆ significance of β and β , since the effect of education on log(wage) is given 2 3 ˆ ˆ by β 2 + β 3 female. Example2: if one believes female’s and male’s alcohol consumption is determined completely differently 1) run separate regressions for females and males of alcohol consumption on last period alcohol consumption; or 2) run one single regression including a female (or male) dummy, last period alcohol consumption and the interaction term between female (or male) and age. alcoholt = α + β1 female + β 2 alcoholt −1 + β3 female * alcoholt −1 + u Regression with a Binary Dependent Variable So far the dependent variable (Y) has been continuous: wage, GPA, Expenditure… 7 But we might want to understand the effect of X on a binary variable Y: Y= whether one works or not Y = whether one attends college or not Y = whether one smokes or not Y = whether one commits a crime or n...
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