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【正文】 means that, everything else in () held fixed, another year of education increases the probability of labor force participation by .038 Limitations of the LPM ? Some Shortings: ? predictions either less than zero or greater than one. ? Linear constant marginal effect unrealistic ? Smaller marginal effect of subsequent children on working probability of women ? It usually works well for values of the independent variables that are near the averages in the sample. ? Heteroskedasticy ? Unbiasedness。 incorrect statistic ? Dummy Dependent and Explanatory Variables: ? The coefficient measures the predicted difference in probability when the dummy v. goes from zero to one. Using Dummy V. in Multiple Categories: Interpretation ? Adding a dummy v. married ? Same “marriage premium” for men and women。 (0,1)。 (1,1)。 (1,0)。 (0,0) ? Different “marriage premium” ? Three dummy variables? ? marrmale, marrfem, and singfem. ? (1,0,0)。 (0,1,0)。 (0,0,1)。 (0,0,0) ? Ordinary Variable: ? to define dummy variables for each value or each categories of respective information Example (,) The Determination of log Hourly Wage: ? Explanatory Variables: educ, exper, tenure, marriage, gender ? Dummy Variables: ? Same “marriage premium”。 (0,1)。 (1,1)。 (1,0)。 (0,0) ? Different “marriage premium”。 (1,0,0)。 (0,1,0)。 (0,0,1)。 (0,0,0) ? Adding Interaction Term ? Regression: ? Inference: ? we can use this equation to obtain the estimated difference between any two groups. ? Unfortunately, we cannot use it for testing whether the estimated difference between single and married women is statistically significant. to choose one of these groups to be the base group and to reestimate the equation. ? Interpretation: Example (,) The Determination of log Hourly Wage: Interaction Effects Involving with Dummy Variables ? Adding Interaction Term ? The marriage premium depends on gender ? the rest of the regression is necessarily identical to (). ? Equation () is just a different way of finding wage differentials across all gendermarital status binations. It has no real advantages over ()。 in fact, equation () makes it easier to test for differentials between any group and the base group of single men. Interaction Effects: Differences in Slopes ? Adding Interaction Term: Differences in Slopes ? The return of education depends on gender ? Hypothesis Test: ? the return to education is the same for women and men. ? average wages are identical for men and women who have the same levels of education: F test Testing for Differences in Regression Functions Across Groups ? H0: two populations or groups follow the same regression function, against the alternative that one or more of the slopes differ across the groups. ? Chow Statistic: ? Caution: there is no simple R2 form of the test if separate regressions have been estimated for each group。 the R2 form of the test can be used only if interactions have been included to create the unrestricted model. ? One important limitation of the Chow test: regardless of the method used to implement it, is that the null hypothesis allows for no differences at all between the groups. Policy Analysis and Program Evaluation with Dummy Variables ? Policy analysis。 Program evaluation ? Control group。 experimental (treatment) group ? be careful to include factors that might be systematically related to the binary independent variable of interest. ? SelfSelection Problems: ? The term is used generally when a binary indicator of participation might be systematically related to unobserved factors. ? another way that an explanatory variable can be endogenous. ? Solutions: ? Data ? more advanced methods Example: the effect of the job training grants on worker productivity ?Consider again the Holzer et al. (1993) study, where we are now interested in the effect of the job training grants on worker productivity (as opposed to amount of job training, example ). References ?Jeffrey M. Wooldridge, Introductory Econometrics——A Modern Approach, Chap 4－ 7.
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