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dEconomics 8119 (was 616)
Quantile Regression Problem Set
For this problem set you will need the data set dummies.xls.
1. Using the data set fit the following model by OLS:
Wage = a0 + a1*age + a2*age2 + a3*Educ + a4*Educ2 + a5*sex + u
2.i. Test the hypothesis that a2 = 0.
ii. Test the hypothesis that a4 = 0.
iii. Test the hypothesis that a2 = 0 and a4 = 0.
3. Suppose that it were more costly to make an over prediction of wages than an under-prediction, perhaps because you are the tax authority responsible for estimating tax revenue at the time that a new spending plan is being authored.
i. Are under and over prediction weighted equally in the estimation method of the model in question 1?
ii. How would you modify your prediction?
4. Now consider the possibility that the dispersion and perhaps even the shape of the conditional density of wages depends on the sex-age-educ variables. Consider a quantile regression model of the type specified in question 1.
i. Estimate the first, second and third quartiles and interpret your result.
ii. Plot the values taken by the ai against the quantiles for a large number of quantiles. Interpret these graphs. To see an example look at page 150, Koenker and Hallock, JEP 15(4), Fall 2001. I believe that there is R code in either the vignette written by Koenker or the examples of R-code linked to your syllabus.
5. Test for location and scale shirts for the coefficients and for the model using the method of Khamaladze-Koenker. Interpret your results. See the paper by Morra, Hearn and Buck linked to your syllabus on April 2nd. In the R package quantreg there is a program call that will do this.
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