Introduction to Econometrics 3rd Edition by James Stock, James Stock

تمرين 21

Use the data set ColIegeDistance described in Empirical Exercise to answer the following questions.
Exercise
A regression of average weekly earnings ( AWE, measured in dollars) on age (measured in years) using a random sample of college-educated fulltime workers aged 25-65 yields the following:
a. Explain what the coefficient values 696.7 and 9.6 mean.
b. The standard error of the regression ( SER ) is 624.1. What are the units of measurement for the SERI (Dollars Years Or is SER unit-free )
c. The regression R 2 is 0.023. What are the units of measurement for the R 2 (Dollars Years Or is R 2 unit-free )
d. What is the regression's predicted earnings for a 25-year-old worker A 45-year-old worker
e. Will the regression give reliable predictions for a 99-year-old worker Why or why not
f. Given what you know about the distribution of earnings, do you think it is plausible that the distribution of errors in the regression is normal
g. The average age in this sample is 41.6 years. What is the average value of AWE in the sample
a. Discuss the internal validity of the regressions that you used to answer Empirical Exercise. Include a discussion of possible omitted variable bias, misspecification of the functional form of the regression, errors in variables, sample selection, simultaneous causality, and inconsistency of the OLS standard errors.
Exercise
After reading this chapter's analysis of test scores and class size, an educator comments, "In my experience, student performance depends on class size, but not in the way your regressions say. Rather, students do well when class size is less than 20 students and do very poorly when class size is greater than 25. There are no gains from reducing class size below 20 students, the relationship is constant in the intermediate region between 20 and 25 students, and there is no loss to increasing class size when it is already greater than 25."The educator is describing a "threshold effect" in which performance is constant for class sizes less than 20, then jumps and is constant for class sizes between 20 and 25, and then jumps again for class sizes greater than 25. To model these threshold effects, define the binary variables
STRsmall = 1 if SIR 20, and STRsmall = 0 otherwise;
STRmoderate = 1 if 20 STR 25, and STRmoderate = 0 otherwise; and
STRlarge = 1 if STR 25, and STRlarge = 0 otherwise.
a. Consider the regression TestScore i = ßo + ß 1 STRsmall 1 + ß 2 STRlarge i + U i. Sketch the regression function relating TestScore to STR for hypothetical values of the regression coefficients that are consistent with the educator's statement.
b. A researcher tries to estimate the regression TestScore i = ß 0 +ß 1 STRsmall i + ß 2 STRmoderate i + ß 3 STRlarge i + u i and finds that her computer crashes. Why
b. The data set ColIegeDistance excluded students from western states; data for these students are included in the data set ColIegeDistance West. Use these data to investigate the (geographic) external validity of the conclusions that you reached in Empirical Exercise.