econ sse
4th Statistical computing assignment
1) Use the data in CPS78_85. Thinking of this estimated regression:
a. How do you interpret the coefficient on ? Does it have an interesting interpretation?
b. Holding other factors fixed, what is the estimated percent increase in nominal wage for a male with 12 years of education? Propose a regression to obtain a confidence interval for this estimate.
c. Re-estimate the above regression, but let all wages be measured in 1978 dollars. In particular, define the real wage as for 1978 and as for 1985. Now, use in place of and estimate the model. Which coefficients differ from the original estimation?
d. Explain why the from your regression in part (c) is not the same as the original estimation?
e. Describe how union participation changed from 1978 to 1985.
f. Starting with the original estimation, test whether the union wage differential changed over time.
g. Do your findings in parts (e) and (f) conflict? Explain
2) Use the data in KIELMC
a. The variable is the distance from each home to the incinerator site, in feet. Consider the model
If building the incinerator reduces the value of homes closer to the site, what is the sign of ? What does it mean in ?
b. Estimate the model in part (a) and report the results in the usual form. Interpret the coefficient on . What do you conclude?
c. Add and to the equation. Now, what do you conclude about the effect of the incinerator on housing values?
d. Why is the coefficient on both positive and statistically significant in part (b), but not in part (c)? What does this say about the controls you used in part (c)?
3) Use CRIME3 data for this exercise
a. In the model (from example 13.6)
Test the hypothesis
b. If , show that the differenced equation can be written as
Where and is the average clear up percentage over the previous two years.
c. Estimate the equation in part (b). Compare the adjusted R-squared with that in equation 13.22 in our text (. Which model would you finally use?
4) Use the data in RENTAL for this exercise. The data on rental prices and other variables for college towns are for the years 1980 and 1990. The idea is to see whether a stronger presence of students affects rental rates. The unobserved effects model is
Where is city population, is average income, and is student population as a percentage of city population.
a. Estimate the equation by pooled OLS and report the results in the standard form. What do you make of the estimate on the 1990 dummy variable? What do you get for ?
b. Are the standard errors you report in (a) valid? Explain
c. Now, difference the equation and estimate by OLS. Compare your estimate of with that from part (a). Does the relative size of the student population appear to affect rental prices?
d. Estimate the model by FE to verify that you get identical estimates and standard errors as those in part (c).
5) In example 13.8 in our text, we used the unemployment claims data from Papke (1994) to estimate the effect of enterprise zones on unemployment claims. Papke also uses a model that allows each city to have its own time trend:
Where and are both unobserved effects. This allows for more heterogeneity across cities.
a. Show that, when the previous equation is first differenced, we obtain
Notice that the differenced equation contains a fixed effect, .
b. Estimate the differenced equation by fixed effects. What is the estimate of ? Is it very different from the estimate obtained in Example 13.8? Is the effect of the enterprise zones still statistically significant?
c. Add a full set of year dummies to the estimation in part (b). What happens to the estimate of ?
6) Please see example 14.4 in our text.
a. In the wage equation in Example 14.4, explain why dummy variables for occupation might be important omitted variables for estimating the union wage premium.
b. If every man in the sample stayed in the same occupation from 1981 through 1987, would you need to include the occupation dummies in a fixed effects estimation? Explain.
c. Using the data in WAGEPAN include 8 of the occupation dummy variables in the equation and estimate the equation using fixed effects. Does the coefficient on union change by much? What about its statistical significance?
7) Add the interaction term to the equation estimated in Table 14.2 to see if wage growth depends on union status. Estimate the equation by random and fixed effects and compare the results.