C8 Use the data in MATHPNL.RAW for this exercise. You will do a fixed effects version of the first differencing done in Computer Exercises 11 in Chapter 13. The model of interest is
math4it 5 d1y94t 1 ... 1 d5y98t 1 1log(rexppit) 1 2log(rexppi,t1)
1 1log(enrolit) 1 2lunchit 1 ai 1 uit ,
where the first available year (the base year) is 1993 because of the lagged spending variable.
(i) Estimate the model by pooled OLS and report the usual standard errors. You should include an intercept along with the year dummies to allow ai to have a nonzero expected value. What are the estimated effects of the spending variables? Obtain the OLS residuals, vˆit.
(ii) Is the sign of the lunchit coefficient what you expected? Interpret the magnitude of the coefficient. Would you say that the district poverty rate has a big effect on test pass rates?
(iii) Compute a test for AR(1) serial correlation using the regression vˆit on vˆi,t1. You should use the years 1994 through 1998 in the regression. Verify that there is strong positive serial correlation and discuss why.
(iv) Now, estimate the equation by fixed effects. Is the lagged spending variable still significant?
(v) Why do you think, in the fixed effects estimation, the enrollment and lunch program variables are jointly insignificant?
(vi) Define the total, or long-run, effect of spending as 1 5 1 1 2. Use the substitution
1 5 1 2 to obtain a standard error for ˆ1. [Hint: Standard fixed effects esti- mation using log(rexppit) and zit 5 log(rexppi, t1) log(rexppit) as explanatory variables should do it.]