Use the data in SCHOOL93_98 to answer the following questions. Use the command xtset schid year to set the cross section and time dimensions.

(i) How many schools are there. Does each school have a record for each of the six years? Verify that lavgrexpp is missing for all schools in 1993.

(ii) Create a selection indicator, s, that is equal to one if and only if you have nonmissing data on math4, lavgrexpp, lunch, and lenrol. Next, define a variable tobs to be the number of complete time periods per school. How many schools have all given years of available data (noting that 1993 is not available for any school when we use lavgrexpp)? Drop all schools with tobs = 0.

(iii) Use random effects to estimate a model relating math4 to lavgrexpp, lunch, and lenrol. Be sure to include a full set of year dummies. What is the estimated effect of school spending on math4? What is its cluster-robust t statistic?

(iv) Now estimate the model from part (iii) by fixed effects. What is the estimated spending effect and its robust confidence interval? How does it compare to the RE estimate from part (iii)?

(v) Create the time averages of all of the explanatory variables in the RE/FE estimation, including the time dummies. You need to use the selection indicator constructed in part (ii). Verify that when you add these and estimate the equation by RE you obtain the FE estimates on the time-varying explanatory variables. What happens if you drop the time averages for y95, y96, y97, and y98?

(vi) Is the random effects estimator rejected in favor of fixed effects? Explain.