Use the data in ELEM94_95 to answer this question. The data are on elementary schools in Michigan. In this exercise, we view the data as a cluster sample, where each school is part of a district cluster.
(i) What are the smallest and largest number of schools in a district? What is the average number of schools per district?
(ii) Using pooled OLS (that is, pooling across all 1,848 schools), estimate a model relating lavgsal to bs, lenrol, Istaff, and lunch; see also Computer Exercise C9.11. What are the coefficient and standard error on bs?
(iii) Obtain the standard errors that are robust to cluster correlation within district (and also heteroskedasticity). What happens to the t statistic for bs?
(iv) Still using pooled OLS, drop the four observations with bs > .5 and obtain βbs and its cluster-robust standard error. Now is there much evidence for a salary-benefits tradeoff?
(v) Estimate the equation by fixed effects, allowing for a common district effect for schools within a district. Again drop the observations with bs > .5. Now what do you conclude about the salary-benefits tradeoff?
(vi) In light of your estimates from parts (iv) and (v), discuss the importance of allowing teacher compensation to vary systematically across districts via a district fixed effect.