Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 19

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, lstaff, and lunch; see also Computer Exercise 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 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.

Use the data for the year 1993 for this question, although you will need to first obtain the lagged murder rate, say mrdrte-1.

(i) Run the regression of mrdrte on exec, unem. What are the coefficient and t statistic on exec? Does this regression provide any evidence for a deterrent effect of capital punishment?

(ii) How many executions are reported for Texas during 1993? (Actually, this is the sum of executions for the current and past two years.) How does this compare with the other states? Add a dummy variable for Texas to the regression in part (i). Is its t statistic unusually large? From this, does it appear Texas is an “outlier”?

(iii) To the regression in part (i) add the lagged murder rate. What happens to exec and its statistical significance?

(iv) For the regression in part (iii), does it appear Texas is an outlier? What is the effect on exec from dropping Texas from the regression?

Step 1 of 8

(i)

The smallest number of schools in a district is 1 and the largest number of schools in the district is 162

There is one district id for which the number of schools is 162, that is 82010 and there are 271 district ids for which the number of schools is 1 each

There is 1010 unique district id in the datasets and there are 1848 school ids reported to be in these 1010 unique districts. Hence, on average there are 1.829703 schools per district on an average