## Temple University

## Department of Economics

## Introductory Econometrics

## Heteroscedasticity Homework

## Practice

For this problem set use the dataset on home characteristics and prices. The data description can also be downloaded.

1. Local government and public schools are largely financed by property taxes. One's property tax bill is based on the tax rate and the assessed value of the house. From time to time the local tax authority must revise the assessed values of houses in the jurisdiction. To bring some regularity to the re-assessment process the authority often uses regression models. The dataset hprice1.wf1 has data on assessed value and house attributes. It is your job to help with the modeling of home attributes and assessed value.

a. Estimate by OLS the regression coefficients of and report your results.

b. For the same model as that in part a, use EVIEWS to find the heteroscedasticity robust standard errors for the coefficients and report your findings.

c.Compare and contrast your results for parts a and b.

d. Use EVIEWS to conduct a Breusch-Pagan test for heteroscedasticity at the 5% level and report your results.

e. Revise the model to by taking logs of *assess*, *lotsize* and *sqrft*, but not *bdrms*. Conduct a Breusch-Pagan test for heteroscedasticity at the 5% level.

f. In reviewing your resutls for aprts d and e, did transforming the data mitigate the heteroscedasticity problem in any way?

## Theory

2. Consider the linear regression model where the number of observations, n, is equal to 3m. The first three rows of the X matrix are

and every subsequent group of three rows is identical to this first group. The error covariance matrix Ω is
diagonal, with typical diagonal element equal to where ω > 0 and x_{2t}
is the t^{th} element of the second column of X.

a. What is the variance of , the OLS estimator of
?

b. What is the probability limit, as n →∞, of the ratio of the conventional
estimate of this variance, which assumes homoscedasticity, to a
heteroscedasticity consistent estimate based on ?