Temple University

Department of Economics

Econometrics II

Heteroscedasticity

On the web you find a file titled HETERO.DAT (or you can just click here) which contains the data for this problem set. The data is a cross section of 60 households. The dependent variable is weekly earnings. The independent variables are quality adjusted education and years of experience. You will note that households have been matched. That is, we have three sets of observations on the dependent variable for given values of the treatment variables. In effect, t he assumption that "the independent variables are constant in repeated samples of size n" has been operationalized.

1. Using the data on the diskette use OLS to estimate the parameters of

Save the residuals.

2. The error term in (1) is heteroscedastic.

A. Is the OLS estimator minimum variance?

B. Is the matrix calculated by the computer and purported to be an estimate of the
variance of the least squares estimator 'correct'?

C. If the reported coefficient covariance matrix is not correct, compute the correct
covariance matrix when using OLS in the presence of heteroscedasticity.

3. For the moment let us blunder ahead. Test the following hypotheses using the output from question 1:

What are your conclusions?

4. Redo question 3 using the correct coefficient covariance matrix for the uncorrected
OLS estimator.

Do you arrive at the same conclusions?

5. Order the data, including the saved residuals, on the basis of the magnitude of
experience.

a. Plot earnings against experience. What do you see?

b. Plot the residuals against experience. Describe what you see.

6. Use the Goldfeld-Quandt procedure to test for heteroscedasticity.

7. Use the Breusch-Pagan Lagrange multiplier test for heteroscedasticity. Is your conclusion consistent with your conclusion in question 5?

8. The variance of the error term in (1) is given by

Can you use this information to trick the computer into constructing an efficient estimator? That is, construct the weighted least squares estimates of the coefficients in (1).

9. Using your new, efficient estimator results reconstruct the tests of hypothesis in question 3. Compare the conclusions you reach in this question with those you reached in the earlier questions.