How to use GLS in the presence of heteroskedasticity

INSTRUCTIONS TO CANDIDATES

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Topics covered in this lab:

• Effect of heteroskedasticity

• How to detect heteroskedasticity

•How to use GLS in the presence of heteroskedasticity

Data Description

There are 6 variables in the data, with descriptions in order as follows: cigs, number of cigarette smoked per day, income, annual income in dollars, cigpric, state cigarette price, cents per pack, educ, years of schooling, age, in years, and restaurn, a dummy variable which equals 1 if state imposes restaurant smoking restrictions.

Tasks

1. Read in the data from the external text file, carry out the necessary data transformations and additional variable creation.

2. Use the reg procedure to carry out the following tasks.

ORegress cigs on log(income), log(cigpric), educ, age, age2, and restaurn. Save and submit a copy of the results.

• Carry out the White test. Is there evidence of heteroskedasticity?

• Test whether coefficients of log(income) and educ are significant or not using the heteroskedastic-robust standard errors. Report the results of the tests.

3. Follow the following steps to use the weighted least squares to implement the feasible GLS.

• Run the original regression and save the residuals as uhat.

• Create log(uhat2) by first squaring the OLS residuals and then taking the natural log.

• Run the regression of log(uhat2) on the same set of the regressors and save the fitted values; call these ghat. Are these regressors jointly significant?

• Take the reciprocal of the exponentiation of the fitted values to get h_hat = 1/exp(ghat).

• Estimate the original equation by WLS, using h_hat as weights. Save and submit a copy of the results.

• Conduct the White test for the WLS. Is there still evidence of heteroskedasticity?

 

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