| Objectives: Testing for Heteroskedasticity using the Breusch-Pagan
(BP) and White tests using the gas10.xls
data
file in example 10.5 on pages 355-361. The data file contains information
for the 50 states on PCON (petroleum consumption in each state), REG (motor
registrations in each state), and TAX (the gas tax in each state).
PCON is measured in millions of BTUs, REG is measured in thousands, and
TAX is cents per gallon.
Assignment:
You will have to run an ordinary least squares regression of PCON against
REG and TAX, plot the error (residual) terms against the explainer values,
conduct the B-P and White tests for heteroskedasticity, and re-estimate
the results correcting for the latter using the White and HC3 corrections.
a. Generate descriptive statistics for the PCON, REG and
TAX variables using EALimdep (click here
for help). What do they tell us about the average values and
dispersion of the variables. Discuss in the specific terms in which
each variable is measured.
b. Run an ordinary least squares (OLS) regression
of PCON on REG and TAX and (1) plot the error (residual) terms against
the explainer values [after you specify the PCON and ONE, REG and TAX variables
in the regression, click on the OUTPUT tab and click on <Plot residuals><Against
variable>< REG>], and (2) save the error terms as a new variable [also
on the OUTPUT tab, click on <Keep residuals as variable> and type in
ERROR as the name]. What does the plot suggest about the distribution
of the error terms? Rerun the regression but plot the residuals against
the TAX variable. What does this plot suggest about the distribution
of the error terms? Do your conclusions agree with Studenmund's on
p. 373?
d. Generate the Breusch-Pagan (B-P) test for heteroskedasticity
by re-running the regression of PCON on ONE, REG and TAX, and on the regression
procedures <OPTIONS> tab, click on <Robust VC matrix><hetero (HC3)>.
Conduct a B-P test for heteroskedasticity. By specifying <hetero.(HC3)>,
EALimdep generates the HC3 corrected results. Compare the HC3 corrected
results to the OLS results.
e. To generate the necessary information for the White test for
heteroskedasticity, you must create squared error terms and also squared
values for the explainers and an interaction term between the two explainers.
Since you saved the residuals as a variable named ERROR in the first regression,
you can create a squared error variable by clicking on <Project><New><Variable>
and typing in ERRORSQ in the NAME box, and ERROR*ERROR as the Expression.
Similarly you can create a squared REG variable by clicking on <Project><New><Variable>
and typing in REGSQ in the NAME box, and REG*REG as the Expression.
Likewise you can create a squared TAX variable by clicking on <Project><New><Variable>
and typing in TAXSQ in the NAME box, and TAX*TAX as the Expression. To
create the interactive variable, click on <Project><New><Variable>
and type in REGTAX in the NAME box, and REG*TAX as the Expression. Then
run a regression with ERRORSQ as the dependent variable and REG, REGSQ,
TAX, TAXSQ and REGTAX as the explainers. Then conduct the White test.
f. What are the consequences of using Ordinary Least Squares
if the error terms are heteroskedastic? |