Econometrics
NENU, Spring 2018
S. Yen
7/2/18
A random sub-sample of 184 credit card holders was draw from a study sample of credit card
holders in Malaysia. Variables (underlined) include card debt (in hundreds of RM (Malaysian
Ringgit, US$1.00 RM4.23), household size (hhsize), age (in years), number of loan
commitments (loans), and dummy variables indicating ownership of a current/checking account
(checking), gender (male), high school education (hs), tertiary education (tertiary), and residence
in the territories (States) of Kuala Lumpur (kl) and penang. You will estimate two equations:
debt = β0 + β1 hhsize + β2 age + β3 loans + β4 checking + β5 kl + β6 penang + β7 hs
+ β8 tertiary + u (Model 1)
debt = β0 + β1 hhsize + β2 age + β3 loans + β4 checking + β5 kl + β6 penang (Model 2)
debt = β0 + β1 log(hhsize) + β2 log(age) + β3 loans + β4 checking + β5 kl + β6 penang (Model 3)
When a heteroscedasticity specification is called for, consider using (hhsize, age) in the equation.
In all tests of hypothesis, state your null and alternative hypotheses, test statistic, rejection
region, carry out the test, and interpret the test result in the context of the problem. Use an
appropriate level of significance deemed appropriate (i.e., among 0.01, 0.05, and 0.10 levels).
a. Estimate both models by OLS.
b. Test for statistical significance of age in Model 1, using t-test.
c. Test for joint significance of the education variables (hs, tertiary) in Model 1, using F test.
d. Estimate the true slope coefficient of age, based on in Model 1. Use a 95% confidence level.
e. Repeat with a Wald test.
f. Repeat with a likelihood-ratio (LR) test.
g. Repeat with a Lagrange multiplier (LM) test.
h. Repeat with a heteroscedasticity-robust LM test.
i. Calculate the variance-inflation factors for all variables used in in Model 1. Interpret your
results.
Base your remaining analysis on in Model 2, unless indicated otherwise.
j. Test for overall significance of the restricted model, using F test.
k. Repeat with a Wald test.
l. Repeat with an LR test.
m. Bootstrap standard errors for OLS estimates of the restricted model, with 1000 replications.
Use a random seed of 12345671.
n. Estimate the mean of debts at (hhsize, age, loans, checking, kl, penang) = (4, 35, 2, 1, 0, 0).
Interpret the result.
o. Estimate the (actual) amount of debts at the aforementioned values of explanatory variables.
Interpret the result.
p. Test for equality of all coefficients between males and females, using the interaction-term
approach, with a Wald test.
q. Test for equality of all slope coefficients between males and females, using the interaction-
term approach, with a Wald test.
r. Test for equality of all coefficients between males and females, using the segmented-sample
approach.
s. Test for equality of all slope coefficients between males and females, using the segmented-
sample approach.
t. Test for equality of the coefficients of hhsize and age, between males and females.
u. Calculate heteroscedasticity-robust standard errors for the OLS estimates for the restricted
model, and compare them with the conventional standard errors.
v. Test for heteroscedasticity of error terms, using Breusch-Pagan (BP) test.
w. Repeat with a modified White test.
x. Repeat with a Breusch-Pagan-Godfrey (BPG) test.
y. Estimate Model 2 with feasible generalized least-squares (FGLS) procedure.
z. Replicate the FGLS estimates long-hand.
aa. Based on the FGLS estimates, test for statistical significance of hhszie.
ab. Now, revisit Model 1 and estimate it with FGLS as well. Test for statistical significance of
the education variables (hs, tertiary), using F test.
ac. Repeat with a Wald test.
ad. Test for overall significance of the estimates for Model 2 (estimated with FGLS above),
using Wald test.
ae. Repeat with an F test.
af. Estimate Model 2 with exponential heteroscedasticity, again, using (hhsize, age) in the
heteroscedasticity equation.
ag. Based on the ML estimates, test for heteroscedasticity with a Wald test.
ah. Repeat with an LR test.
ai. Repeat with an LM test.
aj. Test for possible misspecification in Model 2, using a RESET test. What kind of
misspecification are you testing for?
ak. Carry out a test to choose between Model 2 and Model 3, using the encompassing model
approach of Mizon and Richard (1986). Your test comprises two parts: against Model 2 and
against Model 3.
al. Repeat with an augmented-regression approach of Davidson-MacKinnon (1981). Again, your
test comprises two parts.
am. Repeat with Vuong’s (1989) nonnested specification test.