Name:
Lab Exercise 2
Wing Hong Chan
EC395
Topics of Today’s exercise:
1. Heteroskedasticity
2. Goldfeld-Quandt, White, and BPG (LM) Tests
3. FGLS model (Multiplicative and Additive forms)
1. Suppose you want to examine the total travel expenditure from 51 states in the
U.S. and you setup the following model:
Et = β1 + β2Yt + β3Pt + ut
where
E = Travel Expenditure in million dollars
Y = Total Income in billion dollars
P = Total Population (billions)
Estimate the model by OLS and write out the results.
=
N=
R2 =
Adjusted R2 =
2. A Critic suggests that the variance of the error terms might change according to
the size of the total population. Carry out a Goldfeld-Quandt Test to confirm
his claim. (Drop the observations from 22 to 30)
H0 : variances are equal
H1 : sigma 1 sq < sigma 2 sq
df 1 =
df 2 =
Level of Significance =
Under H0, GQ ⇠ F(df 1, df 2) and the test statistics calculated is
GQ =
The critical value isDecision:
1
F c(df 1, df 2) =
3. Perform the White test
H0 :
df 1 = 5
H1 :
Level of Significance = 5%
Under H0, Whit <- 2 (df ) and the test statistics calculated is
White = N * R2 =
The critical value is
Decision:
4. Perform the BPG (LM) test
H0 :
df 1 =
H1 :
Level of Significance =
Under H0, LM ⇠
2(df )
and the test statistics calculated is
LM =
The critical value is
Decision:
2
5. Assuming that the variance of the error terms have the following structure
V ar(ut) = σ2Pt
Estimate the model by GLS and write out the results. (Write out the transformed
model and estimate the transformed model by OLS)
6. Assuming that the variance of the error terms have the following multiplicative
form
𝑉𝐴𝑅(𝑢𝑡 ) = 𝜎 2 𝑃t𝑡𝛿
Estimate the model by FGLS and write out the results. (Write out the transformed model and estimate the transformed model by OLS)
R2 =
Adjusted R2 =
N =
7. Assuming that the variance of the error terms have the following additive form
𝑉𝑎𝑟(𝑢𝑡 ) = 𝛼1 + 𝛼2 𝑃𝑡
Estimate the model by FGLS and write out the results. (Write out the transformed model and estimate the transformed model by OLS)
R2 =
Adjusted R2 =
N =
8. What is the marginal effect of income on travel expenditure?
OLS=41.06
FGLS (multiplicative) =19.625
FGLS (additive) = 15.085
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