Econometrics I: Specification Tests
Dean Fantazzini
Dipartimento di Economia Politica e Metodi Quantitativi
University of Pavia
Overview of the Lecture
1st EViews Session IV: Structural breaks
Econometrics I: Specification Tests
Dean Fantazzini 2
Overview of the Lecture
1st EViews Session IV: Structural breaks
2nd EViews Session V: Heteroskedasticity and Autocorrelation tests
Econometrics I: Specification Tests
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EViews Session IV: Structural breaks
a) Open the workfile misspecification_p121.wf1. You find the following
variables:
Variable Description
Y log of per capita real expenditure on gasoline and oil
X2 log of the real price index for gasoline and oil
X3 log of per capita real disposable personal income
The dataset ranges between 1959q1 1992q1 and it is taken from
Econometric Methods by Johnston and DiNardo (1997). We want to
reproduce the example described in Section 4.4 on page 121-126.
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EViews Session IV: Structural breaks
b) Estimate the following equation:
Y = β0 + β1 · X2 + β2 · X3 + ε.
Since the first oil shock hit in 1973q4, we chose a sample period from
1959q1 to 1973q3, a period for which it might seem reasonable to postulate
parameter constancy.
⇒ Therefore, we use the first 51 observations for estimation (1959q1 -
1971q3), and the following 8 for the Chow Forecast test. Save it as eq p123.
c) Has β̂1 and β̂2 the sign you expected? Interpret.
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EViews Session IV: Structural breaks
e) Now estimate the same equation but with the full sample 1959q1 -
1973q3, save the equation as full sample and perform the Chow forecast
test as follows:
View -> Stability Tests -> Chow Forecast Test
and insert the date 1971q4 as the breakpoint date. What do you get?
f) Use the same procedure for the Chow Breakpoint test. What do you get?
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EViews Session IV: Structural breaks
g) The presence of major specification error in this too simple equation is
more firmly demonstrated by the recursive tests!
Compute the recursive residuals along with two standard error bands by
using the option
View -> Stability Tests -> Recursive Estimates -> Recursive
Residuals
with the full sample equation. Discuss.
h) Follow the same procedure to get the Recursive Coefficients and the
CUSUM tests. Discuss.
i) Finally, compute the RESET test. What are the null and the alternative
hypothesis? Do you reject the null hypothesis?
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EViews Session V: Heteroskedasticity and Autocorrelation
tests
a) Open the workfile Heteroskedasticity_tests_page_172.wf1. This
dataset contains a random sample of 100 observations from the Current
Population Survey, 1988. You find the following variables:
Variable Description
lnwage log of wage
grade years of education
potexp years of experience
exp2 years of experience squared
union 0/1 dummy variable for membership in a union
We want to reproduce the example described in Section 6.3.2 on page
172-174 of the book Econometric Methods by Johnston and DiNardo
(1997).
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EViews Session V: Heteroskedasticity and Autocorrelation
tests
b) Estimate the following conventional earnings equation:
lnwage = β0 + β1 · grade + β2 · potexp + β3 · exp2 + β4 · union + ε.
where the estimation sample goes from 1 to 100. Save this equation as
eq p172 and compute the residuals series as
Proc -> Make Residuals Series -> Ordinary
c) Has β̂1 , β̂2 , β̂3 β̂4 the sign you expected? Interpret.
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EViews Session V: Heteroskedasticity and Autocorrelation
tests
d) Compute the White Heteroskedasticity test by clicking on
View -> Residuals Tests -> White Heteroskedasticity test (cross
terms)
1. What are the null and alternative hypotheses?
2. What is the number of degrees of freedom?
3. Find the 5% critical value
4. Do you reject the null hypothesis?
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EViews Session V: Heteroskedasticity and Autocorrelation
tests
e) To apply the Breusch-Pagan test, one must specify the variables that
one thinks influence the heteroskedasticity. We select grade, potexp and
union as possible candidates. We generate the squared residuals
Genr -> ressq=resid01∧ 2
and we then compute the following regression (save it as breusch pagan):
ressq = β0 + β1 · grade + β2 · potexp + β3 · union + ǫ.
Remembering that the Breusch-Pagan test statistic is computed as
1 1 R2
2
ESS = 2 1−R2
RSS, and you have to correct this quantity for the scale
factor σ̂ 2 , i.e. the residuals sample variance, answer these questions:
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EViews Session V: Heteroskedasticity and Autocorrelation
tests
1. What are the null and alternative hypotheses?
2. What is the number of degrees of freedom?
3. Find the 5% critical value
4. Do you reject the null hypothesis?
If we use the alternative test statistics nR2 , which is asymptotically
equivalent, what do we get?
f) Finally compute the Breusch-Godfrey test in eq p172 by clicking on
View -> Residual Tests -> Serial Correlation LM Test - 4
1. What are the null and the alternative hypotheses?
2. What is the number of degrees of freedom and which distribution does
this test statistic follow?
3. What is the 5 % critical value?
4. What is the result of the test?
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