= 0 for (f) The model is augmented with four additional explanatory variables, S₁, S₁-U₁-1, St DU, and S₁ DP-1, where S, is a dummy variable such that S, t≤ 31 and S = 1 for t≥ 32. For the augmented model, SSR = 0.1047 and R² = 0.6127. (i) Use a conventional F-statistic to test the hypothesis that the coefficients on the four additional explanatory variables are jointly equal to zero at significance level 10% (the critical value for the test is 2.0091). State clearly what the distribution of the test statistic is under the null hypothesis. (ii) What do you conclude from this test? Explain. (g) Replacing the explanatory variable DP₁-1 in the original model with DW₁-1 gives a model with SSR = 0.1445 and R² = 0.4641. Compare the new model to the original model using the standard error of the regression, Akaike's infor- mation criterion and the coefficient of determination. Which is your preferred model?
= 0 for (f) The model is augmented with four additional explanatory variables, S₁, S₁-U₁-1, St DU, and S₁ DP-1, where S, is a dummy variable such that S, t≤ 31 and S = 1 for t≥ 32. For the augmented model, SSR = 0.1047 and R² = 0.6127. (i) Use a conventional F-statistic to test the hypothesis that the coefficients on the four additional explanatory variables are jointly equal to zero at significance level 10% (the critical value for the test is 2.0091). State clearly what the distribution of the test statistic is under the null hypothesis. (ii) What do you conclude from this test? Explain. (g) Replacing the explanatory variable DP₁-1 in the original model with DW₁-1 gives a model with SSR = 0.1445 and R² = 0.4641. Compare the new model to the original model using the standard error of the regression, Akaike's infor- mation criterion and the coefficient of determination. Which is your preferred model?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
can you answer part f and g for this
![1. Using n=97 observations on the rate of wage inflation (DW₁), the rate of price
inflation (DP,) and the unemployment rate (U₂), the following regression results are
obtained by ordinary least squares; the dependent variable is DW₁, t = 1, 2,..., n.
Variable
constant
U₁-1
DU
DP₁-1
Coefficient SE HCSE HACSE
0.0242 0.0081 0.0103 0.0062
0.0836 0.1505
0.0177
0.0968
-0.9536
0.1430 0.2085
0.2044
0.6359
0.0837 0.1221 0.0758
R² = 0.5248
SSR = 0.1285
RESET= 1.4605 [0.2299]
WH 13.727 [0.0000]
BG= 5.8774 [0.0040]
=
DU₁ = U₁ - U-1 is the change in the unemployment rate; SE is ordinary estimated
standard error; HCSE is heteroskedasticity consistent standard error; HACSE is
heteroskedasticity and autocorrelation consistent standard error; SSR is the sum
of squared residuals; R² is the coefficient of determination; RESET is Ramsey's
regression specification error test; WH is White's heteroskedasticity test; BG is the
Breusch-Godfrey test for second-order autocorrelation; figures in brackets are the
p-values of tests.
(a) For each of the three diagnostic tests, RESET, WH and BG, what does the
outcome of the test mean?
(b) In light of your answer in (a), which is your preferred choice among SE, HCSE
and HACSE, and why?
(c) In light of your answers in (a) and (b), test the null hypothesis that the coef-
ficient on DP-1 is equal to 1 against the alternative that it is less than 1 at
significance level 10% (the critical value for the test is -1.2907). State clearly
what the distribution of your test statistic is under the null hypothesis.
(d) In light of your answers in (a) and (b), compute a 90% confidence interval
for the coefficient on U-1 (the 0.05 quantiles that are needed for the interval
are 1.6614). Given this confidence interval, would you say that U-1 has a
significant effect on DW,? Explain.
(e) Use a conventional F-statistic to test whether the slope coefficients are jointly
equal to zero at significance level 10% (the critical value for the test is 2.1436).
State clearly what the distribution of the test statistic is under the null hy-
pothesis. In light of your answers in (a) and (b), is this test reliable?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96167457-d811-4af3-a382-0d03304a1ad0%2Fdfd19f15-bb86-4307-8d3f-61c8c71a52eb%2Fl8fs9up_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Using n=97 observations on the rate of wage inflation (DW₁), the rate of price
inflation (DP,) and the unemployment rate (U₂), the following regression results are
obtained by ordinary least squares; the dependent variable is DW₁, t = 1, 2,..., n.
Variable
constant
U₁-1
DU
DP₁-1
Coefficient SE HCSE HACSE
0.0242 0.0081 0.0103 0.0062
0.0836 0.1505
0.0177
0.0968
-0.9536
0.1430 0.2085
0.2044
0.6359
0.0837 0.1221 0.0758
R² = 0.5248
SSR = 0.1285
RESET= 1.4605 [0.2299]
WH 13.727 [0.0000]
BG= 5.8774 [0.0040]
=
DU₁ = U₁ - U-1 is the change in the unemployment rate; SE is ordinary estimated
standard error; HCSE is heteroskedasticity consistent standard error; HACSE is
heteroskedasticity and autocorrelation consistent standard error; SSR is the sum
of squared residuals; R² is the coefficient of determination; RESET is Ramsey's
regression specification error test; WH is White's heteroskedasticity test; BG is the
Breusch-Godfrey test for second-order autocorrelation; figures in brackets are the
p-values of tests.
(a) For each of the three diagnostic tests, RESET, WH and BG, what does the
outcome of the test mean?
(b) In light of your answer in (a), which is your preferred choice among SE, HCSE
and HACSE, and why?
(c) In light of your answers in (a) and (b), test the null hypothesis that the coef-
ficient on DP-1 is equal to 1 against the alternative that it is less than 1 at
significance level 10% (the critical value for the test is -1.2907). State clearly
what the distribution of your test statistic is under the null hypothesis.
(d) In light of your answers in (a) and (b), compute a 90% confidence interval
for the coefficient on U-1 (the 0.05 quantiles that are needed for the interval
are 1.6614). Given this confidence interval, would you say that U-1 has a
significant effect on DW,? Explain.
(e) Use a conventional F-statistic to test whether the slope coefficients are jointly
equal to zero at significance level 10% (the critical value for the test is 2.1436).
State clearly what the distribution of the test statistic is under the null hy-
pothesis. In light of your answers in (a) and (b), is this test reliable?
Transcribed Image Text:(f) The model is augmented with four additional explanatory variables, St, St-U₁-11
S DU and S DP-1, where S, is a dummy variable such that S
<= 0 for
t≤ 31 and S = 1 for t≥ 32. For the augmented model, SSR = 0.1047 and
R² = 0.6127.
(i) Use a conventional F-statistic to test the hypothesis that the coefficients
on the four additional explanatory variables are jointly equal to zero at
significance level 10% (the critical value for the test is 2.0091). State clearly
what the distribution of the test statistic is under the null hypothesis.
(ii) What do you conclude from this test? Explain.
(g) Replacing the explanatory variable DP-1 in the original model with DW₁-1
gives a model with SSR= 0.1445 and R2 = 0.4641. Compare the new model
to the original model using the standard error of the regression, Akaike's infor-
mation criterion and the coefficient of determination. Which is your preferred
model?
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