1. Using n = 97 observations on the rate of wage inflation (DW), the rate of price inflation (DP) and the unemployment rate (U₁), the following regression results are obtained by ordinary least squares; the dependent variable is DW₁, t= 1,2,...,n. Variable Coefficient SE HCSE HACSE constant 0.0242 0.0081 0.0103 0.0062 0.0177 0.0836 0.1505 0.0968 -0.9536 0.1430 0.2085 0.2044 0.6359 0.0837 0.1221 0.0758 U₁-1 DU DP-1 R² = 0.5248 SSR = 0.1285 RESET 1.4605 [0.2299] WH=13.727 [0.0000] BG=5.8774 [0.0040] DU₁ = U₁ - U₁-1 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? (e) 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 U₁-1 (the 0.05 quantiles that are needed for the interval are 1.6614). Given this confidence interval, would you say that U₁-1 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?
1. Using n = 97 observations on the rate of wage inflation (DW), the rate of price inflation (DP) and the unemployment rate (U₁), the following regression results are obtained by ordinary least squares; the dependent variable is DW₁, t= 1,2,...,n. Variable Coefficient SE HCSE HACSE constant 0.0242 0.0081 0.0103 0.0062 0.0177 0.0836 0.1505 0.0968 -0.9536 0.1430 0.2085 0.2044 0.6359 0.0837 0.1221 0.0758 U₁-1 DU DP-1 R² = 0.5248 SSR = 0.1285 RESET 1.4605 [0.2299] WH=13.727 [0.0000] BG=5.8774 [0.0040] DU₁ = U₁ - U₁-1 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? (e) 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 U₁-1 (the 0.05 quantiles that are needed for the interval are 1.6614). Given this confidence interval, would you say that U₁-1 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?
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 parts d and e
![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%2Fbdb68573-357f-4fc0-a2b1-22d1977cc6b6%2Fqnjbwk3_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?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: Write the given information.
VIEWStep 2: Explain the outcome of the test for each of the three diagnostic tests, RESET, WH and BG.
VIEWStep 3: Determine the preferred choice among SE, HCSE and HACSE.
VIEWStep 4: Test the null hypothesis that coefficient on DPt-1 is equal to 1.
VIEWStep 5: 90% confidence interval for the coefficient on Ut-1.
VIEWStep 6: Test whether the slope coefficients are jointly equal to zero at significance level 10%.
VIEWSolution
VIEW
Step by step
Solved in 7 steps with 7 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman