Chat with AI
Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge
Edition 6ISBN: 130527010XIntroductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge
Edition 6ISBN: 130527010XConsider a standard multiple linear regression model with time series data:
![Consider a standard multiple linear regression model with time series data: Assume that Assumptions TS.1, TS.2, TS.3, and TS.4 all hold. (i) Suppose we think that the errors {<i>u</i><sub>t</sub>} follow an AR(1) model with parameter and so we apply the Prais-Winsten method. If the errors do not follow an AR(1) model– for example, suppose they follow an AR(2) model, or an MA(1) model–why will the usual Prais-Winsten standard errors be incorrect? (ii) Can you think of a way to use the Newey-West procedure, in conjunction with Prais- Winsten estimation, to obtain valid standard errors? Be very specific about the steps you would follow. [Hint: It may help to study equation (12.32) and note that, if {<i>u</i><sub>t</sub>} does not follow an AR(1) process, <i>e</i><i>t </i>generally should be replaced by <i> </i>where <i> </i>is the probability limit of the estimator <i> </i> Now, is the error serially uncorrelated in general? What can you do if it is not?] (iii) Explain why your answer to part (ii) should not change if we drop Assumption TS.4.](https://d2lvgg3v3hfg70.cloudfront.net/SMCC2709/91b4e9f3_14f6_488e_a199_d747c5565a0a_SMCC2709_11.jpg)
Assume that Assumptions TS.1, TS.2, TS.3, and TS.4 all hold.
(i) Suppose we think that the errors {ut} follow an AR(1) model with parameter ![Consider a standard multiple linear regression model with time series data: Assume that Assumptions TS.1, TS.2, TS.3, and TS.4 all hold. (i) Suppose we think that the errors {<i>u</i><sub>t</sub>} follow an AR(1) model with parameter and so we apply the Prais-Winsten method. If the errors do not follow an AR(1) model– for example, suppose they follow an AR(2) model, or an MA(1) model–why will the usual Prais-Winsten standard errors be incorrect? (ii) Can you think of a way to use the Newey-West procedure, in conjunction with Prais- Winsten estimation, to obtain valid standard errors? Be very specific about the steps you would follow. [Hint: It may help to study equation (12.32) and note that, if {<i>u</i><sub>t</sub>} does not follow an AR(1) process, <i>e</i><i>t </i>generally should be replaced by <i> </i>where <i> </i>is the probability limit of the estimator <i> </i> Now, is the error serially uncorrelated in general? What can you do if it is not?] (iii) Explain why your answer to part (ii) should not change if we drop Assumption TS.4.](https://d2lvgg3v3hfg70.cloudfront.net/SMCC2709/c098183d_a0d5_4b5d_953b_b8d086d8df7a_SMCC2709_11.jpg)
and so we apply the Prais-Winsten method. If the errors do not follow an AR(1) model– for example, suppose they follow an AR(2) model, or an MA(1) model–why will the usual Prais-Winsten standard errors be incorrect?
(ii) Can you think of a way to use the Newey-West procedure, in conjunction with Prais- Winsten estimation, to obtain valid standard errors? Be very specific about the steps you would follow. [Hint: It may help to study equation (12.32) and note that, if {ut} does not follow an AR(1) process, et generally should be replaced by ![Consider a standard multiple linear regression model with time series data: Assume that Assumptions TS.1, TS.2, TS.3, and TS.4 all hold. (i) Suppose we think that the errors {<i>u</i><sub>t</sub>} follow an AR(1) model with parameter and so we apply the Prais-Winsten method. If the errors do not follow an AR(1) model– for example, suppose they follow an AR(2) model, or an MA(1) model–why will the usual Prais-Winsten standard errors be incorrect? (ii) Can you think of a way to use the Newey-West procedure, in conjunction with Prais- Winsten estimation, to obtain valid standard errors? Be very specific about the steps you would follow. [Hint: It may help to study equation (12.32) and note that, if {<i>u</i><sub>t</sub>} does not follow an AR(1) process, <i>e</i><i>t </i>generally should be replaced by <i> </i>where <i> </i>is the probability limit of the estimator <i> </i> Now, is the error serially uncorrelated in general? What can you do if it is not?] (iii) Explain why your answer to part (ii) should not change if we drop Assumption TS.4.](https://d2lvgg3v3hfg70.cloudfront.net/SMCC2709/628543b6_2e23_4f75_b77b_2ba1a8e92069_SMCC2709_11.jpg)
where ![Consider a standard multiple linear regression model with time series data: Assume that Assumptions TS.1, TS.2, TS.3, and TS.4 all hold. (i) Suppose we think that the errors {<i>u</i><sub>t</sub>} follow an AR(1) model with parameter and so we apply the Prais-Winsten method. If the errors do not follow an AR(1) model– for example, suppose they follow an AR(2) model, or an MA(1) model–why will the usual Prais-Winsten standard errors be incorrect? (ii) Can you think of a way to use the Newey-West procedure, in conjunction with Prais- Winsten estimation, to obtain valid standard errors? Be very specific about the steps you would follow. [Hint: It may help to study equation (12.32) and note that, if {<i>u</i><sub>t</sub>} does not follow an AR(1) process, <i>e</i><i>t </i>generally should be replaced by <i> </i>where <i> </i>is the probability limit of the estimator <i> </i> Now, is the error serially uncorrelated in general? What can you do if it is not?] (iii) Explain why your answer to part (ii) should not change if we drop Assumption TS.4.](https://d2lvgg3v3hfg70.cloudfront.net/SMCC2709/83cd048a_f911_4271_8a89_d0778f0a0f72_SMCC2709_11.jpg)
is the probability limit of the estimator ![Consider a standard multiple linear regression model with time series data: Assume that Assumptions TS.1, TS.2, TS.3, and TS.4 all hold. (i) Suppose we think that the errors {<i>u</i><sub>t</sub>} follow an AR(1) model with parameter and so we apply the Prais-Winsten method. If the errors do not follow an AR(1) model– for example, suppose they follow an AR(2) model, or an MA(1) model–why will the usual Prais-Winsten standard errors be incorrect? (ii) Can you think of a way to use the Newey-West procedure, in conjunction with Prais- Winsten estimation, to obtain valid standard errors? Be very specific about the steps you would follow. [Hint: It may help to study equation (12.32) and note that, if {<i>u</i><sub>t</sub>} does not follow an AR(1) process, <i>e</i><i>t </i>generally should be replaced by <i> </i>where <i> </i>is the probability limit of the estimator <i> </i> Now, is the error serially uncorrelated in general? What can you do if it is not?] (iii) Explain why your answer to part (ii) should not change if we drop Assumption TS.4.](https://d2lvgg3v3hfg70.cloudfront.net/SMCC2709/4795f489_2d0f_4201_8f12_8b5efa96f675_SMCC2709_11.jpg)
Now, is the error ![Consider a standard multiple linear regression model with time series data: Assume that Assumptions TS.1, TS.2, TS.3, and TS.4 all hold. (i) Suppose we think that the errors {<i>u</i><sub>t</sub>} follow an AR(1) model with parameter and so we apply the Prais-Winsten method. If the errors do not follow an AR(1) model– for example, suppose they follow an AR(2) model, or an MA(1) model–why will the usual Prais-Winsten standard errors be incorrect? (ii) Can you think of a way to use the Newey-West procedure, in conjunction with Prais- Winsten estimation, to obtain valid standard errors? Be very specific about the steps you would follow. [Hint: It may help to study equation (12.32) and note that, if {<i>u</i><sub>t</sub>} does not follow an AR(1) process, <i>e</i><i>t </i>generally should be replaced by <i> </i>where <i> </i>is the probability limit of the estimator <i> </i> Now, is the error serially uncorrelated in general? What can you do if it is not?] (iii) Explain why your answer to part (ii) should not change if we drop Assumption TS.4.](https://d2lvgg3v3hfg70.cloudfront.net/SMCC2709/1ae0a96b_37f4_4731_866e_bac081ef6431_SMCC2709_11.jpg)
serially uncorrelated in general? What can you do if it is not?]
(iii) Explain why your answer to part (ii) should not change if we drop Assumption TS.4.
Verified
Step 1 of 3
(i)
If the errors follow an
or
then the standard errors will not be correct because any strange transformation will not be able to completely eliminate the serial correlation in
. The regression estimates of the residuals having a single lag can be expected to constantly calculate the correlation coefficient, on the other hand, the variables which are transformed as
are expected to have serial correlations which is represented by
.
Step 2 of 3
Step 3 of 3
Why don’t you like this exercise?
Other
