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The regression model speclfies that wlnning bld and shlpplng cost are Ilnearly related Conduct test (at the signlficance eve significant Iinea relationship between ...

Question

The regression model speclfies that wlnning bld and shlpplng cost are Ilnearly related Conduct test (at the signlficance eve significant Iinea relationship between shipping cost and winning bid when the seller has ow reputatlon;05) forThe value of the test statistic isand you conclude that there is significant linear relationship between shipping cost and winning bid_ The result of the significance test consistent with the notion that buyers pay attention to surcharge when it is levied by low&qu

The regression model speclfies that wlnning bld and shlpplng cost are Ilnearly related Conduct test (at the signlficance eve significant Iinea relationship between shipping cost and winning bid when the seller has ow reputatlon; 05) for The value of the test statistic is and you conclude that there is significant linear relationship between shipping cost and winning bid_ The result of the significance test consistent with the notion that buyers pay attention to surcharge when it is levied by low" reputation seller: The 95% confidence Interva estlmate of Bi Is Since in the confidence interval, vou conclude that there is significant linear relationship between shipping cost and winning bid, This result consistent with the notion that buyers pay attention to surcharge when it is levied by low-reputation seller: Conduct an test (at significance evel 05) of overall significance for the regression. (With degree of freedom in the numerator and n 2 _ 89 degrees of freedom in the denominator; 3.949 provides an area of 0.05 in the Upper tail,) The test statistic is and you conclude that there is significant linear relationship between shipping cost and winning bid.



Answers

This question asks you to study the so-called Beveridge Curve from the perspective of cointegration analysis. The U.S. monthly data from December 2000 through February 2012 are in BEVERIDGE.RAW.
(i) Test for a unit root in urate using the usual Dickey-Fuller test (with a constant) and the augmented DF with two lags of curate. What do you conclude? Are the lags of curate in the augmented DF test statistically significant? Does it matter to the outcome of the unit root test?
(ii) Repeat part (i) but with the vacancy rate, vrate.
(iii) Assuming that urate and vrate are both I(1), the Beveridge curve,
$$u r a t e_{t}=\alpha+\beta vrate +u_{t}$$
only makes sense if urate and vrate are cointegrated (with cointegrating parameter $\beta<0 )$ . Test for cointegration using the Engle-Granger test with no lags. Are urate and vrate cointegrated at
the 10$\%$ significance level? What about at the 5$\%$ level?
(iv) Obtain the leads and lags estimator with $cvrate_{t}$, $cvrate_{t-1}$ and $cvrate_{t+1}$ as the I(O) explanatory variables added to the equation in part (ii). Obtain the Newey- West standard error for $\hat{\beta}$ using four lags $(\mathrm{so} g=4$ in the notation of Section 12.5$) .$ What is the resulting 95$\%$ confidence interval for $\beta$ How does it compare with the confidence interval that is not robust to serial correlation (or heteroskedasticity)?
(v) Redo the Engle-Granger test but with two lags in the augmented DF regression. What happens? What do you conclude about the robustness of the claim that urate and vrate are cointegrated?

First one. The test for a unit root in series you rate unemployment rate using the usual dickey fuller test with a constant yeah. And the augmented dickey fuller with two legs of change of unemployment rate. I find that seven both times we are unable to reject the now hypothesis that unemployment rate series is a unit fruit. The legs are not significant. However, the significance of the legs matters. So the outcome of the unit root test, we will repeat what we have done in part one two series vacancy rate and report the result in part two. I guess similar result. So the rate is a unit root. Well part one and two. I use package the R. Package A. T. S. A. And the function is a D. F. Dot test. R. Three. We assuming that unemployment rate and vacation re rate are both integrated of level one. We test for co integration using the angle grandeur test with no legs. So the step the steps are as follow. We first regress, you read on the rate then we yet the residual and we run the key fuller has on the residual to see whether the residuals our unit root. I find that you're right and we rate Arco integrated at the 5% level. Yeah Heart Forest. I get the leads and lacks estimator of the change in vacancy rate and I did note that uh CB rates up minus one. This is for the lack and plus one is for the lead. This is a regression result. So the usual centered errors are in green and in round brackets, the robots that Iran's are in blue and in square brackets you can see that the main estimate on vacancy rate is highly significant. This one is not correct. So the centered errol the usual one for the estimate of the first lack of change in vacancy rate is 164 In all cases except for the estimate of the lead of C. V. Right. The robust standard Iran's are larger than the usual standard errors. This is usually the case it happens but rare that the robot standard errors are smaller than the usual standard errors. The r square of this regression is 0.77 So for the rate, because the robot standard error is larger than the usual standard error. So we will get a wider confidence interval if we use a robot standard error and for confidence interval you will run this function in our count in and you impose the name of the regression. It was spits all the 95% confidence intervals for all explanatory variables. The default version is the 95% interval. But because the standard barrel of this estimate is are very close, two versions are very close to each other so the confidence intervals should be roughly equal. Yeah. Last part. What you could say about real business of the claim that you rate and the rate are co integrated. Yeah. When I run the test and good grandeur, the results are not consistent across alternative types of process. In one case I can reject the notion that the residuals are united and for all the cases I cannot reject. So I conclude that the claim that you rate and be rate our co integrated is not robust.

Part one. This is the result of the simple regression equation. The estimate on education is 0.1 oh one with a standard barrel of 10.7 This variable is highly significant, and you can calculate the 95% confidence interval of the return to education as a range of from 8.7% to 11.5%. Recall that the 95% confidence interval is calculated as the estimate plus or minus the margin of error and the margin of error is the standard error times a critical value. We need to look at the alpha level of 5% because we need the 95% confidence. Yeah, you should have the alpha level because this is a two sided interval. The degree of freedom is the number of observations minus two. We need to degree of freedom or two pieces of information to estimate the slope. And there, uh, the to intercept the intercept and the slope coefficient. So this is what you get. Part two. The simple regression of education on C two. It gives the variable see to it is not significant. The T statistic, which is the ratio of the estimate over the standard error is minus 0.59 And so we cannot use see to it as an instrument for education. Part three. The multiple regression equation estimated by L s is as follows. The coefficient on education is 1.137 experience 0.11 to experience square point oh three. And we have other factors which are not our main focus in this problem. Mhm, even the estimate on education. You can see that the estimated return to education is now higher 13.7%. We convert the estimate on education 2% because our dependent variable, the left hand side variable is in log and education is in level Part four in the multiple regression above. In part two. Mm hmm. No. The one with other explanatory variables. In part three, the coefficient on C two. It is minus point 165 Yeah, and the T statistic is minus 2.8. So an increase of $1000? Yeah. In institution reduces years of education by about Hong 165 Remember that the Tunisian variables are measured in thousands. Part five. Now we estimate the multiple regression model by Ivy using See to it as an I V for education. The I V estimate of beta education is point 25 with a standard error of 250.1 to 2. The point estimate seems large, but the 95% confidence interval is very white from 1.1% to 48.9%. We could reject the value zero for beta education, but this confidence interval is too white to be useful. Lastly, part six very large standard error of the Ivy Estimate in Part five shows that the ivy analysis is not very useful. Yeah, and see to it is not convincing as an I V, as we can see also from part two mhm.

Part one. For the series lock of s and. p 500. The augmented dickey fuller statistic with our trend is T Equals -179. And the statistic with a train is minus 2.2. These are both above their respective 10 critical values and the estimated route close to one or the other series. The lock of industrial production index. The augmented dickey fuller statistics without a trend is -1.37 and with a trend it is -2.52. These again are not close to restricting even at the 10 level And the estimated roots are again very close to one part two. The simple regression of Lockett S&P 500 unlock of industrial production index is as follows. The T. Statistic for variable L. I. P. Is almost 70 and the R. Square is very close. 21 These are signs of a spurious regression or three Women. Is the residual U.T. had obtained from the model. In part two, we will run an augmented dickey fuller test and the statistic is -1.57. The estimated route is over fine 99 There's no evidence of co integration, March four Oops. This is part five. We should do part 4 1st We add a linear tantra into the regression from part two and again we run the augmented dickey fuller test. The T. Statistic from the test Is -1.88. And the estimated route Is again about .99. Yeah. So we come back to the conclusion in part three. There is no evidence of co integration. Even with a tam trinh R five, It seems that two series do not move together. Even if we allow them to have unrestricted timely near trends, linear time trends. The analysis that's not point is to a long run equilibrium relationship.


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