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TABLE #-Coellicients and Hazard Rauos 0 tfe Hultvanable Sunpilied Cox Proportonal Hazard Eorkel tor 10-Year Risk ot ICVdWoman(6"Cl 10+ 1-1.0 50136" 0ssi 1...

Question

TABLE #-Coellicients and Hazard Rauos 0 tfe Hultvanable Sunpilied Cox Proportonal Hazard Eorkel tor 10-Year Risk ot ICVdWoman(6"Cl 10+ 1-1.0 50136" 0ssi 104 1.05-1.13Kdc, / SHP , Mm Hg €zu489 0UJobo2777 ~0,5489 0,58" 0 36-0 92 3104 8267 0 4t 02+0,62 Retcien 10 Aeletem 100 0.4011 0.93-241 2294 0.66-2.32 0,8073 2.24+ 14} 351 0.7970 22 128-].84 1.7041 5,3+ 343-8 80 1,3874 303 223-6,01 2 5327 1234 745-21,28 18483 6.331 342-|1.8120-129 130-139 14-150 16-179 2i80 BML kym'3737 Rct

TABLE #-Coellicients and Hazard Rauos 0 tfe Hultvanable Sunpilied Cox Proportonal Hazard Eorkel tor 10-Year Risk ot ICVd Woman (6"Cl 10+ 1-1.0 5013 6" 0ssi 104 1.05-1.13 Kdc, / SHP , Mm Hg €zu 489 0 UJobo 2777 ~0,5489 0,58" 0 36-0 92 3104 8267 0 4t 02+0,62 Retcien 10 Aeletem 100 0.4011 0.93-241 2294 0.66-2.32 0,8073 2.24+ 14} 351 0.7970 22 128-].84 1.7041 5,3+ 343-8 80 1,3874 303 223-6,01 2 5327 1234 745-21,28 18483 6.331 342-|1.8 120-129 130-139 14-150 16-179 2i80 BML kym' 3737 Rcterem 10 3591 Aelerem 1153 0 2864 133 100-1,78 1422 6762 1971 131-2.,88 Tota| chokalctol , MmolL 2362 3.62-516 2517 Rc'creti 1.0 Aclctent 10 3082 ~0,0070 0,9 059-1,69 2976 0886 0C2 04-1,93 1127 0.304 071-234 1218 2064 0.62-2.73 Cunteit Elokcl; Tezro 3591 0.7082 204 142-290 0.4892 10" 111-232 Dabctec, Yeeino 0.0651 1.07 0.58 1.98 0.9599 261+ 157-43] Baselne surnal functon 10 yeare. St10 0,9835 0948 sep Indicales Eystle bbod Pleesure; BMi, body max Anei "001-Pc00s: tooi< 00; #Pcoco; Coetliacnt and batclint surhal unclins Etcd uIle totom tt Gbla 0ro Ucd comnpute cxponcital model bascd variables Iisted the Abk methxd Exacoy amboous ttat used In the Fnmingtam model the United Su7es, The Hazard Ratio for SBP >180 reported in the table as 12.59. Assuming that the corresponding beta coefficient correct; what can you say about the reported HR= 12.59? Choose one correct statement belaw HR is correct because the hand-calculate value 12.5901 HR is correct because the hand-calculate value 12.5875 HR is not correct because the hand- calculate value 9292 HR is not correct because the hand calculate value 1.2587



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.

Okay, so I actually learned something new today. Apparently, there's a formula that kind of tells you when a fledgling bird is going to be able to fly on its own. And it's the ratio of two functions of time, one of which kind of gives an indication for how long their wings are and the other one is their body mass. Okay, so whenever these ratios kind of approach one, whenever FFT approaches one thing, the fledging fledgling is able to fly on its own. You didn't know all this question is asking us to do is to interpret the physical meaning behind those and described the units associated with them. Okay, so the 1st 2 shouldn't be too difficult, right? Because M prime of tear is the time derivative. It's the time derivative of em of tea. It's a rate of change. It's how fast this function changes with respect to time. And since we're given that the average body mass is measured in grams, this is gonna be essentially grams per per unit time and that the time is in weeks, by the way, since grams per weeks and just like I said, ah, the interpretation of physical meaning is how fast the body mass is changing with respect to time. It's the rate of change of body mats. Okay, for w prime of tea, that's again the time derivative of W T. Which is the length of the wings. And since they said that wing length was gonna be measured in millimeters, this rate of change is millimeters per week. And again, it's just how fast the length of the ones you're changing F prime of tea has to have special analysis because, um, f prime of TIA is the time derivative of f of tear. But f of tia is the ratio. Oh, the length of the wings and the average body mass. These air two functions that change. So we actually do have to use the quotient rule, which is lo de I minus high. Do you low swearing the bottom and we're gonna determine the units of this function As far as a physical meeting goes out, I said half of Tia as FFT approaches one, then the fledgling is gonna be more able to fly. This is a rate of change of that. So if this is a really, really positive number, then it's going to rapidly go towards, and it's gonna take a lot less time for to be able to fly. Maybe it's some sort of growth spurt. So all that remains to do is to find the units of this I'm of Tia. Ah was measured in grams w prime of tea we said was millimeters per week. Okay, W of tea waas um millimeters and M prime of tea is grams per week, divided by AM of T squared M of T is measured in grants. This is just grams squared. Okay, so we have a grams times of millimeters minus of grams, times of millimeters, all divided by a week. Okay, so this is gonna be some sort of of grams times millimeters. We don't know. Of course you know how exactly these variables are changing, so they're obviously not gonna be the same necessarily. So when you subtract two things that are like each other, you're gonna get something else that's like each but that's like those two things. So this is gonna be some grams millimeters divided by weeks, all divided by Graham Sward, which is gonna be grams times, millimeters times, weeks times one over. Graham squared. One of these grams cancels with one of those, and then we're left with millimeters Her grands week. Here we go.


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