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The file FISH contains 97 daily price and quantity observations on fish prices at the Fulton Fish Markein New York City. Use the variable log(avgprc) as the dependent variable.$\begin{array}{l}{\text { (i) Regress log(avgprc) on four daily dummy variables, with Friday as the base. Include a linear }} \\ {\text { time trend. Is there evidence that price varies systematically within a week? }}\end{array}$$\begin{array}{l}{\text { (ii) } \text { Now, add the variables wave } 2 \text { and wave, which are measures of wave heights over the past }} \\ {\text { several days. Are these variables individually significant? Describe a mechanism by which }} \\ {\text { stormy seas would increase the price of fish. }}\end{array}$$\begin{array}{l}{\text { (iii) What happened to the time trend when wave } 2 \text { and wave } 3 \text { were added to the regression? What }} \\ {\text { must be going on? }}\end{array}$$\begin{array}{l}{\text { (iv) Explain why all explanatory variables in the regression are safely assumed to be strictly }} \\ {\text { exogenous. }} \\ {\text { (v) Test the errors for AR (1) serial correlation. }}\end{array}$$\begin{array}{l}{\text { (vi) Obtain the Newey-West standard errors using four lags. What happens to the } t \text { statistics on }} \\ {\text { wave } 2 \text { and waves? Did you expect a bigger or smaller change compared with the usual OLS }} \\ {t \text { statistics? }} \\ {\text { (vii) Now, obtain the Prais-Winsten estimates for the model estimated in part (ii). Are wave? and }} \\ {\text { wave } 3 \text { jointly statistically significant? }}\end{array}$

(i) See video. No evidence (ii) See video. Yes. A negative supply shock (iii) Time trend smaller and insignificant (iv) See video (v) strong evidence (vi) small changes compared to usual OLS (vii) See video

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Chapter 12

Serial Correlation and Heteroskedasticity in Time Series Regressions

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part one. This is the O. L s regression result. We regret the lock of average price on a temp trend T and with days Dummies. We have 97 observations and the our square is point 086 After estimating we win test a hypotheses where the estimates on the Day of the week dummies are zero, the test for joint significance is F equals 0.3 to 3 and a P value of 0.92. So we are unable to reject the non hypotheses. There is no evidence that the average price of fish vary systematically within a week. Part two, this is Theis. Estimated equation. We will include Wave two and Wave three dummies in the equation. You still have the time trend on Day of the Week dummies, and here are the results four wave to and wave three again. There are 97 observations, and our square of the regression is a little bit better than the previous one. We have 10.31 Yeah, so, based on their size, the relative size of the standard Iran's and their estimates, we find that each of the way variables is statistically significant with with to being the most important. The standard error of way to estimates is much smaller than the estimate itself. You can compare 0.2 and 0.9 for Wave three. It's standard error is also smaller than the estimate, so 0.2 is smaller than 0.4 but not as substantial as for wave, too. We can argue that bad sea conditions, as measured by highways, would reduce the supply of fish, and this would result in an increase in price. Let me write that down part three. We can see that after adding the wave dummies, the time trend coefficient becomes much smaller and statistically insignificant. And the reason could be admitted Variable bias without Wave two and Wave three dummies. The coefficient on the time trend seems to have a downward bias. Since we know the coefficients on Wave two and Wave three are positive, this is from the equation. In part two, it means the way variables are negatively correlated with tea. Yeah, in other words, the seas were rough for at the beginning of the sample period, and you can confirm the correlation between waves and time trend by regressing with two on T and with three auntie Hard. For we can argue that the temp Tran and daily dummies to be strictly exogenous because they are functions of time. And the collender, also the height of the ways is not influenced. Bypassed. Unexpected changes in the log of average price. First is, uh, calendar time. Yeah. And second, there's no feedback. Okay? From past information of the dependent variable. Her five we win. Regress the old L s residuals you had on one leg. Mhm. This is u t. Had on this is U T head minus one. Okay, we will get road ahead The coefficient on U T minus one of 0.618 with a standard error of 0.81 And the T value is very high. 7.6. So there is a strong evidence off Positive serial correlation art. Sixth women calculate the new E West standard errors and for two variables, wave two and weigh 53 dummies. We get 0.234 for wave to you and 0.1954 Wave three. They're not much different from their usual incorrect standard errands. This is surprising because parked fi. We showed that there is a significant amount of a are one serial correlation. Okay, Okay. Part seven. You will estimate the equation with prayers, Winston and you in test the joint significance of way to and way three. So I'm not sure why the textbook asked you to do that. Because the joint significance hypotheses, um, is somewhat advanced. And in the textbook itself, it doesn't mention how to you test that kind of hypothesis, so I wouldn't skip this part. How?

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