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Use the data in APPROVAL to answer the following questions. See also Computer Exercise $\mathrm{Cl} 4$ inChapter 10.(i) Compute the first order autocorrelations for the variables approve and lrgasprice. Do they seem close enough to unity to worry about unit roots?(ii) Consider the modelapprove$_{t}=\beta_{0}+\beta_{1} l c p i f o o d_{t}+\beta_{2}$lrgasprice$_{t}+\beta_{3}$unemploy$_{t}$$+\beta_{4} s e p 11_{t}+\beta_{5}$iraqinvade$_{t}+u_{r}$where the first two variables are in logarithmic form. Given what you found in part (i), why might you hesitate to estimate this model by OLS?(iii) Estimate the equation in part (ii) by differencing all variables (including the dummy variables) How do you interpret your estimate of $\beta_{2} ?$ Is it statistically significant? (Report the $p$ value.)(iv) Interpret your estimate of $\beta_{4}$ and discuss its statistical significance.(v) Add $l s p 500$ to the model in part (ii) and estimate the equation by first differencing. Discuss what you find for the stock market variable.

(i) Both rho's are about 0.93, high enough to worry about unit roots (ii) spurious regression (iii) (iv) see video (v) effect not significant

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Chapter 11

Further Issues in Using OLS with Time Series Data

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part one for two variables approved and lock riel gas price. The first order. Auto correlation coefficients are about 0.93 very close to one. So we should worry about these two. Siri's being you knit groups. Okay, Yeah. Given what we know in part one, we might hesitate to estimate this model by all ls because we're gonna violate one important old L as assumption the Siris in the regression need to be weekly dependent. So central limit your, um can apply, and we could yield unbiased estimates, which you need worth. Siris are not weakly dependent. You could try estimating the model, and you will find that the model has a high r squared. And almost all explanatory variables are highly significant. That is the expected result of a spurious regression. In Part three, we will estimate the equation in part to buy difference ing all variables, including the dummy variables. This is the result. Wait a two or estimate on the change in lock of riel gas price yeah, is statistically significant. At the 10% level, it has a value of minus 13.96 implying that if the ratio of riel gas price which is gas prize adjusted for inflation. If this ratio a real gas price to its past value changes by 1% then the approval rate changes. E should say if this ratio increases by 1% holding other variables fixed. Yeah, the approval rate when decreases when decreased by 13.9% points. Hartz four. We will interpret the estimate of beta for, or the coefficient of a dummy variable, the 9 11 event. This variable is highly significant. It is significant at the 1% level Wow controlling for other factors, The 9 11 event increases the approval rate at the same period by 15.6% point. In Part five, we will add to the equation the change in the lock of S and P 500 index. Yeah, the estimate on this new variable is four point 180 with a centered error of 12 point 777 That gives a T value of almost zero. We can conclude that the stock market variable does not have a significant effect on approval rate

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