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Use the data in TRAFFIC2 for this exercise.$\begin{array}{l}{\text { (i) Run an OLS regression of prefat on a linear time trend, monthly dummy variables, and the }} \\ {\text { variables wkends, unem, spdlaw, and beltlaw. Test the errors for AR (1) correlation }} \\ {\text { using the regression in equation }(12.14) . \text { Does it make sense to use the test that assumes strict }} \\ {\text { exogeneity of the regressors? }}\end{array}$$\begin{array}{l}{\text { (ii) Obtain serial correlation- and heteroskedasticity-robust standard errors for the coefficients on }} \\ {\text { spdlaw and beltlaw, using four lags in the Newey-West estimator. How does this affect the }} \\ {\text { statistical significance of the two policy variables? }}\end{array}$$\begin{array}{l}{\text { (iii) Now, estimate the model using iterais-Winsten and compare the estimates with the OLS }} \\ {\text { estimates. Are there important changes in the policy variable coefficients or their statistical }} \\ {\text { significance? }}\end{array}$

(i) Some evidence of positive serial correlation. See video for arguments for strict exogeneity (ii) Still significant for speed law but insignificant for belt law (iii) no important changes

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Chapter 12

Serial Correlation and Heteroskedasticity in Time Series Regressions

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part one. We get the old l s residuals u T hat. Then we run their regression with U T hat on its first leg. The coefficient on U T had minus one is row het and it is 0.281 with a standard error of 0.94 This produced a T statistic of 2.99 So there is evidence for serial correlation in the errors. Yeah. Yeah, this test required strict XO gen ity and we can make a case that all explanatory variables are strictly exhaustion is for the dummies such as, Ah, seasonal dummy and we can dummies. And also the time trend. They must be exogenous because they are determined by the calendar. Yeah, For statewide unemployment rate, it is safe to assume that unexplained changes in P R C F 80 the dependent variable today do not cause future changes. Instead, wide unemployment rate human makes Yeah, and lastly for the two policy variables speed limit law and sit Bell Law, it's reasonable. Thio assume these variables to be strictly exhaustion ists because over this period the policy changes were permanent once they occurred. Part two, we are still estimating the Betas by old L s. But we're computing different standard errors that have some raw business to serial correlation. The Beta head of speed law is 0.6 71 with a standard error of 0.267 and the Beta head of seat belt law is minus 0.2 95 and the standard error is 950.331 Compared to the old L as standard error and T statistic, you may find that the T statistic four speed law has fallen to about 2.5. But the variable is still significant. Yeah. For seat belt law, the T statistic is less than one in absolute value. So given the new computation of standard error, we find little evidence that sit Bella had an effect on the percent of, um, accidents, resulting in fatality for three. This is the estimates using P W method, and I skip the results for the Tan Trinh and the monthly Dummies. Row Hot is 0.289 You may find that there is no important changes. Both policy variable coefficients get closer to zero, and the standard heroines are bigger than the incorrect old l s standard errors, so the basic conclusion is the same. The increase in the speed limit appeared to increase PR cf 80 but the seat belt law, why it is estimated to decrease PR CF 80 does not have a statistically significant effect.

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