The file TRAFFIC2 contains 108 monthly observations on automobile accidents, traffic laws, and some other variables for California from January 1981 through December $1989 .$ Use this data set to answer the following questions.
(i) During what month and year did California's seat belt law take effect? When did the highway speed limit increase to 65 miles per hour?
(ii) Regress the variable log(totacc) on a linear time trend and 11 monthly dummy variables, using January as the base month. Interpret the coefficient estimate on the time trend. Would you say there is seasonality in total accidents?
(iii) Add to the regression from part (ii) the variables wkends, unem, spdlaw, and beltlaw. Discuss the coefficient on the unemployment variable. Does its sign and magnitude make sense to you?
(iv) In the regression from part (iii), interpret the coefficients on spdlaw and beltlaw. Are the estimated effects what you expected? Explain.
(v) The variable prefat is the percentage of accidents resulting in at least one fatality. Note that this variable is a percentage, not a proportion. What is the average of prefat over this period? Does the magnitude seem about right?
(vi) Run the regression in part (ii) but use prefat as the dependent variable in place of log(totacc). Discuss the estimated effects and significance of the speed and seat belt law variables.

Answer

The simple average of prcfat over the period $1981-1989$ is 0.88563$\%$

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Introductory Econometrics

Chapter 10

Basic Regression Analysis with Time Series Data

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Video Transcript

Hartman. The variable belt law is the binary variable. It changes from 0 to 1 AT T equals 61 and that value is associate it with the date January 1986. For variable speed law, another binary variable. It changes from 0 to 1 AT T equals 77 and that corresponds to a date of May 19 87. This is the old L s result when we regress Total accident log of total accident on a time trend and monthly dummies, The coefficient of the time trend is 0.2 e and significant at the 1% level so controlling for seasonality total accident group by about 3% for a month over this period. And we can convert that to an annual rate of you take 12 times three, which is 3.6% of annual rate. Look at the estimates on the monthly dummies. We find a strong evidence of seasonality here. The base is January and when you look at the magnitude of other dummy coefficients, you may find that Ali February dummy has a negative coefficient. The one with the highest coefficient is December dummy. We can conclude that Ali February has a lower number of total accidents than January, which is the basement okay, and total accidents peak in December. Definitely there are 9.6% more accidents in December over January. In the average year, we can also test for joint significance of the monthly dummies. We will find the F statistic to be by 0.15 degrees of freedom are 11 and 95 respectively, and the P value of this F statistic is almost zero. So we are able to reject the non hypotheses in other words, the data such as a strong favor to the joint significance of the monthly dummies or seasonality. Let's move to Part three, where we add new variables to the right hand side of the equation. The coefficients are reported in blue, and it's standard Arrow is in green. The estimates on unemployment rate is negative and significant. The sign of this estimate makes sense if we see unemployment as a measure of economic activity. When economic activity increases, unemployment decreases, we expect more driving, and so more accidents. A 1% point increase in the unemployment rate reduces total accident okay by about 2.1% part four. When we look at the estimates of speed, law and belt law, we see that they are negative and positive, respectively. These seem counterintuitive what the binary speed law implies. That speed limit was increased from 55 to 65 mines per hour. That should increase the total accidents, but we have a negative estimates here for belt law about law. Binary variable implies that the law makes it mandatory for driver to wear seat belt. That should decrease the total accidents. However, we have a positive estimate. Our explanation could be for speed love. As speed limit increase, people become more cautious and that brings down the number of total accidents or the lot on seat belt. The possible explanation is the opposite. As people are asked to wear seat belts, they could become Yeah, more reckless. Well, yeah, that eventually increases the number of total accident. Part five. We wouldn't have a new dependent variable, the percent of fatality per accident. The percent of accidents result in a fatality. The average is 0.886 which mean all accident results to a less than 1% of fatality. The highest value of this variable is 1.217 meaning there was one month where 1.5% of all accidents resulting in a fatality. We will explain this new variable with the Tam Trine seasonality and for new variables. In part three, I will report the estimates on the new variables only. We have the estimates of unemployment rate to be negative and significant speed law and belt law. The is not very significant, but they have our expected sign from previous part. The Beta head of speed law is positive, implying that higher speed limit. Okay, increase the percent off fight. All accident. Okay, 5.67% each point. Yeah. The beta head of seat belt law is negative, implying that Okay, The change in seat Bella is expected to decrease the percent of fatal accident. Yeah, 5.3 However, this variable again is not statistically significant. Statistically different from zero. There is no significant even at the 10% level. This one is significant. Alright. For economic activity, which is proxy seed by unemployment rate, a lower unemployment rate is an indicator of better economic activity. Thank. And with growing economic activities, federal accidents the percent of fatal accidents increase. This could be because Mawr trucks are on the roads and these probably increase the chance that an accident becomes a fatality.

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