Homework 6. Each question is worth 3 points, for a total value of 42 points 1. Suppose you are interested in using time series data to estimate the following population model: yt = β0 + β1xt + β2xt-1 + β3xt-2 + β4zt-1 + ut a. Based on this population model, how much would you expect y to change between period 1 and period 4 if x increased by 1 unit in period 1 and then stayed at that level from period 2 to period 5? (Your answer will not be a number, but will be expressed in terms of βs). b. Based on this population model, what is the expected value of y3 – y0 if x increased by one unit in period 1 then returned to its original level in the next period and did not change after? c. If you estimated this model using OLS, and you wanted to test the hypothesis “changes in x have an impact on y”, how would you test this hypothesis? (You answer this by explaining what stata command(s) you would use, by describing what you would do with Stata output, or by describing a statistical test in words). d. True, false, explain: OLS estimates of the β coefficients of this model will be biased if xt is correlated with xt-1 e. True, false, explain: OLS estimates of the β coefficients of this model will be biased if xt-1 is correlated with ut. f. True, false, explain: OLS estimates of the β coefficients of this model will be biased if ut-1 is correlated with ut. For the remaining questions, use the data set accident.dta, which is monthly time series data pertaining to about automobile accidents in a particular state. The data cover the nine years from 1981 to 1989, creating 108 observations (12 months X 9 years = 108). In January of 1986, the state passed a law requiring all passengers in automobiles to wear a seat belt. In mid 1987, the state raised its speed limit on interstate highways from 55 mph to 65 mph. Below is a list of the variables in the data set: year year of observation ( 1981 to 1989) totacc statewide total accidents fatacc statewide fatal accidents t time trend variable , 1 to 108 unem state unemployment rate speed =1 in months that 65 mph speed limit, 0 in months with 55 mph speed limit belt =1 in months with seatbelt law in effect, 0 in other months. wkends # weekends in month Eleven month dummies, feb =1 if month is February mar =1 if month is March and so on to dec =1 if month is December ltotacc log(totacc) lfatacc log(fatacc) prcfat 100*(fatacc/totacc) prcfat_1 prcfat lagged once In this question, you will be working with models that explain prcfat, the percentage of all automobile accidents in a month that are fatal. This variable is measured on a zero to 100 scale, and its mean is .8 (meaning that on average, a little less than 1 percent of all automobile accidents were fatal). 1. type the command tsset period This tells stata that the variable “t” defines the time period in this time series data set. (You must type this command each time you open the data set before doing any other analysis) Next, type the command twoway (tsline prcfat) This creates a time series graph with time period on the horizontal axis and prcfat on the vertical. a. What sort of trend, if any, does prcfat appear to have? b. Based on the average values of totacc and fatacc, if prcfat rises by 1, about how many additional fatal accidents does that represent? 2. type the command reg prcfat t feb mar apr may jun jul aug sep oct nov dec a. complete this sentence: based on the estimated coefficient for t, we can say that, other things equal, the percentage of all accidents that are fatal _____________ each year by _____________ percentage points. b. Other things equal, in what season of the year (summer, fall, winter, or spring) is prcfat the highest? 3. Now consider a model that looks at the impact of the unemployment rate, the speed limit, and the seatbelt law on prcfat, by typing the command: reg prcfat unem speed belt t feb mar apr may jun jul aug sep oct nov dec a. based on this regression, do changes in the unemployment rate have a statistically significant effect on the percentage of all accidents that are fatal? b. Would a recession that increased the unemployment rate by 3 points have a practically significant impact on the number of fatal accidents in the state? Explain your reasoning. c. Interpret the coefficient on speed. d. Re-estimate the model, but leave out the time trend (the variable t) reg prcfat unem speed belt feb mar apr may jun jul aug sep oct nov dec Note that the coefficient of speed falls in absolute value and becomes insignificant, while the coefficient on belt becomes more negative and more statistically significant. Explain why this happens.
