1. Wages and productivity. One way to consider the relationship between wage and productivity is to estimate the elasticity of hourly wage with respect to output per hour. The file earns contain annual data for the non-farm business sector in the U.S. from 1947 to 1987. The variable hrwage is average hourly wage, and outphr is output per hour, one measure for labor productivity.
(a) What might be the problem if we directly run the model below? (hint: check out the time plots for these two key variables.) log(ℎ�����!) = �" + �# log(����ℎ�!) + �!
(b) Now add a time trend to the above model and report the results. Interpret the estimated elasticity. (c) Do you find high or low first order autocorrelation? Provide the plots for the Autocorrelation Function (ACF) of these two variables.
(d) Now re-estimate the equation in first differences (no longer need a time trend). Interpret the estimated elasticity. Is the estimated elasticity statistically different from a unity elasticity?
(e) We define the growth in hourly wage and output per hour as the change in the natural log: �ℎ����� = ∆���(ℎ�����) �����ℎ� = ∆���(����ℎ�) Allow an increase in productivity growth to have both a current and lagged effect on wage growth by revising the previous model to the following: �ℎ�����! = �" + �#goutphr! + �$goutphr!%# + �! Report the results. Is the lagged value of goutphr statistically significant?
(f) If �# + �$ = 1, a permanent increase in productivity growth is fully passed on in higher wage growth after one year. Test �# + �$ = 1 as a null hypothesis and what can you conclude? (g) Does �����ℎ�!%$ need to be in the model? Explain.
2. Do changes in traffic laws affect traffic fatalities? 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.
(a) 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?
(b) 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?
(c) Add to the regression from part (b) the variables wkends, unem, spdlaw, and beltlaw. Interpret the coefficients on the unemployment variable, spdlaw and beltlaw. Do their signs and magnitude make sense to you? Are the estimated effects what you expected? Explain.
(d) The variable prcfat is the percentage of accidents resulting in at least one fatality. What is the average of prcfat over this period? Use prcfat as the dependent variable in place of log(totacc). Discuss the estimated effects and significance of the speed and seat belt law variables.
(e) Compute the first order autocorrelation coefficient for the variable prcfat. Are you concerned that prcfat contains a unit root? Do the same for the unemployment rate.
(f) Estimate a multiple regression model relating the first difference of prcfat, Dprcfat, to the same variables in part (d), except you should first difference the unemployment rate, too. Then, include a linear time trend, monthly dummy variables, the weekend variable, and the two policy variables; do not difference these. Do you find any interesting results?
(g – extra-credit) Using the standard Dickey-Fuller (k=0) regression, test whether prcfat has a unit root. Can you reject a unit root at the 5% level?
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