Suppose that you are conducting a study in which you estimate a regression model to predict wages as a function of job-related mortality risks and several other variables. Your regression model looks like the following:
lnWAGE = Xb + bR*RISK + random error where WAGE = after-tax annual wages = $60,000, RISK = number of expected fatalities per 10,000 workers per year, and Xb captures the effects of all the other variables (such as age, sex, race, seniority, union membership, etc.) that you included in your model. NOTE: because the dependent variable is lnWAGE, we know that d(lnWAGE) = dWAGE/WAGE or dW/W using W for WAGE.
Suppose that you use a statistical software package to estimate the parameters of your model, and your results indicate that bR = 0.0163.
A. Using the results of your regression model, estimate the willingness-to-pay per statistical fatality avoided.
B. Using this model, what is the change in annual wages that you would expect workers to demand in order to accept an annual mortality risk increase of 1,000 in 10,000?
C. Suppose now the wage equation estimated is: WAGE = Xb + bR*RISK + random error. Again assume that annual wages are $60,000 and that RISK = number of expected fatalities per 10,000 workers per year, and Xb captures the effects of all the other variables (such as age, sex, race, seniority, union membership, etc.) that you included in your model. Suppose that you use a statistical software package to estimate the parameters of your model, and your results indicate that bR = 978. Using the results of your regression model, estimate the willingness-to-pay per statistical fatality avoided.
D. Now suppose we estimate: lnWAGE = Xb + bR*RISK + random error where lnWAGE is now the HOURLY wage rate, and bR = 0.10. Assume that workers work 2,000 hours per year and that mean hourly after-tax wages are $15.00. Calculate the value of a statistical year of life.