The Effect of Occupational Danger on Individuals Wage Rates. A fundamental problem confronting the implementation of many healthcare

Transcription

1 The Effect of Occupational Danger on Individuals Wage Rates Jonathan Lee Econ Spring 2003 PID: A fundamental problem confronting the implementation of many healthcare policies is the issue of attaching a monetary value to human life. Intuitively upon first glance it would seem that one couldn't possibly attach any monetary value to human life. Upon further inspection, however it becomes obvious that one must be able to attach a monetary value on human life in order to perform an effective cost-benefit analysis of a suggested healthcare policy. Model In the past, forgone wages have often been suggested as a means to estimate the value of human life. This approach, known as the human capital approach, "estimates the present value of an individuals future earnings" (see Folland, Goodman,& Stano, 2001). The problem with this approach is that it places a higher value of life on individuals that have a higher wage rate. The human capital approach is therefore simply an accounting measure of the value of life, because it completely leaves out any theory of utility in the benefit estimation process. Economic value however, is not the same as accounting value and the human capital approach completely leaves out any measure of the intrinsic value that an individual may place on his or her life. Theoretically, a person making a very low wage could place an extremely high value on his or her life, while someone making a higher wage may not place such a high value on life. In light of this, it is quite likely that any estimation of the value of life that solely uses the human capital approach will vastly underestimate the true value of life. Intuitively, it makes sense to include the intrinsic Lee 1

2 values that individuals place on their life in the estimation of the value of human life. The problem with including these intrinsic values, however is that they cannot be easily measured quantitatively. The purpose of this study is to construct a model that measures individuals intrinsic value of life by measuring their willingness to pay for safety. In order to measure this willingness to pay for safety (life); it is necessary to construct a model in which individuals wage rates are dependent upon a variable for danger in the job place. Intuitively, one would expect there to be a positive correlation between wage rate and danger, because individuals would have to be paid more to work in a job that is dangerous. The model will also have to include variables for age, race, and education in order to isolate the effects of these variables on the wage rate. Age and education are expected to be positively correlated with the wage rate, while the effects of race will be dependent upon the variables included for race. Data All of the data in this data set, except the data on fatality percentages, came from the Panel Study of Income Dynamics. This is a study out of the University of Michigan that has been conducted since The data on fatality percentages came from statistics collected by the Bureau of Labor for the year The industry classification in the PSID data for the head of the household was made using an industry code from the 1970 census. The data on industry fatality percentages on the other hand, was classified according to the requirements of the 1987 Standard Industrial Classification Manual. It was therefore necessary to convert the 1970 industry codes into the industry codes specified in the 1987 SIC manual to insure the correct industry-fatality specification in the model. Lee 2

3 Variable Description Mean(SE) wagerate ageofhead yearsofeducation black latino other fatalitiescent Ageofhead2 This is a measure of the hourly wage rate for the head of the interviewed household. This is a variable for the age of the head of the interviewed household. This is a variable for the years of completed education for the head of the interviewed household. =1 if the race of the head of the interviewed household is black. =1 if the race of the head of the interviewed household is Latino. =1 if the race of the head of the interviewed household is something other than black, Latino, or white. This is a measure of the percentage of the fatalities in the industry that the head of the interviewed household works in. (# of fatalities/# of workers in industry, at the 2digit SIC level). This is a variable for the squared age of the head of the interviewed household ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Estimation A Feasible Generalized Least Squares technique was used to estimate the model, since the possibility of heteroskedasticity could not be rejected with the White test. This is a weighted test that ensures estimates will be efficient, and will have accurate t- statistics. The estimated model had a very high F-statistic of , so the hypothesis that the coefficient on all of the variables is actually zero can be rejected at the 99% confidence level. Furthermore, the model had a fairly high R 2 value of.2432 suggesting that approximately 24% of the behavior of the data is explained by the regression. Hypothesis tests were performed on all of the variables, and they were all found to be statistically significant except for the variable fataliescent. Ageofhead, yearsofeducation, black, latino, ageofhead2, and the constant variable were all statistically significant at the Lee 3

4 99% confidence level. The variable other was also statistically significant at approximately the 98% confidence level. Significant variables have been highlighted in the regression results. Number of obs = 4281 F( 7, 4273) = Prob > F = R-squared = Root MSE = Variable Wage Rate Coef. Std. Err. t-statistic P> t [95% Confidence Int.] Ageofhead Yearsofeducatio n Black Latino Other Fatalitiescent Ageofhead Constant Discussion The coefficients on all of the variables have the expected effect on the wage rate. Wage increases with age, but the negative coefficient on ageofhead2 indicates that the wage rate levels off as age gets higher. The wage rate also increases with education, and decreases if the head of the household is any other race than white. The coefficient on fatalitiescent is positive as one would expect, but unfortunately the hypothesis that the coefficient is actually zero cannot be rejected with any significant degree of confidence. Since the fatalitiescent variable is statistically insignificant, the hypothesis posed in the introduction cannot be effectively answered with this data set. It could very well be that job safety has no significant effect on the wage rate, which would suggest that individuals Lee 4

5 place no intrinsic value on safety. On the other hand, job safety could have a fairly large effect on the wage rate as can be seen in the wide range of the 95% confidence interval for the variable. No definitive answers however can be drawn regarding the interaction between wage rate and fatality percentages. Conclusions All of the variables for predicting the wage rate have been show to be statistically significant with high t-scores, except the variable fatalitiescent. The robust regression technique employed therefore does an excellent job of predicting the wage rate, and is an effective regression technique for this model. Overall, the data from the PSID survey is very effective. There were over 7000 original observations, so inconclusive observations and outliers could be thrown out without fear of jeopardizing data results. There are however, limitations with the data in terms of the industry identification codes. The 1970 census industry identification codes from the PSID data were only convertible to 2 digit SIC codes from the 1987 SIC manual. Unfortunately, the 2 digit SIC codes are a fairly broad classification of industries, while the fatality data from the Bureau of Labor Statistics is available at the 2, 3, and 4 digit SIC levels. If the fatality percentages could be provided for individuals in the PSID survey at the 3 or 4 digit SIC level, the model would likely do a much better job of predicting individuals willingness to pay for safety via forgone wages. Appendix The preliminary regression for my project consisted of regressing the wage rate against a variable for age, years of education, number of fatalities (2 digit Sic), a dummy Lee 5

6 variable for black race, a dummy variable for Latino race, a dummy variable for other races (not black, white, or Latino), and a variable for age 2. Source SS df MS Number of obs = F( 7, 4360) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = wagerate Coef. Std. Err. t P> t [95% Conf. Interval] ageofhead yearsofedu~n black latino other fatalities~t ageofhead _cons With the basic model in place, the Hadi method was then used to test for outliers in the variables at the 5% level. Beginning number of observations: 4368 Initially accepted: 2 Expand to (n+k+1)/2: 2185 Expand, p =.05: 4281 Outliers remaining: 87 Lee 6

7 The Hadi method found 87 outliers in the data for wage rate. When the regression was performed again with the deleted outliers, the R 2 value nearly doubled along with the t statistic for the variable of fatality percentages. Source SS df MS Number of obs = F( 7, 4273) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = wagerate Coef. Std. Err. t P> t [95% Conf. Interval] ageofhead yearsofedu~n black latino other fatalities~t ageofhead _cons In order to test for Multicollinearity in the model, it was necessary to first examine the R 2 value and t-statistics. One symptom of multicollinearity is a high R 2 value with low t-statistics. This doesn't seem to be the case in the estimated regression, because all the t-statistics are fairly high. Another symptom of multicollinearity is high pair-wise correlation for some of the independent variables in the model. Lee 7

8 ageofhead yearsofed. black latino other fataliescent ageofhead ageofhead yearsofedu~n black latino other fatalitiescent ageofhead There was some evidence for multicollinearity between the variables for ageofhead and ageofhead2, but this is expected since ageofhead2 is derived directly from ageofhead. Since this is really the only evidence for multicollinearity in the model, it seems that the best solution is simply benign neglect since the OLS estimates are still BLUE and MLE. The White test was then used to test for heteroskedasticity in the regression. White's general test statistic : Chi-sq(28) P-value = 2.7e-52 Due to the high Chi-square test statistic, the null hypothesis that there is heteroskedasticity in the model could not be rejected. The Feasible Generalized Least Squares technique (robust regression) reported in the estimation section was therefore used as the final regression technique in order to get accurate t-statistics. References Folland, Sherman, Allen C. Goodman, and Miron Stano. The Economics of Health and Health Care. New Jersey: Prentice-Hall, "Panel Study of Income Dynamics, 2001." Online. Internet. 16 Mar Available Lee 8

9 "Industry fatalities by event or exposure, 2001." Bureau of Labor Statistics. Online. Internet. 11 Feb Available Lee 9