Social Insurance and Truncated Benefits: Measuring the Impacts of Workers' Compensation

Table 2

Estimates for machinists in 1990^∗.

Dependent variable is natural logarithm of real hourly wage
Model specification	Benefit coefficients	$1 in benefit°	Elasticity
OLS with individual-specific temporary weekly benefit level	𝐵𝑖 = 0.0037502 (38.25)	+$1.53	0.87*
OLS with individual-specific temporary weekly benefit ratio; (i.e., benefit/weekly wage)	𝑅𝑖 = −1.972772 (−31.82)	−$1.25	−0.84*
2SLS with individual-specific temporary weekly benefit ratio; (i.e., benefit/weekly wage)	𝑅𝑖 = −0.4543988 (−3.34)	−$0.45	−0.25*
2SLS with individual-specific temporary weekly benefit level	𝐵𝑖 = 0.0014911 (7.05)	+$0.56	0.30*
Modified Heckman for “-” wage workers based upon state-specific temporary weekly benefit ratio (i.e., benefit/weekly wage)	𝑅𝑖 = −1.204623 (−4.05)	−$1.16	−0.81*
Modified Heckman for “high-” wage workers based upon state-specific temporary weekly benefit level	𝐵𝑖 = 0.0017827 (10.26)	+$0.90	0.52*
OLS with state-specific temporary weekly benefit index	𝐵𝑖 = −0.0000485 (−0.09)	−$0.07	−0.04
OLS with state-specific comprehensive annualized (expected) benefit index^+	𝐵𝑖 = 1.748117 (1.99)	+$1.75	0.06*

* All benefits are given in real US dollars, (t-statistics are in parentheses). Each coefficient comes from a separate regression that includes education, experience, regional and demographic variables. These full regression estimates are shown in Appendix D. Higher levels of education tend to correspond to higher wages; experience raises wages but at a decreasing rate. Greater overtime hours depress hourly wages, and race and residential/geographic location also impact wages.
°These are calculated by increasing the average weekly benefit by $1. The value of the “benefit” is then recalculated, and this new value is multiplied by the estimated elasticity (located in Table 3) to obtain the change in the real hourly wage. To find the change in the weekly wage, the change in the real hourly wage is multiplied by the average weekly hours. For the final OLS model (state-specific comprehensive annualized expected benefit index), the extra benefit is the actual regression coefficient, so no manipulations are required. Moreover, the index includes the probability of injury and is therefore not directly comparable to the other estimates.
⁺This model uses the real annual wage as the dependent variable, and the benefit is an “expected” benefit.