Cabral and Dillender (2021) compute the MVPF of an expansion in the generosity of workers’ compensation benefits in the US. Workers’ compensation is a state-regulated insurance system that provides covered employees with cash and medical benefits for work-related injuries or illnesses. In 2016, workers’ compensation insurance paid $62 billion of benefits in the US, roughly equivalent to the size of the Earned Income Tax Credit (EITC) and Supplemental Nutrition Assistance Program (SNAP). Benefit levels are set at the state level. In 2006, the state of Texas increased the maximum weekly benefit amount from $540 to $674. Authors exploit this policy change to implement a differences-in-differences design and estimate the impact of increases in the benefit amount on benefit duration and medical spending. They find that the increase in benefits does not impact the number of injured workers claiming benefits but increases the duration of benefits received by 11% (2 weeks) and increases medical expenditures in the first five years after injury by 10% ($1,219 on average). These estimates imply an elasticity of benefit duration with respect to benefit amount of 0.68 and an elasticity of medical expenditures with respect to benefit amount of 0.63.
MVPF = 0.5
The authors report four primary components that are used to calculate the net cost of the policy. First, a $1 increase in benefit subsidies costs $1 upfront. Second, the benefit increase leads to higher benefit duration, which in turn increases expenditure on benefits. For a marginal increase in the benefit amount, the marginal increase in benefit duration is given by the elasticity of benefit duration with respect to benefit amount (0.68, estimated by authors). Third, authors found that higher benefit amounts led to higher medical expenditures, covered by insurers, and ultimately paid by government subsidies. The size of this extra cost if given by the marginal impact of a benefit increase in weekly medical expenditures (12.86, estimated by authors) divided by the average duration of benefits (17 weeks), for a total of 1/17 * 12.86 = 0.76. Fourth, higher benefit amounts lead to extra time out-of-work, which decreases government income tax revenue. The extra cost to the government through this channel is given by the elasticity of time out-of-work with respect to benefit amount (0.68, assumed to be equal to the elasticity of benefit duration) times the tax rate (17.9% on average) divided by the typical benefit replacement rate (63% on average in the sample), for a total of 0.68 * 0.179/0.63 = 0.19. The total cost of a marginal increase in benefit amount is therefore 1 + 0.68 + 0.76 + 0.19 = $2.63.
The authors report two primary components that are used to calculate the willingness to pay for the policy. First, one extra dollar in compensation insurance subsidies mechanically increases welfare by $1. Second, workers value the fact that insurance smooths consumption over time. To calibrate this component, authors assume a constant relative risk aversion utility function. The welfare increase due to insurance is then given by the product of the average percentage fall in consumption when a shock occurs (10.1%, calibrated from Health and Retirement Study (HRS) data) and the coefficient of relative risk aversion (2 in the preferred specification). Total willingness to pay is therefore 1 + 2 x 0.101 = 1.202.
The MVPF is then the ratio of the willingness to pay to the total cost, 1.202/2.63 = 0.46 in the preferred specification. Authors also present alternative estimates varying the coefficient of relative risk aversion in the assumed utility function. These range from 0.43 (when the coefficient of relative risk aversion is 1) to 0.58 (when the coefficient of relative risk aversion is 5).
Cabral, Marika, and Marcus Dillender (2020). The impact of benefit generosity on workers’ compensation claims: Evidence and implications. No. w26976. National Bureau of Economic Research. https://www.marikacabral.com/CabralDillender_WCBenefitGenerosity.pdf