# Estimating the elasticity of health insurance offering for firms: Part II

How does the price of health insurance affect the probability that a firm will offer health insurance to their workers?  A previous post provides a variety of estimates of the elasticity of firm health insurance offering with respect to premiums.  A more recent article by Gruber and Lettau (2004) needs to be added to this mix.

This paper uses data from the 1983-1995 National Compensation Surveys to determine that “there is a moderately sized elasticity of insurance offering with respect to after-tax prices (-0.25), and a larger elasticity of insurance spending (-0.7). We also find that the elasticities are driven primarily by small firms, for whom the elasticity is larger.” Additionally, the authors claim that if the tax subsidy to employer-provided health insurance were eliminated, 15 million fewer workers would be offered health insurance.

The key regressor of interest is the tax-price of insurance for each worker. This is computed as:

• TP=(1 – τf – τs – τss – τmc)/(1 + τss + τmc).

The variable τf is the federal income tax marginal rate, τs is the state income tax marginal rate, τss is the marginal payroll tax rate for the OASDI program, and τmc is the marginal payroll tax rate for the Medicare HI program.  Gruber and Lettau also include firm characteristics, and state and year dummy variables as explanatory variables in their regression.

The authors rightly worry that “variables used to create the tax measure (hours, industry, occupation, earnings, state, and year) could be simultaneously correlated with the demand for insurance, biasing our estimates in an indeterminate manner.” To counteract this endogeneity problem, the authors use the individual’s simulated (rather than actual) tax price based on his or her state or residence, the year, and their income decile. Because state and year dummy variables are already included, the model is identified only through the interaction of states, earnings groups and years.

Using this specification, the authors find that the elasticity of health insurance offer is about -0.25. However, for firms with fewer than 100 employees, this elasticity grows in magnitude to -0.69. For firms with 100-999 employees, the elasticity is -0.195. On the other hand, for large firms, almost all firms offer health insurance to their employees and thus no elasticity can be calculated.