Since you read Marc Bellemare’s ‘Metric Monday posts (right???), you undoubtedly caught this:
Unfortunately, as Spanos (1986), quoted by Kennedy (2008), wrote: “No economic theory was ever abandoned because it was rejected by some empirical econometric test, nor was a clear cut decision between competing theories made in light of the evidence of such a test.”
With that in mind, what about the theory that labor market participants respond to total compensation, which implies a dollar-for-dollar trade-off between health insurance benefits (or any benefits) and wages? The theory does have some support. But it does not have the support of every study of the issue, as documented in “Premium Copayments and the Trade-off between Wages and Employer-Provided Health Insurance,” by Darren Lubotsky and Craig Olson:
We find no evidence that changes in teachers’ salaries within a district over time are related to changes in insurance premiums. […]
A sizeable literature exists on the trade-off between wages and health insurance premiums. Despite the size of the literature, a consensus on the size of the trade-off does not exist: Currie and Madrian’s 1999 literature survey indicates that many studies find no statistically significant relationship between wages and health insurance costs, or find a positive relationship between the two. [Footnote 5: In addition to Currie and Madrian’s (1999) review, also see the discussions in Levy and Feldman (2001), Simon (2001), Lehrer and Pereira (2007), and Royalty (2008).] Other studies find evidence of a negative relationship. Anand (2011) and Clemens and Cutler (2014) are the most closely related studies to ours. […] As we [Anand] estimates the within-firm correlation between total health insurance premiums, wages, and employee contributions and finds that all of the adjustments occur through employee contributions towards premiums. [..] She finds no salary offsets or effects on other employee benefits. Clemens and Cutler (2014) study the relationship between aggregate fringe benefit spending and salaries between 1998 and 2007 across about 16,000 school districts nationwide. They instrument the change in fringe benefit spending with a measure of the predicted growth in health expenditures. Their results indicate that a dollar increase in benefits is associated with about a fifteen cent decline in salaries, though the estimate is quite imprecise and not statistically distinguishable from zero or from a much larger wage offset.
A number of other studies find some evidence of salary offsets: Eberts and Stone (1985) study public school teachers in New York and find that each dollar increase in health insurance costs between 1972 and 1976 was offset by about an 83 cent decrease in salary. […] Baicker and Chandra (2006) find evidence of a fully compensated offset for those covered by employer-provided health insurance using medical malpractice settlement size as an instrument for health insurance costs. Kolstad and Kowalski (2012) study the 2006 Massachusetts health insurance mandates and conclude that wages adjusted to fully offset the cost of employer-provided health insurance. […]
Gruber (1994) found that working women of childbearing age with health insurance saw their wages decline when their state required insurance policies issued by insurance companies were required to offer maternity benefits. Sheiner (1999) found a flatter age-earnings profile for workers in markets with high medical care prices. Pauly and Herring (1999)[*] found that predicted medical expenditures have a negative impact on the wages of older workers. Bhattacharya and Bundorf (2009) found a significant wage differential between obese and thinner women for those covered by health insurance, but no differential for those without insurance. While we have highlighted a few papers that find evidence consistent with the hypothesized wage-benefit trade-off, many studies fail to find any relationship and there is not yet an empirical basis for a consensus on the magnitude of any wage offset.
Either the premium-wage trade-off varies by context or some of these studies methods are not revealing the true effect, whatever it is. I don’t know the answer, but it’s probably some of both. I do know it’s very hard to study correctly.
* Not included in the references.