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You can add health care to the causes of growing wage inequality in America. There’s a largely unknown paradox at work. Companies that try to provide roughly equal health insurance plans for their workers — as many do — end up making wage and salary inequality worse. A new economic study shows how this perverse bargain works.

It’s simple arithmetic, writes Mark Warshawsky of the Mercatus Center at George Mason University, author of the study. Paying for expensive health insurance squeezes what’s left for wage and salary raises. Economic inequality increases, because health insurance typically represents a larger share of total compensation for lower-paid than higher-paid workers. Their wages are squeezed the most.

To see why, consider a simple example. Assume an imaginary company with two employees: one makes \$50,000 a year, the other \$100,000. Suppose that the firm has purchased a family health plan, costing \$12,000, for each. So the company’s total compensation costs — wages, salaries and fringe benefits, including health insurance — are \$112,000 for the higher-paid worker and \$62,000 for the lower-paid employee.

Now look what happens when the company decides to raise its annual compensation costs by 5 percent, but health-care spending is increasing 10 percent. The insurance cost goes up \$1,200 (that’s 10 percent of \$12,000). This reduces what’s left for wages. The lower-paid worker receives an overall compensation gain of \$3,100 (5 percent of \$62,000), but after deducting the \$1,200, only \$1,900 is left for wages. Meanwhile, the higher-paid worker receives a \$5,600 gain, which — after deducting \$1,200 for insurance — leaves \$4,400 for wages.

Presto, wage inequality has increased. Even though the company raised its compensation package by 5 percent for all workers, the wage and salary gap between the best- and worst- paid workers widened. Pursuing one type of equality (health coverage) inadvertently worsened another type of inequality (wages and incomes).

This example is telling, though the precise numbers are exaggerated to make the point clearly. Despite government health programs — notably Obamacare, Medicare and Medicaid — employer-provided insurance remains the largest source of coverage, affecting 147 million people in 2015, says the Kaiser Family Foundation. And the average employer-paid policy cost its company sponsor \$12,591.

What Warshawsky sought to answer was how much rapidly rising health spending was crowding out wage and salary increases. Sure enough, he found that total compensation (including higher health costs) rose faster than just wages and salaries for workers at all income levels — but as expected, the gap was largest at lower income levels. From 1992 to 2010, about half the increase in wage and salary inequality is explained by rising health costs, Warshawsky estimates.

(To reach this conclusion, he used the National Compensation Survey from the Bureau of Labor Statistics. It shows, for different income levels, how much workers earned in wages and salaries and in total compensation, including all fringe benefits.)

The problem, as Warshawsky notes, is that “earnings are noticed much more by workers (and hence politicians) than compensation.” It’s not just perceptions. People can’t buy groceries with health insurance, and although it may provide peace of mind, the benefits elude many Americans. About half the population has little health spending, and the 5 percent sickest Americans account for almost half of all spending, according to government figures.

There is a clash of goals. Everyone wants comprehensive health coverage, but hardly anyone wants growing economic inequality. We are playing musical chairs, as health costs are shifted between players. To hold down their spending, companies now require higher deductibles (the average exceeds \$1,000). This may boost wages and salaries, but it also raises workers’ out-of-pocket medical costs.

The way to break this cycle, Warshawsky says, is to slow “the rate of increase in health costs.” There has been some progress, but it’s easier said than done.

Read more from Robert Samuelson’s archive.