Is healthcare part of compensation?

As reiterated by Mankiw:

A common argument, often made by ostensibly sophisticated commentators, is that the United States needs to reform its health care system to maintain its international competitiveness. Regardless of your views of health care reform, this particular argument is, to put it bluntly, nonsense. Long ago, Paul Krugman wrote a nice piece demolishing the whole concept of international competitiveness as a motive for national economic policy. More recently, the Congressional Budget Office has done a nice job explaining why the idea of international competitiveness as a reason for health care reform is fallacious. The passage below, from page 167 of the CBO analysis, is written in the CBO's traditional understated way, but the point is clear:

Some observers have asserted that domestic producers that provide health insurance to their workers face higher costs for compensation than competitors based in countries where insurance is not employment based and that fundamental changes to the health insurance system could reduce or eliminate that disadvantage. However, such a cost reduction is unlikely to occur, except in the short run.

The equilibrium level of overall compensation in the economy is determined by the supply of and the demand for labor. Fringe benefits (such as health insurance) are just part of that compensation. Consequently, the costs of fringe benefits are borne by workers largely in the form of lower cash wages than they would receive if no such benefits were provided by their employer.

Replacing employment-based health care with a government-run system could reduce employers’ payments for their workers’ insurance, but the amount that they would have to pay in overall compensation would remain essentially unchanged. Even though changes to the health care system could have various effects on the supply of labor, the underlying amount of labor supplied at any given level of compensation would hardly beaffected by a change in the health care system. As a result, cash wages and other forms of compensation would have to rise by roughly the amount of the reduction in health benefits for firms to be able to attract the same number and types of workers.

But what if the worker does not know the value of the health insurance package? When I receive job offers, the only real number I pay attention to is gross wages. Health insurance is something I expect to be provided and the value of the package to me is unknown. Enrollment in Kaiser costs me nothing and then the contribution for health insurance increases if I opt for PPO or a plan that offers more choices. But the true cost itself is not known.

What if I tried to enroll myself in health insurance? Kaiser's individual rates are around $500 per month but it costs employers less than that since there is some pooling of risks. Do I include the $500 in my evaluation of a job offer? No.

What should employers do? They should explicitly state this in job offers. What is the implication of workers not knowing the cost of health insurance but expecting it as a right? If a firm makes an offer, it has to be higher to offset the cost of purchasing individual health insurance. But as noted earlier, there are some gains to pooling health risks. Government can play a role by providing partial risk pooling that an individual cannot give to a HMO or PPO.

The mechanics would be something as follows:
1. Firm makes an offer without health insurance plus an offset for the worker to participate in government health insurance.
2. The government pays part of the premium and the individual pays part of the premium equal to the offset from the firm. (This does not exclude the role of private insurers since the government can contract with them as well.)
3. What if the worker opts out and chooses to take the money? Under this scheme it would be disallowed. The worker has to participate just as I participate at minimum with Kaiser. If I opt for more choices then some allowance can be given and I would contribute a portion of my salary greater than the offset.

What's wrong with this argument? It points out that the fallacy is perhaps not so fallacious after all. True, firm costs do not fall if the monetary offset provided equals the insurance that the individual can buy in the market. But what if pooling of risks along with some bargaining power can achieve some reduction in insurance costs?