I come back to Austin Frakt’s post calculating how much the Federal subsidy for health insurance is worth every few months, and I think I have to re-study it every time. It’s a hugely important post.

Probably a lot of others don’t read wonky health-insurance blogs quite as obsessively as I do, so the background is like so: your employer (if you’re lucky enough to have an employer that supplies health insurance) doesn’t pay taxes on the health-insurance fringe benefit. When they pay you a dollar in wages, they have to pay their part of Medicare and Social Security taxes. Once they’ve paid their taxes and passed your wages on to you, you have to pay taxes on them. Health insurance isn’t like that: your employer doesn’t pay taxes on health benefits, and neither do you. So one dollar in health insurance is worth more than one dollar in wages to you and to your employer.

Turns out that the subsidy is really distorting. Professor Frakt’s exercise may already be clear to everyone, but I don’t think it was clear to me for a while. So in bullet form, trying to make it as clear as possible (to myself as much as to everyone else) it’s like so:

• For every dollar an employer pays out in wages, a certain fraction of that dollar goes to taxes (employer pays Medicare and Social Security). Call that fraction T.
• So for every dollar in wages that the employee receives, the employer pays \$(1+T).
• Flip that around: for every dollar in wages that the employer pays, the employee receives \$1/(1+T).
• Now the employee has his dollar in wages. Of that, a certain fraction goes to taxes (Medicare, Social Security, federal, state). Call that tax fraction E.
• So the employee is left with \$(1-E) of his dollar.
• But his dollar was already \$1/(1+T) of what the employer spent.
• So of every dollar the employer spends on wages, what ends up in the employee’s pocket is \$(1-E)/(1+T). Call this F, for “Final amount in the employee’s pocket.”
• This means that \$(1-F) goes to taxes, for every dollar the employer spends on wages.
• Put another way: a dollar spent on health insurance, which no one pays taxes on, loses the government \$(1-F). 1-F is called the “tax price.” Professor Frakt links here to a paper by the omnipresent Jon Gruber, an MIT professor who was central to building Massachusetts’ universal-coverage system, and who advised President Obama on the Affordable Care Act. The paper — “The Impact of the Tax System on Health Insurance Coverage” — sounds interesting.

To put some flesh on the numbers:

• when the employer pays you a dollar (in wages, but not in health insurance), it spends 6.2 cents on Social Security and 1.45 cents on Medicare Part A. So T = .062 + .0145 = 0.0765.
• you pay Social Security and Medicare Part A (same percentages as your employer), plus your Federal marginal tax rate (I’m in the 28% bracket), plus your state marginal rate (Massachusetts’ is 5.3%). So my marginal rate is 40.95%, whence E = .4095.
• So when my employer spends a dollar on health insurance rather than on wages, the government loses 45 cents that it would have picked up in taxes. (Professor Frakt ends up with 37 cents using more-conservative assumptions, namely that the state tax rate is 5% and that my Federal marginal rate is 20%.)

This distorts the labor market — encouraging employers to buy more-expensive health-insurance plans — and costs the government money that it could be spending on other valuable things.

And it’s regressive: if you’re in the top (35%) bracket, you’re getting more of a benefit from the health-insurance subsidy than is someone in the 28% bracket. Same goes for the mortgage-interest deduction, and it may be even worse there: not only do higher-income people get more off their taxes for every dollar they spend on mortgage interest than do lower-income people, but the more you spend on a house, the more you can take off your taxes. Assuming Bill Gates’s house cost the \$97 million that some random web page says it did, that he put 20% down, and that he financed it with a 2%, 30-year fixed-rate mortgage, he’ll be able to use the mortgage-interest deduction to avoid paying taxes on \$26,345,019.10 in income over the life of the mortgage. Assuming he’s in the 35% bracket, that’s \$9,220,756.69 that the mortgage-interest deduction saved him. Whereas if you’re in the 28% bracket and finance a \$350,000 home the same way, you’ll save \$33,270.77 over those same 30 years.

These “tax expenditures” cost the government money in the same way that buying a bomber or building a road costs it money. But tax expenditures haven’t, until recently, appeared on the radar in the same way that a \$500 toilet seat does. We may well be paying for Bill Gates’ \$500 toilet seat, but it hasn’t had the same visceral effect.