Everyone is talking about the welfare implications of Obamacare. Here's how welfare economics works.

2/04/2014 03:51:00 PM
A graph showing the traditional efficiency calculation in microeconomics. This is only half of the welfare story, as it ignores gains and losses from redistribution.
The CBO came out with an updated forecast of the effects of the Obamacare, which now estimates that the labor force will decline by 2 million, way more than the previously estimated 800,000. A lot of commentators now are complaining about the "job-killing" effects of Obamacare causing people to drop out of the workforce. Matt Yglesias's rebuttal is...ok, but Josh Barro nailed it.

It is typical to think of a decline in employment as a bad thing, but we actually can't draw any welfare conclusions one way or another without more information. There's two sides to the welfare effects of any policy. On one side are matters of distribution--to the extent that we value all individuals equaly (and individual utilities are concave increasing), a distribution of wealth that is closer to equal is associated with higher aggregate welfare than one further away from equality. On the other side are matters of efficiency--to the extent that some individuals experience losses that cannot be redistributed, the allocation is inefficient.

In general, as Barro notes, policies have both wealth effects and substitution effects. If I give you $1000 and you go out and buy a new computer, then that change in your consumption habits is a pure wealth effect. If, on the other hand, I promise to pay you 50 percent of the cost of a new computer, then we have a combination of wealth effects (I'm giving you money still) and substitution effects (you are diverting funds from other activities to buy the computer). And just as Barro says, to the extent that it was the substitution effect, rather than the wealth effect, that caused you to buy the computer, my policy is inefficient--I have induced you to buy a computer whose total, unsubsidized price is greater than the value you will derive from it--that computer should have gone to someone who needs it more. This is an example of an economic loss from inefficiency. On the other hand, to the extent that it is the wealth effect that caused you to buy the computer, the welfare significance is ambiguous. If you are poorer than I am, then it could increase aggregate welfare by redistributing from someone with a lower marginal utility (me) to someone with a higher marginal utility (you)--this would be an example of an economic gain from redistribution.

Now, neither wealth nor substitution effects are unambiguous. Obvioulsy, to the extent that a policy's wealth effects involve redistributing from poor to rich, it is welfare reducing. Substitution effects are usually welfare reducing, but can actually be welfare increasing in the presence of certain kinds of market failures, such as the substitution that occurs when we tax negative externalities like pollution.

How do we measure these gains and losses? There is a very long venerated tradition in economics of analyzing matters of efficiency. To do this, all you need is to estimate what's called a compensated (or "hicksian") demand curve. This demand curve is similar to a normal demand curve except that rather than showing how a person's demand changes in response to a change in price alone, it shows how much their demand would change in response to a price change if they were given lump-sum transfers compensating them for the wealth effects of the price change (so, a lump-sum tax when the price falls, and a lump-sum cash payment when the price rises). The compensated demand curve, therefore, tells us the pure substitution effects, excluding any wealth effects. There are a couple of approaches here, but the point is that the efficiency loss/gain can be easily calculated by summing up the cumulative substitution effects along these curves.

Calculating the gains from redistribution is more problematic because it requires that we make some assumptions that, while reasonable, cannot be empirically verified, even in principle. Conservatives use this difficulty as a club with which to protest any effort to make the poor better off, and I think that's extremely unfortunate--they are, implicitly, engaged in precisely the same fallacy but refuse to make their assumptions explicit. The problem arises because we can't empirically test the cardinal properties of a utility function--two identical people with identical incomes and identical choice structures could potentially have durastically different levels of utility. It requires a philosophical leap to say it isn't so, but nevertheless this is the only reasonable course of action, and one that has been widely applied across all fields of economics (see, for example, the Mirrlees optimal tax theory).

Now returning to our example where I make an offer to a poor person to pay half the cost of a computer, there is an efficiency loss because I've produced a substitution effect (a computer is not necessarily his most pressing need), but also a resdistributive gain because he's poorer than me. It is possible that this transaction produces a net-welfare gain if the redistribtutive gain exceeds the efficiency loss (ok, obviously we could increase the redistributive gain and eliminate the efficiency loss if I just offer the same amount in cash rather than tying it to a computer, which is why I think liberals are being lazy when they ask "is this policy progressive?").

So what is happening with Obamacare, according to the CBO report? There's a little bit of a substitution effect as a few employers cut workers' hours--this is clearly bad. There's also some possible inefficiency from the substitution effect whereby the mandate causes people to buy more insurance than they wanted (though, to the extent that adverse selection was the reason whey weren't buying before, this is a market failure and the substitution effect could be welfare-improving). But the vast majority of the decrease in labor force appears to be people who left because of the wealth effect--with health benefits paid for, they no longer feel the need to work. The welfare effects are somewhat ambiguous because we can't be totally sure their benefits were financed by people richer than they, but most likely this is a good thing, representing a redistributive gain (rich people don't have trouble finding insurance coverage).