The Antinomies of Welfare Economics

The mysteries of welfare economics

There is a whole discipline that profoundly shapes government decisions everywhere. Even some very educated people know nothing about it. It is laden with philosophically and politically interesting and debatable premises. Despite this, some relatively modest technical barriers mean the public scarcely ever talks about it. It’s called welfare economics, and in respect of how it influences our life, it may be the most important subfield in the social sciences. It’s obscure even in the academic world. Even among working academic economists, it’s sometimes considered a bit of a backwater.

The antinomy of welfare economics

Consider two plausible claims:

1. The government shouldn’t spend more money on services or infrastructure for one person, just because they are richer than another person. A government might justly choose to provide additional expenditure on essential services for the poor (e.g. to deal with disadvantages) but they shouldn’t do the opposite. To spend more on health, infrastructure, education or whatever else for the rich rather than the poor would be an affront to both democracy and fairness.

2. It is generally preferable to redistribute through direct payments, rather than the provision of services.

These two premises are actually contradictory, yet they are both eminently supportable. Hence they are an antinomy. I call this the antinomy of cost-benefit analysis. Let me explain why they are contradictory and why I call the contradiction by that name.

There’s a procedure used by almost all governments called cost-benefit analysis. Consider some project called P. Let’s say P is building a new bridge. Version one of the project involves building the bridge at location Oneish. Version two of the project involves building the bridge at location Twoish.

Now we work out how much it costs to build the bridge. Let’s say that, in this particular case, the cost constraint is irrelevant except that we can only build one bridge- either project one or project two- that is to say either at location Oneish, or location Twoish.

We approach the problem by working out how much people would be willing to pay for project one, and if there is anyone who would be willing to pay to prevent project one and then doing the following sum:

(Total amount all people would be willing to pay to have the bridge built at Oneish MINUS total amount people would be willing to pay to not have the bridge built at Oneish)

Then do the same sum for project two, and determine which sum is greater. That is to say determine whether net willingness to pay is higher for project one or project two.

Now consider how this might work out in practice. To simplify things we’ll assume a case in which no one would pay to stop the bridge from being built in either location. In the town of Oneish, there are three hundred people who are all willing to pay 500 each to have the bridge built there. This may not sound like much, but it is a lot of money for the impoverished residents of Oneish. Meanwhile, at the hamlet of Twoish, there is a small community of multi-millionaires- 20 people- who would each be willing to pay 10,000 dollars to have the bridge built there. This might sound like a lot of money, but to them it is a trifle, representing the slightly greater convenience that will accrue to them if the bridge is built in the hamlet of Twoish.

(10,000*20=200,000)>(300*500=150,000). So the maths says we should go ahead with project two. Hopefully, this illustrates how cost-benefit analysis favors rich people because rich people, having more money, are often willing to pay more money for projects than poor people.

Now there is a way to redress this. Rather than looking at how much money people are willing to pay, we can look at how much money people are willing to pay but weighted according to their income. The simplest weighting, though not necessarily the justest, is proportional weighting. To do a proportional weighting we look at how much each person is willing to pay as a proportion of their income. Simple, right?

Here’s the rub, at least according to some economists. If we adopt weighted cost-benefit analysis the tax rate on the rich is effectively raised. This will, presumably, disincentivize labor shrinking the economy. The argument goes that if the government isn’t more likely to build bridges in rich neighborhoods, the people, being rational agents, will notice this. They will therefore find the idea of becoming rich less attractive because being rich will come with fewer extra goodies. Therefore, they will be less likely to work that extra hour or go to extra trouble to get a qualification. For these economists, using weighted cost-benefit analysis is much like raising the highest marginal tax bracket in terms of its effects on labor supply and the economy.

If you’re anything like me you probably reply “well, so what, we need to raise the tax rate on the rich anyway”. Fair enough, but the problem is that, for various reasons, many economists think that while redistribution is well and good, they would prefer to do it through taxes and transfers, rather than in kind. There are some mathematical results that seem to suggest that giving people cash, rather than giving them goods and services, will be a more efficient form of redistribution. Thus, these economists propose, we shouldn’t try to redistribute wealth through goods like bridges, roads, parks, hospitals and schools. Instead, we should use standard, unweighted cost-benefit analysis and hence give the lion’s share of these things to the rich, but generously redistribute through taxation.

One advantage of this approach, I will concede, is that it allows us to entirely separate out two questions: A) The question of how redistributive the government should be B) The optimal level of public goods provision. In a manner of speaking, it delinks questions of the size of government from questions about distributive justice. Yew Kwang Ng makes this point.

Now I have numerous problems with this argument for giving the rich more stuff, but I’m going to focus on two here. The first problem is an empirical problem, I’m not convinced that the rich experience, say, having extra parks in the same way that they would experience having extra money. For example, I’m not convinced people make the calculation that they’re going to become an anaesthesiologist because there are more parks for rich people. At the very least, I anticipate that, as a matter of behavioral economics, the number of parks is less of an incentive on the rich than whatever the top marginal tax rate is.

The second problem is a matter of political philosophy. Unweighted cost-benefit analysis is effectively a form of voting in which the number of votes you have is determined by how much income you have. In other words, it is a form of direct plutocracy and, if you’re anything like me, you probably think that plutocracy, whether direct or representative, is an unconscionable way to run a government.

But I’ll freely admit, I don’t have all the answers here. That’s why I call this problem an antinomy. There are both really good reasons to think that redistribution should be done through transfers rather than in kind, and also really good reasons to think that building more parks for rich people than poor people is unconscionable. At the VERY least, building more hospitals and schools for rich people than poor people certainly seems terrible.

Although intellectually I am uncertain, my heart makes me fall on the side that says unweighted cost-benefit analysis cannot be allowed to stand. I am very wary of rationalizations for giving more things to rich people. I think such rationalizations will tend to get more support than they deserve anyway- whatever their intellectual merits. The rich will always have their ideologists to speak out in favor of them.

Here’s what I think is going on here with this antinomy. There’s a tension between capitalism and democracy. We talk about liberal democracies or capitalist democracies like they were the most natural thing in the world, but democracy and capitalism are two two very different organising principles that we have allocated different roles to. The market can be seen as a social planner in its own right. Assume that marginal utility in income is decreasing, so that your 100,000th dollar matters one quarter as much as your 50,000th dollar. As Brad de Long points out:

“The market system's social welfare function gives each individual a weight inversely proportional to his or her marginal utility of wealth.”

Insomuch as, from the point of view of the market, your 100,000th dollar is worth as much as my 50,000th dollar, even though my 50,000th dollar matters four times as much to me, your consumption preferences are weighted four times more heavily than mine in deciding what gets produced and who consumes it. Capitalism is an oligarchical system for making social decisions about production and consumption.

Public goods like parks etc. are things which it is not, generally efficient for individuals to purchase for themselves. Thus the government makes purchases on our behalf. But this brings the normally concealed tension between democracy and capitalism into the open because there’s a border dispute between capitalism and democracy as social ordering principles. The purchase of public goods does not clearly belong to the oligarchical domain ordered by the market or democratic domain which is (in theory at least) ordered by the electorate. We don’t know whether buying parks or schools should be treated more like buying cars, except collectivized to avoid the free-rider problem, or whether buying parks or schools should be treated as something more like drafting criminal laws- something that shouldn’t be influenced by money. That’s why this antinomy arises- it reveals the seam between capitalism and democracy as social choice principles.

Making the perfect the enemy of the good- Welfare economics and social welfare functions

As you can imagine, unweighted cost-benefit analysis is controversial, because it effectively implements a direct-oligarchic voting system, in which each person’s power over social decisions is proportional to their income.

Yet nonetheless, despite a great deal of skepticism among economists and political philosophers, most governments around the world tend to use unweighted cost-benefit analysis, although the UK is a notable exception, using weighted CBA for many purposes.

The rationale for this? Well, there are numerous reasoned defenses, including the one I talked about above. But I don’t think these intellectual defenses are what has ultimately been effective. I think what has been effective is the fact that weighting cost-benefit analysis by some factor of income would oblige you to take a stand on values. Unweighted cost-benefit analysis wins because it is the default you slide into if you don’t set up a weighting system. Even though it is far from value-neutral.

The conversation tends to go like this:

Aria: I propose that we adopt a roughly utilitarian weighing system.

Bravo: Aha! You say we should aggregate desires or happiness. But any comparison between the desires or happiness of two people is purely a matter of value judgment. There is no non-normative way to aggregate desires.

Aria: Come now, common sense, empirical psychology, psychometrics, and results from welfare economics like Lerner’s equal ignorance theorem give us more than enough basis for reasonable comparisons between persons. In principle really not much different to comparing the temperature of objects.

Bravo: [Walks off disgruntled and clearly unconvinced]

Carol: Your utilitarian weighting system doesn’t pay special attention to the worst off in society. We need prioritarianism.

Dylan: Your utilitarian weighing system ignores that there are higher things than mere pleasure and desire satisfaction. We need to use the capabilities approach.

Erol: I fell on my head as a child and for some reason believe that a Rawlsian maximin social welfare function is appropriate.

A figure returns. It looks suspiciously like Bravo, but with a glued-on mustache.

Not Bravo: Oh well this is just all too difficult, we had best just stick with unweighted cost-benefit analysis so we can make fewer value judgments.

Everyone all at once shouts no, but they are also shouting at each other. The treasury department resolves to use unweighted cost-benefit analysis because it looks easier than getting involved with all this mess.

When I first started working on my Ph.D., my solution was simple. Argue that all the critics of unweighted cost-benefit analysis had an interest in strategically adopting utilitarianism, because, from the perspective of all the popular alternatives, e.g. prioritarianism, the capabilities approach, maxmin, utilitarianism will be an improvement over unweighted cost-benefit analysis. What I was suggesting was a kind of political maneuver within political philosophy itself- rally around utilitarianism. The logic was that of the Pareto improvement- utilitarianism is better for all political philosophies at play than unweighted cost-benefit analysis.

This kind of argument is no longer really central to my thesis, but I still think about this a lot, viz: A) The way incumbent models can win out for lack of a unified opposition B) The possibility of forming political coalitions within normative political thought.

Making the perfect the enemy of the good part II- Welfare economics and psychometrics

Think about the inadequacies of willingness to pay as a measure of welfare.

The most glaring is that it treats the desires of the rich as many-fold more intense than the desires of the poor, but there are other issues as well. There are many technical problems with measuring it- for example, how should we work out how much people are willing to pay for clean water?

The simplest method would be to ask them “how much extra tax would you be willing to pay a year to get clean water”, but this verbal approach is considered suspect by many economists. Alternatively, we could look at commercially available water filters, see how much they go for, and value a population of people getting clean water as equal to how much it would cost to get them filters. Alternatively, we could look at their lifetime expected additional healthcare costs if they don’t get clean water, and value it at that- how much they would be willing to pay to get healthcare to deal with the consequences of not having clean water. We could also look at how much they’re willing to pay for bottled water. These and numerous other models contend together in the air, but there’s no clear way to choose between them. People’s willingness to pay is often context-bound, unreliable, and wildly divergent depending on how you look at it.

What are some other ways you could measure the welfare impacts of economic policy? Well, a natural suggestion is that we measure happiness using the subfield of psychology known as psychometrics.. Alternatively, perhaps we could adopt a hybrid model, where we use willingness to pay, but adjust it on the basis of various results from the study of subjective wellbeing. For example, if we know that happiness increases as a log function on income, treat the value of an extra dollar to a person as proportional to log income. My willingness to pay a dollar (at 50,000 income) is thus treated as equivalent to your willingness to pay two dollars (at 100,000 income).

But, the objections begin:

1. Which kind of happiness? Pleasure? The satisfaction of desires? Eudaimonia?

2. How do we know that the happiness scale is relatively constant between groups? [Never mind that we know for a fact that the willingness to pay scale isn’t constant.]

3. What about (insert technical measurement problem here) [Again, this seems unfair, because while there are unknown technical details regarding how accurate the measurement of happiness is, we know that willingness to pay is bad.]

And once again unweighted willingness to pay wins out, due to a disunited opposition and institutional inertia.