Uses and Abuses of Pareto Optimization in Economics

Simon Wren-Lewis posts on Pareto optimization here.  The post is worth a read, as are the comments that follow.  Oddly, no one showed up in the comment thread to defend Pareto optimization in economics, though a few offered the standard criticisms of aggregate social utility functions.  However, there seems to be a few different interpretations of what it means to make Pareto efficiency the goal in economics, and what implications follow from it.  There is a widely held misconception that this road leads to Libertarianism.  On the contrary, accepting this goal as a premise leads to virtually no interesting conclusions about what we should favor in economics whatsoever.

Let's start with some definitions:

Given an initial allocation of goods among a set of individuals, a change to a different allocation that makes at least one individual better off without making any other individual worse off is called a Pareto improvement. An allocation is defined as "Pareto efficient" or "Pareto optimal" when no further Pareto improvements can be made.

This definition suggests what I will call the Weak Pareto Criterion: As a first pass when considering economic policies available to us, we should discard any that lead to outcomes that are not Pareto optimal, because there are superior options among the ones we don't throw out.  Pareto optimality allows us to narrow a large set of options down to a smaller set of options, but we still may reasonably consider making non-Pareto-improving changes that move us from one Pareto efficient outcome to another, as it is not the case that every Pareto efficient outcome is just as good as any other.  This is a very weak criterion indeed, but can easily be abused in ways I will come back to later.

The Strong Pareto Criterion

However, Simon Wren-Lewis and many of the commenters on his post are arguing against a far stronger criterion, which I will call the Strong Pareto Criterion: only consider options that lead to Pareto improvements.  This stronger criterion might just be a straw man, but it's worth knocking down just in case.  This criterion doesn't really have much to do with optimization concerns; it is better understood as a particular definition of fairness or justice, which starts with the Hippocratic "first do no harm": it is unfair to harm anyone against their will, regardless of the benefit that may be realized for others.  Simon Wren-Lewis sees in this a questionable argument for Libertarianism, but if taken seriously this principle doesn't work at all as an argument for Libertarianism: it is an argument for extreme status quo bias.

It is fun to imagine a parallel universe where economists consistently applied the strong criterion. For example, free trade policies have been enacted that have sacrificed the wellbeing of many for the greater good. Where were the economists arguing that NAFTA should not be done because no change should ever be made unless it is a Pareto improvement? Who argues that deregulation and tax cuts should never be done unless you know there is not a single person who will be made worse off?  No one makes these arguments; they decide the benefits outweigh the harms or vice versa even if the benefits and harms aren't to the same people.

Like I said, this one might be a straw man, but even if you do find someone who believes they believe in this criterion, if you look at their actual economic preferences you are likely to find they only follow their principles opportunistically.

The Libertarian Variant

To warp the strong criterion into a Libertarian criterion, you have to ignore the status quo and instead imagine starting over from scratch. You ignore the harms that will be inflicted on people by the changes you would like, and instead ask if you can find anyone who would be harmed in the parallel universe where we were considering moving from a libertarian economy to this one.  This is the Libertarian Variant of the Strong Pareto Criterion:  First do nothing that isn't a Pareto improvement over Libertarianism.  Thus it is fine to harm many if some benefit if you are making the economy more libertarian, whereas it is not fine to support the status quo if some are any worse off than they would be if the economy were more libertarian. Needless to say this kind of thinking is not value neutral at all; it holds Libertarianism up as the ultimate ideal that everything is to be compared to, and alternatives are only to be accepted if they are unarguably better in every way for everyone.  We can safely discard the Libertarian variant as question begging; anyone who's not already convinced of the superiority of Libertarianism has little reason to consider an argument which assumes that the fairness of any outcome should be measured by comparing that outcome to Libertarianism.

The Weak Pareto Criterion

The Weak Pareto Criterion is widely accepted but roughly useless.  It forms the basis of the first and second welfare theorems, which are frequently used to argue for government without economic regulation, but optionally with taxes, spending, and transfers.  However these arguments are logically questionable for reasons I will get into.  These welfare theorems are problematic partly because they make far weaker claims than they seem, but also because their existence and the elegance of their proofs make many economists long to believe that they have shown something worth showing -- that Pareto efficiency is a far more desirable and useful goal than it actually is.

Let's start with some of the (I suspect) uncontroversial shortcomings of Pareto efficiency as a standard:

• Plenty of Pareto efficient outcomes would be reasonably judged by most people to be terrible outcomes, relative to other possible outcomes.  For example, we can imagine the outcome where I own all property in the world and therefore have claim on its output, and everyone else can earn just enough to eat by working full time for me.  Because no one can be made better off without harming me, this outcome is Pareto efficient.  But you can just as easily imagine bad economies where it is, say, Mitt Romney who owns everything instead of me.
• Pareto optimization is intended for the purpose of taking a large set of possibilities and narrow it to a smaller (but probably still quite large) set of possibilities, the latter set certain to contain the most desirable possibilities but probably undesirable ones as well. Pareto efficiency is not intended for the purpose of justifying any particular outcome in the Pareto set as being a good outcome.  The moment you suggest that a particular economic arrangement that will lead to one particular Pareto optimal outcome is one we should prefer, you have necessarily brought in considerations other than Pareto optimization.
• If outcome A is Pareto efficient and outcome B is not, that itself is no reason to believe A is better than B, unless A itself is a Pareto improvement over B.  Even getting rid of regulations that are causing deadweight loss to make a market clear is likely to not be Pareto improving, as illustrated nicely by Steve Waldman.

The most insidious use of arguments from Pareto efficiency come when options are discarded due to the existence of Pareto better options that aren't actually on the table. You should never throw away option A in favor of option B if option B isn't a particularly plausible option and option A is. But this is quite common in economics, because the Pareto set in the welfare theorems is drawn from the outcomes that are theoretically achievable, whereas no consideration is given to what is practically achievable. As a result, options that are Pareto efficient in practice are thrown out because they are not Pareto efficient in theory. This is problematic.

To give an example, consider the minimum wage. It can be argued in theory that if we got rid of it, if we calculated how much each person benefited or lost from that change the winners would be able to compensate the losers such that everyone would be better off than they are with it. Therefore an outcome with a minimum wage is not part of the theoretical Pareto frontier. However, arguing on this basis for getting rid of the minimum wage without any sort of compensation scheme would be a non sequitur as simply eliminating the minimum wage would certainly not be a Pareto improvement. But a more sophisticated argument might be that we shouldn't consider a minimum wage because there are better ideas we could be considering instead. However the better ideas are unrealistic. No one has ever actually laid out a policy that could be enacted into law that would get rid of the minimum wage in a Pareto improving way; this is not practically possible to do. Furthermore, due to its popularity a minimum wage is not just practically possible to write legislation to enact, it is politically possible to build the support necessary to enact it, something other alternatives may lack. For this reason keeping the minimum wage (or raising it to $10, $15, probably even $35) should be considered part of the practical Pareto frontier even if they are not part of the theoretical Pareto frontier.  Now that doesn't mean that raising it to any of those values would be a good idea. There may be good reasons to support lowering the minimum wage or to oppose raising it by too much, but Pareto efficiency is not among those reasons.

And as for the problems with aggregate social utility and interpersonal utility comparisons?  The problems are as real as they are unavoidable.  If you have ever supported a tax cut or a tax hike, opposed a regulation you believed was protecting one industry's profit at everyone else's expense, supported breaking up a monopoly, supported lower or higher trade barriers, or raising, lowering, or eliminating the minimum wage, then you are guilty of interpersonal utility comparisons.  You have supported harming some to help others; if you had any sound reason at all for your position it necessarily relied on some conception of the greater good.  The values you relied on to make that judgement may be reasonable ones, but make them explicit so they can be part of the conversation; do not insist on a contest to see who is best at sweeping them under the rug.

Update: For more on this, including the problematic Potential Pareto criterion which I was not previously aware of, see Steve Waldman's Welfare Economics series.  In fact, read that series before you read any of the other posts I've linked to, or for that matter before you read this post.

On the Origins of Libertarians

Funny comment buried under a post about BitCoin that I thought I'd share.

It is impossible for an accounting identity to have any causal implication or explanation

Paul Krugman, in an apparent attempt to be too generous to the argument he's taking apart, gets something fundamentally wrong about accounting identities:

Here’s what happens: you start with an accounting identity, in this case savings = investment, and treat it as a causal relationship – savings => investment – imagining that this excuses you from the need to lay out a mechanism for this alleged causation. 

The immediate thing Fama should have asked himself, even if completely ignorant of the history of macroeconomics, is why the causation necessarily runs from savings to investment. Why not the other way around? 

Let's stipulate that if the sun comes up tomorrow at 6:30, it will also be the case that tomorrow at 6:30 the sun will come up.  Does the sun coming up tomorrow at 6:30 cause, at 6:30, the sun to come up, or is it the other way around?  Neither.  It makes no sense to say either causes the other when they're the same event.

There are interesting questions around causality in economics.  If the government spends money today, will this cause a private business to hold back on investment?  Maybe, maybe not, but what's important is to understand why no accounting identity can possibly shed any light on this question.  The problem is that now, unlike in the sun example above, we are dealing with two events, and these events are separated by time.  But accounting identities are too absolute to tell us anything about causally linked economic transactions, because they hold over any span of time, including spans of time that include just the cause and those including just the effect.  So even if you find a real causal relationship between some economic transactions, no accounting identity could have required that causal relationship to exist.

This can be stated even more strongly: every single transaction that occurs in the economy preserves the accounting identities all by itself, regardless of what other economic transactions occur.  Therefore, accounting identities only constrain the nature of individual transactions; any conceivable correct or incorrect causal story about how different economic transactions relate to each other will always be consistent with all accounting identities because the individual transactions must be.

Let's work through an example of how savings = investment is preserved in practice.  Let's say I'm considering buying a $5 loaf of bread which is made of ingredients that cost a bakery $3 to acquire.  In the scenario where I buy it, the bakery profits $2, which, because that profit can't immediately be spent will become $2 in savings.  If I don't buy, I save $5, and the bakery has unsold inventory that cost $3 to make, so it has invested $3.  (Yes, when a business makes a good no one wants to buy and ends up throwing it away, that's an example of "investment", why do you ask?)  In the scenario where I buy, there is $3 less saving and $3 less investment.  So did the fall in savings cause the fall in investment or vice versa?  It makes little sense to ask when only one thing has happened.

But won't my decision to consume or to save affect my future decisions to consume or save?  Won't the bakery's profit affect their decisions to consume, save, or invest?  Probably, but the accounting identity does not require this; this single transaction preserved S=I all by itself, and if other future transactions are caused by this they will also need to preserve S=I all by themselves.  My decision to buy or not buy a loaf of bread does not cause some imbalance in the identity that must be corrected by some other economic transaction; no corrective forces in the economy come into play to balance S=I over the long run because S=I can't be violated for even a nanosecond.

Why I believe demand matters over the long run

It seems to be a common belief even among more liberal economists that, while recessions are frequently due to demand side constraints, over the long run supply side economics reigns supreme.  But when you apply supply side thinking to trade, the natural conclusions don't square with how beneficial trade surpluses really are.

Consider the case of China.  They have been purchasing American financial assets with the intent of deliberately manipulating demand -- that is, they are exchanging real goods for financial assets.  This has the effect of increasing demand for Chinese goods relative to American goods.  It also increases the financial capital of America at the expense of China.  This makes it easier than ever to get a loan in the U.S. while having the reverse effect in China.

What consequences should we expect from this from a supply-side perspective?  Because it is easy to get loans in the U.S., it is easier than it otherwise would be to start a business -- where there are opportunities for profit, entrepreneurs will be able to get the money for start-up costs, and, thanks to low interest rates, they will have an easier time paying back loans with those profits.  And as for the goods we import, the effect of that is to redirect China's productive capacity to our benefit.  We don't have to direct our scarce labor and resources to supplying those goods, so we should be able to direct them to providing the productive capital those businesses will need -- factories, technology, etc.  Indeed many economists find it obvious that financial capital and real capital go hand-in-hand.  Meanwhile the reverse should happen in China, so we should see our economy grow while theirs stagnates.  And what would they get out of it?  Well, the financial assets aren't nothing; some day when they decide they want the economy they have been forgoing all these years, those assets should make it easy for them to reverse the situation and take advantage of our productive capacity that they have made it easy for us to create.

Needless to say, nothing about this squares with the real world.  China has increased our supply of financial capital, and the result has been the de-capitalization of our economy and rapid growth in theirs.  In the real world nations like China and Germany that run trade surpluses over the long run see faster growth over the long run, not just in recessions, and they don't have to switch to running trade deficits to benefit from that growth.  This is because it is demand for the potential output of capital that drives private capital investment, not finance, not money circulating around Wall Street.  By driving investment, demand drives long term growth.

Putting the issue of trade aside, there are many other financial-capital-friendly policies we have that make sense only in the logic of supply side economics.  Take, for example, the reduced tax rate that day traders and hedge fund managers pay.  A lower rate on capital gains income means more money will be made available for capital, financial or otherwise.  By either raising income taxes or reducing government spending it similarly reduces demand for the output of our capital.  That is to say, it has exactly the same effect on our economy as running a trade deficit with China.  We should expect it to be exactly as beneficial.

It isn't that supply side economics is entirely wrong -- it is possible for an economy to be constrained by the factors supply-siders worry about -- it's just that given our actual economic situation supply side economics just doesn't matter, and it isn't clear that it has mattered at any point in the past three decades.  If long run trends of technology driven efficiency and automation continue, it seems reasonable to expect that supply side economics will matter even less in the future than it does today.

Concentration of Wealth Simulation

I've been exploring the question of how the super-rich get so rich.  You may have heard that the top 1% controls over 35% of the wealth.  Robert Lenzner recently ran a piece in Forbes noting that the top 0.1% earn half of all capital gains income.

There are two basic ways to make money in a capitalist economy.  One way is through labor -- you can trade your time for money.  The other is through investment -- you can trade your money for more money.  There are plenty of ways to do this -- stocks, finance, hedge funds, but they all share the feature that, if you start with twice as much money, without any more work or skill you make twice as much money.

I made a simple economic simulation to see the range of possible distributions of wealth that can naturally arise from a capitalist economy.  I thought about writing it in Python and sharing the source code, but it occurred to me that now that IE9 has been out for a while, the world ought to be safe for HTML5 and computationally intensive JavaScript, so I've embedded the code for everyone to play with.  Caution: may be painfully slow on your phone.

Savings and Debt

Much like spending and income, savings and debt are opposites from an individual perspective, but are the same thing when considering the economy as a whole.  The only way to earn interest on savings is to loan it to someone else and charge interest.  So there is no trope about our economy that bugs me more than the idea that Americans have too much debt and not enough savings.  This is a problem we can't have -- savings and debt go hand in hand, we can't have one without the other.  Perhaps we have too much debt and too much savings.  Or you could say that the middle class has too much debt and not enough savings, but the corollary of this is that someone else -- perhaps the government or the wealthy -- will need to have less savings or more debt to solve the problem.  "Too much debt" is not a problem that can be solved by encouraging more saving -- more saving is an anti-solution that puts pressure on Wall Street to search the mountains and valleys for anyone who could be convinced to go into more debt.

If for any reason the phrase "fractional reserve banking" ran through your head as you were reading the last paragraph, you're off base.  Sure, the statement applies to fractional reserve banking, but the point is it applies to any sort of banking system.  In fact, the debt that fueled the housing bubble was not created primarily through fractional reserve banking but rather through financial securities such as CDOs.  The only important difference between fractional reserve banking and other forms of finance for the purpose of this discussion is that, in fractional reserve banking, up to 90% of savings become someone else's debt, whereas with other forms of finance 100% of savings are someone else's debt.  As a result of this, the most debt the fractional reserve banking system can possibly create is nine times the money supply, whereas financial instruments like bonds and CDOs allow money to be loaned, spent, loaned, spent, over and over again until one of three things happens: 1) no one is interested in loaning money, 2) no one is interested in borrowing, or 3) the financial system becomes unstable.

Let's continue the thought experiment from the last post and examine another way that money can constrain an economy. 

Spending and Income

Spending and income intuitively sound like opposites. This is because, from the perspective of an individual person, they are -- income is how you get money, spending is how you go broke. We intuitively understand that money must come from somewhere and that it is a finite resource that we will run out of if we’re not careful. But problems arise when we try to apply our intuitions about money to the economy as a whole, because money doesn’t go anywhere. Income and spending are not opposites; in fact they are exactly the same thing, just viewed from different perspectives. Every penny you earn was the result of someone else choosing to spend that penny, and every penny you spend becomes someone else’s income. An economy where everyone is thrifty and does not spend more than they absolutely have to is an economy without much opportunity to make money.

And the economy cannot run out of money due to overspending or be constrained by past overspending. Oil can run out, trees can be cut down more quickly than they regrow, but money is the perfect renewable resource, creating additional income exactly as quickly as it is spent. So if we can never run out of money, the economy cannot possibly be constrained by it, right?

Not so fast. Let’s look at one possible economic scenario that is a lot like running out of money. To keep it simple, we’ll ignore the effects of banking and governments for now.