Thursday, December 31, 2015

Actually, free markets aren't efficient in theory, either

Image: If we don't get the biggest pie, then what's the point? (source)

The fundamental assumption of free market capitalism is that the free market can provide goods more efficiently than the government, or any other system. If the government interferes in the free market--even with the best of intentions--it will only make things worse. Rent controls cause a housing shortage; price controls cause oversupplies; minimum wage laws increase unemployment. The further we get away from a pure free market, the worse the inefficiencies and unintended consequences. It may be necessary to assist the less fortunate sometimes, but government should interfere as little as possible in order to avoid making things worse. Interference will certainly do harm; it could easily do more harm than good.

A more technical way of expressing this free-market-is-always-best ethos is to say that the free market will naturally reach an efficient equilibrium. An equilibrium of prices will ensure efficient allocation goods to all members of society. It may not be the most socially just distribution, but it will certainly be the most efficient distribution that can possibly be attained. Making the distribution more just--that is, making each person's slice of the pie closer to equal--will result in less pie overall. We can have a full pie with very unequal pieces; we can have a smaller pie with less unequal pieces; but we can't have a full pie with less unequal pieces. In other words, there is a trade-off between equity (or fairness) and efficiency. Increasing equity necessarily results in less efficiency.

Pushed to its limits, this idea is actually a liberating, social justice imperative. With a free market ensuring the most efficient outcome, the pie becomes so big that even with very inequitable slices, the poor are still better off. Even with a very unequally-cut pie, free market capitalism creates such an enormous pie that even the poor have a bigger slice than they could ever hope for in any other pie, no matter how egalitarian the slices are cut. Sure, a market might produce winners and losers, but when the pie is big enough, even the losers are better off.

This idea--that government programs which increase equity are necessary less efficient--underpins bipartisan social policy adventures such as school choice vouchers and privatizing social security. The idea is that--because markets are so efficient--any (real or otherwise) problems with anything can be improved by making them function more like free markets.

Obviously, if the equity-efficiency trade-off exists, we are essentially arguing over values. I may prioritize equity over efficiency while someone else may prioritize efficiency over equity, and there is no right answer, per se. But that the equity-efficiency trade-off exists is utterly fundamental to free market capitalism. Without that trade-off, free market capitalism makes no sense. If free market capitalism doesn't produce the biggest pie, then what's the point? If free market capitalism can't produce the biggest pie, why should we tolerate the incredible inequities it creates?

If free market capitalism doesn't produce the biggest pie, then what's the point?

The biggest pie
Below, I'll use the terms "biggest pie" and "efficient equilibrium" a lot. These should be understood as interchangeable, but let's pause for a moment to explain what, exactly, this concept means--first "efficient" and then "equilibrium."

Efficient means that an economy's resources have been organized in such a way that it results in the greatest production of goods with available resources. It's at this point that economy is most productive and most prosperous. Again, this might not be a very equitable point, but it's the point of greatest productive output. All available resources are being used in the most efficient way possible. Of all the pies our economy could create, the efficient outcome produces the biggest pie. Everyone is working hard; factories are churning out goods, stores are selling those goods, and--in the aggregate--we are at our most prosperous. Less efficient configurations result in smaller pies--people unemployed, abandoned factories lying idle, unused goods lying on stores' shelves, etc. For this post, we are only concerned about efficiency and creating the biggest pie. For the moment, we're not concerned with creating a pie that is cut fairly.

Got it? Efficient: everyone working, factories churning out goods, and lots of commerce. Inefficient: idle workers, idle factories, unused resources, unpurchased products, and less commerce.

The second point is equilibrium. Equilibrium is at least as important as efficiency to free market capitalism, and probably more so. Equilibrium is the very bottom of a bowl. A grape can balance on the rim of a bowl, but it won't stay there for long--even the tiniest disturbance will send it rolling to the very bottom of the bowl. I might place a grape somewhere on the inside of a bowl, but as soon as I let go, the grape will roll to the very bottom of the bowl. And once at the bottom of the bowl, the grape will stay there; a grape lying stationary at the bottom of a bowl won't start rolling up the side of the bowl, in defiance of gravity. If the grape isn't at the bottom of the bowl, it will tend to move towards it until it ultimately settles there; once it's there, it won't leave on its own. The bottom of the bowl is the stable equilibrium point.

Putting "efficient" and "equilibrium" together, for free market capitalism to work, the "biggest pie" must occur as an equilibrium. The most efficient configuration of the economy must occur at the bottom of the bowl. It does us no good if the most efficient configuration for our economy is on the side of the bowl; if so, the economy will tend to move away from the biggest pie. And our bowl can't be a plate, either. On a plate, there is no equilibrium point; a grape doesn't role inexorably towards any one point of a plate.

This is the promise of free market capitalism: the most efficient configuration of the economy--the biggest pie--occurs at the bottom of the bowl. Our economy moves inexorably towards it without even trying; once there, it doesn't leave.

To sum up this section: For a free market to create the biggest pie, there must be a most efficient configuration for everything in the economy, and that configuration must be an equilibrium point. An equilibrium point is a point that the economy naturally moves towards as if pulled by gravity, and point where it naturally stays, as if held in place at the bottom of a bowl by gravity. If a free market can't meet these two criteria, then what good is a free market?

Let's get started.

Econ 101
The common understanding of economics is this: based on supply and demand (and their elasticities), buyers and sellers in a competitive market agree on an equilibrium price--based on all the buyers' willingness to buy and all the sellers' willingness to sell. Indeed, any economics 101 student will tell you that she can prove that the market for any single good will reach an efficient equilibrium (efficient meaning that a price is reached where that ensures all mutually beneficial transactions occur).

But that understanding is fundamentally wrong. It's believed that this easy calculation proves that a competitive market will reach equilibrium; in reality, it does no such thing. Rather, it proves that an economy with only one good will reach equilibrium. It's an instructive example, but all complexity has been stripped away: the buyers only buy one good, the sellers only sell one good, and there are no other goods to buy or sell in the entire economy. The sellers don't need to worry about overhead costs of their stores, and the buyers don't need to worry about the cost of food or shelter, because nothing exists beyond this one single good. It isn't a market reaching equilibrium; it's an entire economy that only has a single good that reaches equilibrium.

Social science is very complicated, and this basic econ 101 model strips the world of its complexity to try to understand the basic principles at work. Clearly, there is value the model. It gives us a reasonable understanding of how people might react to supply shocks, price controls, or quotas, for example. It might even hint at policies that can be used for the public good. There's nothing wrong with creating simplified models to try to understand a more complex system. But it's a problem when the simplified model is mistaken for the real world. For example, the econ 101 model can help us intuit the general direction of markets if a quota or price control is imposed, but it can't give us more than a general idea, let alone a precise prediction. More bluntly, this very basic econ 101 model is totally unequipped to predict if the negative effects of a quota or price control outweigh the benefits.

In later weeks in econ 101, students will add another good to their economy, using high school algebra to prove that economies containing two goods--two complements or two substitutes, for example--do indeed reach an efficient equilibrium (again, efficient in the sense that there are no more mutually beneficial transactions that can occur). An economy of two goods is solvable with algebra. Three goods? Three goods cannot be solved with high school algebra--nor, obviously, can algebra be used to prove an entire economy reaches an efficient equilibrium.

Indeed, it took over 100 years for theoreticians to solve the efficient equilibrium problem for an entire economy. The "econ 101 model" of two goods with complements or substitutes was birthed nearly simultaneously with the field of economics, in the late 1800's. Seth Ackerman and Mike Beggs explain the laborious, decades-long development of the Arrow-Debreu model, the next step in solving the efficient equilibrium problem. The Arrow-Debreu model can be used to show that an entire economy can indeed reach an econ 101-style efficient point:
For eight decades, starting in the 1870s, many of the finest minds of economics tried to prove mathematically that if this imaginary perfect free-market economy did exist, it would be both rational and beneficent; that through the blind workings of the free market, supply and demand for every good would spontaneously match and the results would be desirable. (Or at least they tried to discover what conditions would be necessary to guarantee that outcome.) The culmination of that work, in Kenneth Arrow and GĂ©rard Debreu’s Nobel Prize-winning 1954 proof, was long seen by many as the profession’s defining achievement. Arrow and Debreu proved that such an economy would always contain at least one potential configuration of prices and products in which supply and demand would match in every market, and that this configuration would be “optimal,” in the sense that no one could be made better off without someone else being made worse off.
Note what's missing here. The Arrow-Debreu model demonstrates that there is an "efficient" allocation of resources--the biggest possible pie--but it doesn't demonstrate that this efficient allocation of resources is an equilibrium. Remember, for free market capitalism to create the biggest pie, not only does this efficient combination of prices have to exist, but the economy must naturally and inevitably reach this combination of prices--and stay there. It does us no good if this magical point exists but our economy can't actually arrive at it. Arrow and Debreu were only able to show that any economy does indeed have a point of maximum efficiency, but they were not able to determine whether or not this point was an equilibrium point.

It took a couple more decades to advance the Arrow-Debreu model far enough to solve the equilibrium piece of this problem. Jonathan Schlefer explains the history of these efforts:
However, no one ever showed that some invisible hand would actually move markets [in the Arrow-Debreu model] toward [equilibrium]. It is just a situation that might balance supply and demand if by happenstance it occurred.
In 1960 Herbert Scarf of Yale showed that an Arrow-Debreu economy can cycle unstably. The picture steadily darkened. Seminal papers in the 1970s, one authored by Debreu, eliminated “any last forlorn hope,” as the MIT theorist Franklin Fisher says, of proving that markets would move an economy toward equilibrium. Frank Hahn, a prominent Cambridge University theorist, sums up the matter: “We have no good reason to suppose that there are forces which lead the economy to equilibrium.”
The problem has been solved. Free markets do not reach equilibrium.

It took over a century for economic theorists to develop the mathematics needed to model a free market. When they were finally able to do so, the result was simply that what many feel ought to happen, doesn't. A free market economy doesn't tend towards an efficient outcome; it tends toward...nothing. The bowl we imagined above isn't a bowl, but a plate on an unsteady table. The grape rolls around the plate, settling nowhere and moving unpredictably. If free market capitalism creates the biggest pie, it has only done so by accident. And since this efficient point is not an equilibrium, staying at this most efficient point is out of the question. If a free market economy happens to reach a desirable outcome, it will surely remain there only momentarily.

The efficient equilibrium theory is wrong. In theory, free markets don't tend towards--or stay at--an efficient equilibrium. Free markets lurch randomly from boom to bust to boom to bust, and have no tendency to create or maintain an optimal allocation of resources. In a theoretical free market, shuttered factories, idle capital, empty stores shelves, unused goods, and masses of unemployed workers are just as likely as prosperity.

Social policy in an imperfectly Arrow-Debreu world
This section (as well as later posts in this series) will link the theory discussed above to the real world. Here, we'll look at what happens when policymakers assume the efficient equilibrium hypothesis really is true.

But before we can do so, we have to look at how Arrow-Debreu differs from the real world. As we saw above, the mathematics behind the economic modeling of Arrow-Debreu is extremely complicated--so complicated that theoreticians had to make some simplifications to make the problem solvable. Without these simplifications, the problem would simply be too complex to solve mathematically. Coincidentally, these same simplification also make it easier for Arrow-Debreu to reach equilibrium. To get an idea of how this works, we'll look at three specific simplifications: the infinite flexibility of capital, the infinite interchangeability of labor and capital, and the infinite flexibility of labor.

First, in Arrow-Debreu, capital is infinitely flexible. If a firm goes out of business because the economy no longer has demand for its products, the capital of that firm can immediately be converted for a different use that the economy is in need of. If, for example, a steel mill closes for lack of business, the capital of that steel mill--the smelter, the building, the tools, etc--could tomorrow be turned into a computer mainframe. Obviously, massive factories lying dormant are not an efficient point and cannot be in our recipe for the largest pie. Converting that abandoned steel mill into something useful might take years. Thus, when a steel mill closes in the real world, this means that for years our economy cannot possibly reach equilibrium, because that factory cannot possibly be productive until it is retrofitted for a new productive purpose--which could take years. Obviously, being able to assume that capital can be used for any task is a very useful simplification for theoreticians.

Second, in Arrow-Debreu, capital and labor are interchangeable. This means that labor and capital can do each other's jobs, albeit less efficiently. If there aren't enough workers available to fill job openings, companies can invest in capital to automate those jobs and make up for the lack of labor. And if capital is in short supply, companies can hire more labor to take the place of capital. For example, a dozen strong men with shovels could replace a backhoe, and a backhoe could replace a dozen strong men with shovels. It is ideal to have the labor or capital you need when you need it, but if one is unavailable, it is always possible to substitute the other, even if it is less efficient.

It takes very little effort to see how inapplicable the interchangeability of labor and capital is to the real world. Computers can't program themselves, robots can't take care of sick patients, humans cannot use their bodies to heat iron ore enough to melt it, humans cannot be connected to the internet in place of a web server, etc. But it's easy to see how this is useful simplification for theoreticians.

Finally, in Arrow-Debreu, labor is completely flexible. If, for example, a factory closes, the redundant workers might find that their skills no longer match job opportunities; to find work, these unfortunate workers may have to spend years training themselves for new job opportunities. They might go to college or participate in a vocational training program, but retraining redundant workers can take years. Obviously, people willing and able to work who can't find a job simply cannot be an efficient point and cannot be in our recipe for biggest pie. Thus, in the real world, for the entire time a worker spends retraining in order to find a new job, the economy cannot be in efficient equilibrium. Theoreticians simplified Arrow-Debreu by assuming retraining occurs immediately at no cost to anyone; a chemist laid off today can find work tomorrow as a journalist, for example.

These three examples of the simplifications of Arrow-Debreu illustrate how Arrow-Debreu is very different from the real world.

Now, let's assume that you believe that the efficient equilibrium hypothesis is correct in theory. It's not, but let's pretend for a moment that you believe this anyway. If the real world has high unemployment, how do you explain this?

Remember, if the efficient equilibrium hypothesis is true, then unemployment cannot occur in a free market. It's simply impossible; the market will inevitably allocate resources such that all capital is in use and everyone is working. Unemployment is an impossibility in a perfectly free market if the efficient equilibrium hypothesis is true.

Thus, if you believe the efficient equilibrium hypothesis is true, then you will also believe that unemployment can be greatly reduced if we can make our economy more closely resemble the theoretical conditions Arrow-Debreu. If the efficient equilibrium hypothesis is true, then the closer our real world economy resembles Arrow-Debreu, the lower unemployment will fall.

To design a "solution" to unemployment, you will look for the ways that our real world economy is dissimilar from Arrow-Debreu, and find ways to make it more similar to Arrow-Debreu. Recall that in Arrow-Debreu, labor is infinitely flexible because retraining of redundant workers can occur immediately and at no cost. Thus--if the efficient equilibrium hypothesis is true--real world unemployment can only exist because retraining workers takes time and money. With perfect flexibility of labor, those workers would surely be employed. The solution is obvious: implement government programs that facilitate faster and easier worker retraining, thus increasing the flexibility of labor and bringing our real world economy closer to the theoretical conditions Arrow-Debreu. And because the economy is closer to Arrow-Debreu, unemployment must fall.

Of course, this is nonsense. Arrow-Debreu does not tend towards an efficient equilibrium. Making our economy more closely resemble Arrow-Debreu will not ensure that more people get jobs, because full employment is not a feature Arrow-Debreu.

Paul Krugman recently cited some examples of this (he uses the term "skills gap" instead of "labor flexibility"):
The education-centric story of our problems runs like this: We live in a period of unprecedented technological change, and too many American workers lack the skills to cope with that change. This “skills gap” is holding back growth, because businesses can’t find the workers they need. It also feeds inequality, as wages soar for workers with the right skills but stagnate or decline for the less educated. So what we need is more and better education. 
My guess is that this sounds familiar — it’s what you hear from the talking heads on Sunday morning TV, in opinion articles from business leaders like Jamie Dimon of JPMorgan Chase, in “framing papers” from the Brookings Institution’s centrist Hamilton Project. It’s repeated so widely that many people probably assume it’s unquestionably true. But it isn’t...
Krugman goes on to explain that if there truly were a skills gap--or a problem with flexibility of labor--there would be sectors of employment where employers had to compete for scarce workers, and those wages would increase rapidly. Yet there's no evidence this is occurring; wages have been stagnating in nearly every sector of the economy for a very long time. Larry Summers went further:
I think the [education] policies that Aneesh is talking about are largely whistling past the graveyard. The core problem is that there aren't enough jobs. If you help some people, you could help them get the jobs, but then someone else won't get the jobs. Unless you're doing things that have things that are effecting the demand for jobs, you're helping people win a race to get a finite number of jobs. […] 
Folks, wage inflation in the united states is 2%. It has not gone up in five years. There are not 3% of the economy where there's any evidence of hyper wage inflation of a kind that would go with worker shortages. The idea that you can just have better training and then there are all these jobs, all these places where there are shortages and we just need the train people is fundamentally an evasion. [...] 
I am concerned that if we allow the idea to take hold, that all we need to do is there are all these jobs with skills and if we can just train people a bit, then they'll be able to get into them and the whole problem will go away. I think that is fundamentally an evasion of a profound social challenge.
Clearly, the efficient equilibrium hypothesis is of central importance. When policymakers assume the efficient equilibrium hypothesis really is true, it leads them to propose and implement counterproductive policies that do not solve the underlying problems.

It's not hard to find other examples of policies based on the fallacy of the efficient equilibrium hypothesis. School choice attempts to create a free market for schools. Social Security privatization attempts to harness the free market to improve returns. And opposition to minimum wage laws is another obvious example of the false belief that free markets create the biggest pie.

To conclude, I will again repeat that none of this is to say that economic models can yield nothing of use. Indeed, we've learned an extremely valuable lesson from Arrow-Debreu: a free market system does not create the biggest pie except by accident; and even if a free market were to--against all odds--randomly stumble upon the biggest pie, it would rapidly destroy that pie and create a smaller pie, because the biggest pie isn't an equilibrium. Free markets lurch from boom to bust randomly and have no tendency to move towards an optimal arrangement of resources. With the many policy tools at our disposal--universal health care, universal child care, minimum wages, labor unions, mandated paid vacation, etc--we can create a pie that is both bigger and more equitably sliced than the free market, because free markets are anything but efficient.

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