Kenneth Arrow Made Great Models, and Was One
Economics has taken a lot of flak lately – from esteemed sources, no less – for relying on math that’s so abstract that it doesn’t look like the real world at all. There’s something to that critique, and even economists make fun of themselves on this point. Sometimes, however, mathematical abstraction is precisely what enables economics to help us understand and improve the real world.
First, Arrow gave us one of the best abstract models we have of idealized markets. To get a sense of what this looks like, imagine a market in a vacuum: a world in which trading partners are easy to find, goods can be exchanged instantaneously, and all the possible risks of trading are well understood. In worlds like that, markets always make people better off, because anyone who wants to can trade his or her way to a better outcome.
That’s a truly free market, and its outcomes are just as marvelous as free-market romantics like to imagine. But real-world markets don’t actually work that way. (Just ask anyone who has ever tried to buy a house, yacht, or other large investment.)
Just as friction slows wheels down more than ideal physics models predict, real markets have frictions that stop them from looking like the ideal markets in Arrow’s model. Much of Arrow’s work, as well as that of his contemporaries, amounted to figuring out the precise mathematical conditions that make ideal markets work, so as to understand what types of frictions matter, and how to correct them.
So now, just as we might oil a wheel to reduce friction against an axle, we can identify and reduce friction in real-world markets. Today, some economists actually do this. The mechanisms they design for procurement auctions, large-scale resource sales, labor market clearing, and even life-saving kidney exchanges all reduce marketplace friction with an eye toward producing outcomes closer to the Arrow ideal.
Arrow also used his abstract insights to understand real-world markets directly. Using theory, he uncovered two fundamental problems of health insurance: moral hazard (because insurers, rather than patients, pay for service, doctors might order extra tests or treatment) and adverse selection (top-rate health insurance is more likely to be bought by high-risk patients, resulting in an insurance pool that’s too costly to insure). Both of these ideas are now so central to today’s discussions about health-care policy that it’s hard to imagine they ever had to be discovered.
And Arrow changed more than just the way we think about markets. Perhaps most famously, he transformed our understanding of voting.
Arrow found a mathematical proof that no voting rule (or indeed, any rule for making group decisions) is perfectly ideal: Roughly speaking, a rule that fully responds to changes in society’s preferences can’t always yield suitable outcomes. Because this negative result holds even in an abstract, mathematically ideal world, there isn’t a simple way around it. Thus in practice we can’t just go looking for the “best” voting system. Instead, we have to face fundamental trade-offs in how we allocate power and decision-making rights.
Arrow’s abstractions revolutionized economics. They also inspired generations of students, many of whom made their own contributions to economic theory. Arrow himself never stopped pushing the frontiers – even at age 95, he was still writing new papers and mentoring young scholars.
He gave us models to work with and a model to emulate.
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