The Life's Work of Paul Krugman

A revolutionary twice over

Continuing our greatest economists series, which we began with a profile of Banerjee, Duflo, and Kremer, we turn to Paul Krugman. He was born to be a newspaper columnist – even in his papers, he is capable of astonishing clarity and deceptive simplicity. His papers are simple, even slight. They often do not bother calibrating on real world data, as is now the standard. He is a theorist, and only reluctantly interested in working with data. What his papers do do, however, is illustrate all at once the essential points of a system, and in many cases totally revolutionize our understanding of economics.¹

His first great contribution was taking the Dixit-Stiglitz model and applying it to trade in “Increasing Returns, Monopolistic Competition, and International Trade”. Prior analysis of trade had focused on perfect competition. Price was equal to marginal cost, and there were no economies of scale. Trade was simply determined by which endowments a country had – if it had a relative abundance of land, it would export agricultural goods and import manufactured goods, for example. In order for perfect competition to exist, there cannot be fixed costs. If you imagine that the cost of producing an additional unit is constant, then requiring a fixed cost to enter means that the average cost is lowest when there are infinite goods produced. Efficiency depends, therefore, on the size of the market.

The Dixit-Stiglitz model was a necessary step for this. The key advances are that it gives everyone a utility function with constant elasticity of substitution, and treats every firm as producing one part of a continuum of goods. By making firms infinitesimally small, each firm has no impact on the prices of other goods, ensuring that we can easily find an equilibrium. The CES utility assumption allows us to model the utility gained from new goods, keeping total utility finite by having it curve asymptotically toward 0.

Once you allow for monopolistic competition, trade becomes due to increasing returns. This accords with actual trade patterns, in which most trade is between rich countries, and in the same categories of goods. The United States produces Fords, and Japan produces Hondas, and we are better off for exchanging them between us. Trade will exist between countries even if their tastes and preferences are identical, and it is costly to ship between countries. The share of trade is simply the proportion of the total labor force in that country.

Prior work had found factor endowments to be entirely inadequate to explain trade. Wassily Leontief famously tested the Heckscher-Ohlin model in 1953 and found that places with more capital per worker exported products which were more labor-intensive. Now we had an easy way to understand why. Later work, which has expanded to include heterogenous firms, so that another margin from trade is gains from reallocating between different firms, is based entirely on Krugman’s work. In Melitz’s canonical setting, his model is explicitly an extension of Krugman’s 1980 formulation of increasing returns and trade. In fact, if you say that firms draw their productivity from a Pareto distribution (and thus there’s a constant elasticity of substitution) as in Arkolakis, Costinot, and Rodriguez-Clare (2012), they’re the same models!

Krugman followed this up with a couple more papers on trade. “Scale Economies, Product Differentiation, and the Pattern of Trade” extends Krugman 79 to include differences in factor endowments, and makes a fairly strong prediction – bigger countries will have higher wage rates, and countries will export those products which they have relatively larger domestic demand for. Note that the latter, the home market effect, is predicted only in models which have increasing returns. This prediction has held up well – I recall a paper from Costinot, Donaldson, Kyle, and Williams (2019) which used the plausibly exogenous changes in drug demand due to aging from Acemoglu and Linn (2004) to test this.

Krugman then looked at who gains and loses from trade, and when trade benefits everyone. If endowments are identical between two countries, then it will quite obviously benefit everyone. If there are increasing returns, and suddenly everything doubled, then of course we would all be better off. If, however, there are substantial differences in factors, then it is possible (though not necessarily certain) for some people to be made worse off. Only if the importance of different factor endowments exceeds increasing returns will opening trade harm some while helping others. This implies that opening up trade with similar countries will be politically much easier than opening up trade with dissimilar countries. I’m not so sure about this, because he assumes identical firms, and this is one where heterogeneous firms really matters. Our factor endowments with Japan were very similar, but we still had an enormous political reaction to their firms entering the market. Our firms had grown inefficient, and weren’t able to keep up.

He would also, with James Brander, show the conditions necessary for opening trade to reduce total welfare. It shouldn’t be surprising that these conditions are incredibly restrictive, though. Suppose that there are two firms, one for each country, producing one product, and welfare is equal to 1 in the world where they are each producing in their own country. Now suppose that trade barriers fall, and they are in competition with each other. More formally, the percentage of shipped goods which arrive in the other country is equal to 1 minus tau, and tau has fallen from 1 to a lower number. If the form of the competition is Cournot competition, where they choose the quantity of goods they want to make and then compete on price, and new firms are barred from entering, then the firms will ship goods to each other’s markets and waste a bit. Of course, these results are incredibly sensitive both to the form of competition (see Feenstra, page 13) and to the assumption of a barrier to entry. If there is free entry, then any reduction in trade barriers is good. Considering oligopoly in international trade seems to be making a comeback – see Pol Antras’s paper on this.

Krugman’s insight of increasing returns would flow naturally into a much broader question – why is economic activity arranged how it is? The very existence of cities and clusters necessitates increasing returns instead of constant returns. The standard assumption of constant returns would presume that economic activity might as well take place in frictionless points, with trade costs occurring only between nations. Krugman himself would wonder why nobody else got to it first – he felt that he had left it all there in 1979, and it remaining an unanswered question for 12 years was a bit of extraordinary luck.

He gave us an incredibly clean analysis in “Increasing Returns and Economic Geography” (1991). Suppose that there are two regions within a country, West and East. Both places have some land suitable only for agriculture, and we will further assume that there is a fixed supply of labor to work in agriculture. There is also a fixed supply of labor to work in manufacturing. What we are curious about are the conditions under which manufacturing workers would be spread evenly between the regions, and when they would all agglomerate into one region.

We make two assumptions for tractability: transporting the agricultural good is costless, and the transportation costs of manufactured costs are “iceberg”, which means that a fixed percentage of the good is lost when transported (or 1 minus tau). There are then three variables which affect the distribution of manufacturers: the trade cost tau, the share of expenditures on manufactures mu, and the elasticity of substitution between products sigma. He then looks at what happens if industry starts in one region. When will it diverge? If transportation costs are high, then it will be spread out. As transportation costs fall, concentrating becomes more likely. As transportation costs fall to zero, then location is irrelevant. If people spend a high portion of their expenditures on manufactured goods, then the costs of transport costs are magnified. And last, the higher the elasticity of substitution between goods (or in other words, the greater the economies of scale) the more production will be concentrated.

Put concretely, we have the story of American manufacturing laid out. It started dispersed among the population, with agriculture being the main source of employment and consumption. As transportation costs fell and economies of scale rose, production became concentrated, and as transportation costs fell still further, manufacturing dispersed again.

Increasing returns allows for there to be multiple equilibriums. For example, a city might be equally well be located in one place over another, but once people start moving to one place, there’s no incentive to be the first to move to the middle of nowhere where the city could have been. Krugman explores this in “History vs Expectations”, which points out that ultimately all that matters is people’s expectation of future growth. This may be shaped by history, but it is not the same as history, and so it is possible for shocks to people’s beliefs to permanently alter the arrangement of economic activity in the world.

Another relevant application of increasing returns is considering if temporary shocks can have permanent effects on economic activity, which he looks at in “The Narrow Moving Band”. As with much of his work, he is trying to make a concise model for a commonsense observation. Many people think that discovering natural resources might make a country poorer in the long run by shifting their comparative advantage away from manufacturing. If scale economies are external to the firm, then it is possible for a discovery of some resource to shift firms out of the country, and for this to be impoverishing for that country in the long-run. He would also deal with this idea in the context of exchange-rate shocks.

Krugman would be diverted by the Great Recession into macroeconomics, though he had been thinking about it long before. In “It’s Baaack”, he explores the “liquidity trap”, with particular emphasis on its application to Japan. The central bank generally manipulates the supply of money using the interest rates at which it lends money out at. If it lowers interest rates, then people are more willing to borrow, and the supply of money expands. If it raises interest rates, then people borrow less, and the supply of money contracts. Awkwardly, though, the central bank can only raise or lower interest rates relative to the present expected rate of inflation. Thus, interest rates will be high during times of high inflation, and low during times of low inflation.

Still more awkwardly, the interest rate cannot meaningfully dip below zero. If it does, people will just hold onto cash. Once interest rates go down far enough, a central bank may find itself “pushing on a string”, unable to increase inflation or stop deflation. This matters, because wages and prices are somewhat sticky. If the real value of a price goes up, and businesses are at the edge of profitability, then it will push some companies into bankruptcy. Deflation has real effects.

In the case of Japan, they had stagnation throughout the 1990s, and incredibly low rates of inflation. Krugman believes that this is due to the aging population saving too much for retirement, but it really could be anything which reduces employment. He would extend this work to the American economy after the Great Recession, where he would be one of the voices calling stridently for the government to do more – to print more money, to cut interest rates lower, to fund infrastructure investments, to do anything to get us out of the demand-driven slump and unnaturally high unemployment of the period.

No retrospective of his work could be complete without covering some of his many, many, (many!!) essays. I will not even pretend to have read them all, nor would even he, I think, recommend them all. We can cover a few.

His clearest illustration of the problem of Japan, and of how recessions can occur from insufficient demand in general, can actually be found in a column he wrote for Slate called “Baby-Sitting the Economy”. It’s the story of a baby-sitting cooperative in Washington DC. Everyone wants to go out some nights, but they’d need someone to watch their kids. Meanwhile, on the nights when they’re in, it’s not that much of an inconvenience to have someone else’s kids over. In order to make it fair, the co-op issued scrip equal to one hour of baby-sitting time, which could be traded from person to person. The trouble was that some people were saving too much, and the amount of scrip in circulation fell. People reduced the amount that they baby-sat. Everyone was worse off relative to a world of abundant scrip. He then extends this to Japan. You can imagine a world where the “central bank” managed these recessions by changing the interest rate at which it put out scrip. Imagine too that people were more willing to go out during the summer, and more willing to babysit during the winter. The central bank could resolve this by altering the interest rate, unless the interest rate should fall to zero. Then it cannot compel anyone to borrow. The babysitting economy – or Japan’s economy – would slide into recession due to a lack of consumer confidence.

“What Should Trade Negotiators Negotiate About?”, a review of a compendium of essays by economists and non-economists on free trade, is striking for the directness – even tartness – of his pen. Notwithstanding the theoretical objection that large nations could profit from a non-zero tariff (they are in essence raising taxes which are paid partly by foreigners), which he dismisses as a purely theoretical curio which is totally unresorted to by non-economists, he describes trade negotiation as being underlied by an implicit mercantilist theory. The only good thing is increasing exports, and increasing imports is a defeat. To Krugman, the correct course of action is to cut trade barriers, and do it now. It doesn’t matter if other countries don’t do it, or if they are subsidizing their domestic industry, or if their labor standards are different. Lerner symmetry applies, so just cut the trade barriers and let whatever happens happen.

He would return to this theme in “What Do Undergrads Need To Know About Trade?”, and of course, the famous parable of the Hot Dogs and the Buns. (That is to say, “The Accidental Theorist” from 1998). Both of these are a lambasting of what he calls “pop internationalism” – the tendency to see trading nations in competition with each other, and to see changes in productivity which reduce employment in some category of jobs, as bad.

“Two Cheers For Formalism” is a stirring defense of mathematics in economics. To him, math is simply a way of speaking precisely about precise things, and the reason people often dislike it is simply because it often contradicts their cherished notions. Relatedly, “What Economists Can Learn From Evolutionary Theorists” is a somewhat puckish defense of unrealistic assumptions of equilibrium. He is addressing a group of evolutionary economists, which is a school of thought which emphasizes the unsettled nature of economies. Oddly, though, what actual evolutionary biologists do is most similar to neoclassical economists. Species are not modeled as slowly groping toward equilibrium – they’re already there! At all times, to be fair, his opinion is reasonable – he thinks that we should model what we can, but we shouldn’t dismiss ideas just because we can’t model them. He thinks that old-school theories of development were perhaps unfairly treated because we could model external economies of scale, upon which their theories depended, but at the same time that trying to model your theories formally is an important part of building knowledge.

I found his essay “How I Work” to be rather beautiful, and in line with the other defenses of perhaps unrealistic assumptions. In particular, I appreciated the four rules which he has for his research, which are as follows:

1. Listen to the Gentiles

2. Question the question

3. Dare to be silly

4. Simplify, simplify

So, to have good ideas one should consider what intelligent people think outside of the field, and wonder why they think that. In economics, much progress consists not of answering an unsolved question but of formulating the question at all, and that requires trying totally different questions. Economic models are “silly” insofar as they often require weird assumptions, but these assumptions are generally needed to clarify what is actually happening.

Krugman was also always a very sensible person. In “In Praise of Cheap Labor”, he cuts the case against globalization to ribbons. Many people condemn multinational corporations for paying pennies to their workers overseas – but have you considered what else people would be doing? Globalization allows people in other countries jobs which we would consider terrible, but are comparatively much better than the alternative. Campaigns to boycott the produce of the wretched of the earth hurt only the poorest of the poor.

Right now, Krugman is concerning himself mainly with lambasting Trump on his substack. I think his current writing is actually better than the last years of his New York Times column run – I got the sense that they were pushing him to do more politics than economics. I do think that he should write a little bit less, and be a bit more technical, but he has otherwise earned the right to an unchallenging retirement.

This is properly part of series – I will make a general article covering the top ten or so economists living. I am keeping them a surprise, but you should expect to see coverage of Roger Myerson soon.

1. I simply must include Avinash Dixit’s description of his work from the essay in honor of him winning the John Bates Clark Medal: “Here is Paul's typical modus operandi. He spots an important economic issue coming down the pike months or years before anyone else. Then he constructs a little model of it, which offers some new and unexpected insight. Soon the issue reaches general attention, and Krugman's model is waiting for other economists to catch up. Their reaction is generally a mixture of admiration and irritation. The model is wonderfully clear and simple. But it leaves out so much, and relies on so many special assumptions including specific functional forms, that they don't think it could possibly do justice to the complexity of the issue. Armies of well-trained economists go to work on it, and extend and generalize it to the point where it would get some respect from rigorous theorists. In this process they do contribute some new ideas and find some new results. But, as a rule, they find something else. Krugman's special structure was so well chosen that most of its essential insights survive all the extension and generalization. His special assumptions go to the heart of the problem, like a narrow and sharp stiletto. By contrast the followers' work often resembles thoracic surgery, involving much clumsy breaking of ribs; sometimes it proves to be no more than an autopsy of the issue.”