What Role Should Mathematics Play in Economics?

Table of Contents

Paul Krugman

Introduction

Use of Mathematics Has Not Made Economics Irrelevant

Outsider Critics Dislike Conclusions, Not Methodology

Globalization

Mathematics is Essential for Progress in Economics

Summary

Paul Krugman

Use of Mathematics Has Not Made Economics Irrelevant

Krugman addresses criticisms that economics has become so formalized that the discipline has rendered itself irrelevant.  

He starts by using the list of winners of the John Bates Clark Medal as a proxy for what economists consider to be good research – which would include an evaluation of the methodological approach deployed.

Krugman argues that, because the award has been given to individuals who have later assumed high positions in the U.S. government, the economic research of these Clark Medal award winners must have real-world relevance.

This means the profession values and rewards research that is of relevance to real-world issues.

Therefore, Krugman’s argument runs, the profession cannot be said to be out of touch or excessively formal.    

Here is a simple reality check. The American Economic Association's John Bates Clark Medal is a highly coveted award; it is therefore an indicator of what the profession values. And because it must be given to an economist under 40, it reflects research undertaken fairly recently. So what do we learn about the values of the profession - the sorts of work that command the highest rewards - by looking at, say, the last ten Clark Medalists?

Here is the list: 1979, A. Michael Spence; 1981, Joseph Stiglitz; 1983, James Heckman; 1985, Jerry Hausman; 1987, Sanford Grossman; 1989, David Kreps; 1991, yours truly; 1993, Lawrence Summers; 1995, David Card; 1997, Kevin Murphy. In short: two middlebrow theorists whose work on imperfect markets has had major impact both on policy and on corporate strategy; two econometricians whose techniques are widely used in practical applications; two theorists who specialised on issues of information and uncertainty; a trade theorist who focussed on increasing returns and imperfect competition; a macroeconomist with a strong empirical and policy bent; and two very empirically - oriented labour economists. Not one of these economists has worked mainly on perfectly competitive markets, or is a free-market ideologue. And as far as relevance goes, notice that in their subsequent careers some members of the group have found that businesses and governments are willing to pay large sums for work based on their earlier research; one became Chairman of the Council of Economic Advisers, while another is now a very powerful Deputy Treasury Secretary; and one has been known to write reasonably successfully for non-economists.

So where in this group is the excessive formalism, the excessive reliance on the deductive method, of which economists are routinely accused?

You may answer that while the very best economists may be free of the sins for which the profession is criticised, things are different once one goes down the scale. But take any of the fields in which one of the lucky 10 works, and try listing 5 or 10 other successful economists in the same area. How many of them are engaged in arcane algebra that has no relationship to reality? (Some of them, like auction theorists or finance theorists, are indeed engaged in arcane algebra - but it turns out to be very relevant indeed). I have not done this exercise, but I would guess that if one took the 100 economists most cited in the Social Science Citation Index and summarized the nature of their work, it would turn out to be mostly focussed either on real-world problems, or on techniques that other economists have found very useful in addressing real- world problems. (pg. 1830)

Krugman suggests that perhaps the reason some critics believe economics is too formal is that there is a lot of second-rate economic research out there which is pointlessly mathematical, and this has created the image of a discipline that is out of touch.

But this, Krugman argues, is a problem of quality (i.e. a need for better economists) rather than a problem of excessive formalism (i.e. an issue of excessive use of mathematical techniques in economics.)

And anyway, says Krugman, this second-rate research is not influential and is therefore immaterial to any consideration of whether economics is too mathematical.

So where does the picture of economists as a tribe engaged in pointless, abstract mathematical games come from? Perhaps the picture is based on the fact that most economists do not do first-rate research, and that there is a lot of irrelevant mathematical modelling out there. But in what academic field do most people do first-rate research? And if someone is doing work that will not be read or cited, does it matter whether it is boring literary work (as in many humanities), boring experimental work (as in many physical sciences), or boring mathematical modelling? (pg. 1830-1831)

One can make a good case that the intellectual level of economics is not as high as it should be, given the importance of the subject. But that is a complaint about quality, not formalism. (pg. 1831)

Outsider Critics Dislike the Conclusions, Not Methodology

Krugman suggests that a second reason why many – in his view falsely – charge economics as being excessively mathematical is that they disagree with the conclusions which mainstream economics has reached.

In 1997 the editor of Governing magazine published an op-ed attacking the economics profession for denying the obvious fact that globalisation was having devastating effects on the economy (Ehrenhalt, 1997). As an example of just how bad economists are, he quoted an unnamed 'prominent economist' (the reference was actually to Krugman (1996)), who had written that 'there are .... important ideas in economics that are crystal clear if you can stand algebra, and very difficult to grasp if you can't'. This, according to the op-ed writer, was an 'insult', a 'charge of illiteracy'; he went on to assert that algebra could not be essential to economic understanding, because if it were this would delegitimise the opinions of people who had not studied algebra when young and were now too old to retool.

It hardly gets clearer than this. Many, indeed probably most, of the non-economists who attack the field's formalism do so not because that formalism makes the field irrelevant, but on the contrary because economists insist that their equations actually do say something about the real world. And since the critic's view conflicts with what the equations say, this whole business of using mathematics to think about economics must be a bad thing. (pg. 1831)

Globalization

Krugman states that the most animating issue which prompts criticism of the mathematization of mainstream economics by non-economists is globalization.

But for Krugman much of this outside criticism reveals, not deficiencies in the methodology of mainstream economics, but a lack of understanding of simple economic truths on the part of these non-economists.

What sort of equations are we talking about here? Well, how about the equation that says that the sum of a nation's capital account and current account is zero? (pg. 1831)

This is not meant to be a joke. While a number of issues motivate outsider critics of the economics profession, surely the most prominent and emotional involves concerns about the impact of globalisation. Many people (like the op-ed writer cited above) who regard themselves as knowledgeable about economic affairs are convinced that growing international trade and investment are bad things for workers everywhere. The typical story - as found, for example, in the 1994 World Competitiveness Report (World Economic Forum, 1994) or in Greider (1997a) - goes like this: Multinational corporations and other investors are massively relocating capital to low-wage countries, undermining traditional employment in the advanced countries. Meanwhile, hopes that these newly industrialising economies will provide export opportunities and thus alternative jobs for the displaced workers are a mirage: wages and hence purchasing power in these countries will remain low, both because of the sheer size of their labour forces and because they need to keep wages low to attract a continuing inflow of capital. Thus workers in the Third World will see no benefit from the process - their economies will achieve high productivity while continuing to pay low wages - while those in advanced countries will find their position undermined both by trade deficits and by capital outflows. (pg. 1831-1832)

What is wrong with this story? Economists quickly notice that it violates the equation that says that current account plus capital account equals zero. It cannot be true that newly industrialising economies are or will be recipients of large capital inflows and at the same time export much more than they are importing. And once one tries to fix this aspect of the story, the whole thing falls apart. In particular, suppose that one decides that newly industrialising economies will, in fact, attract large capital inflows. Then one must conclude that they will run current account and probably trade deficits rather than surpluses. But how can they run trade deficits when their productivity rises but their wages remain low? Doesn't this cost advantage ensure a trade surplus? Well, something must be wrong with the premise; perhaps wages will not remain low after all. (pg. 1832)

One can immediately see the reason why people hate economists. Here is a compelling, powerful story about the world economy, one that dovetails with the political agenda of those who tell it, and is a clear call to action. Yet economists insist that the story is literally nonsense …. because of an abstract equation. (pg. 1832)

The trouble is that the economists are right. The popular story is literally nonsense: that crucial equation is not some abstract theory, it is a simple accounting identity - and there is no way to save the story while getting the accounting right. Moreover, the facts fit the economist's story quite well. Most newly industrialising economies run trade and current account deficits, not surpluses: of the 25 'emerging market' economies listed at the back of The Economist, 17 were running trade deficits when this essay was written, 20 current account deficits. And wages in rapidly industrialising economies have not stayed low, they have risen sharply: the U.S. Labor Department's index of compensation in newly industrialising Asia rose from 8% of the US level in 1975 to 32% in 1995. (pg. 1832)

(Incidentally, the response of opponents of globalisation when these facts were pointed out helps put their charge that economists are 'impervious to complex evidence' in perspective. Greider (1997b), offered an opportunity to rebut questions about his thesis, simply ignored the contrary evidence and repeated his original assertions without alteration. And other critics of conventional economic views about globalisation, like the Economic Policy Institute, did not disavow Greider or express regret that he had failed to check his facts; they leapt to his defence, attempting to rationalise his claims). (pg. 1832)

This is not an incidental or unusual example. The refusal of economists to accept the popular indictment of globalisation is, to repeat, the most important reason for attacks on the profession in recent years. (pg. 1832)

And thus this story helps reveal what the outsider critics really mean by their critique. By 'formalism' they do not mean differential topology or fixed-point theorems: they mean annoying insistence on adding-up constraints, or such abstruse arguments as the assertion that partial equilibrium reasoning (increased productivity in a given industry may well lower employment in that same industry) does not always carry over to general equilibrium (increased productivity in the economy as a whole is much less likely to reduce employment in the economy as a whole). (pg. 1833)

The truth …. is that when critics attack formalism in economics what they really mean is the infuriating insistence of economists that they mind their arithmetic[.] (pg. 1833)

Mathematics is Essential for Progress in Economics

And finally, Krugman argues that mathematics is necessary for economics to progress because mathematical models help economists “focus and form their intuition.”

Consider once again the questions posed by the rise of newly industrialising economies. The common perception of most people who think about the issue at all is that the emergence of new competitors must surely reduce real incomes in the established economies - indeed, that this has already happened. On the other hand, some business enthusiasts are quite sure that the expansion of world markets will bring vast prosperity to everyone. Thanks to the models of Hicks (1950) and especially Johnson (1958) well - trained economists eventually learn why both intuitions are deeply wrong. Growth in other countries can either help or hurt us: it depends on the effect on our terms of trade, an effect that in turn depends on the bias of that growth. (And as a quantitative, empirical matter the overall effects are very small, both because North-South trade is a small share of Northern income and because there have not been large movements in the terms of trade). This position can eventually be made to seem intuitive, but it would have been very hard to arrive at without the aid of models - in particular, without the aid of Marshall's offer-curve construction. (pg. 1834)

This is not an isolated example. …. Most of the topics on which economists hold views are both different from 'common sense' and unambiguously closer to the truth than popular beliefs involve some form of adding-up constraint, indirect chain of causation, feedback effect, etc. Why can economists keep such things straight when even highly intelligent non-economists cannot? Because they have used mathematical models to help focus and form their intuition. (pg. 1834)

Summary

Krugman argues that looking at what the economics profession rewards – using the John Bates Clark medal as a proxy – indicates that economists value research that is relevant to real-world problems.

This, for Krugman, is evidence that the use of mathematics has not made economics out of touch with the real world.

Krugman suggests that a major explanation for why many non-economists claim economics has become overly mathematical is that these outsiders dislike the conclusions mainstream economics has arrived at.

This is particularly true, Krugman writes, in relation to issues surrounding globalization.

For Krugman, the use of mathematical techniques is essential to progress in economics.

Written By: Aiden Singh Published: November 19, 2020

Sources

Paul Krugman. Two Cheers for Formalism. The Economic Journal. Nov., 1998, Vol. 108, No. 451. pg. 1829-1836.