A V Rajwade: Mathematical models in economics

Results of such models are only as reliable as the assumptions on which the models are based

I started studying mathematical models used in finance (like “value at risk” model for measuring risk; Black Scholes model for option pricing and hedging etc) a couple of decades back. While the models were well accepted and used, as an analyst of the foreign exchange market, I often found the assumptions underlying the models to be artificial, not supported by the reality in the market. (Market participants like Nassim Taleb, author of The Black Swan and other books, are total non-believers in such models and their predictions.) When I started studying the use of mathematical models in macroeconomics, I found the origin to be in the work of Kenneth Arrow, the youngest Nobel laureate in economics, who expired recently. His obituaries have appeared in most business and, indeed, general newspapers in India, testifying to his importance to the way the discipline of economics has evolved over the last half century. Today, no economic paper is taken seriously unless backed by the “rigour” of mathematical models supporting the conclusion. Is such extensive reliance on the use of models in a social science useful or warranted?
 
Early this year, Andy Haldane, chief economist of the Bank of England, had commented that economics is in a crisis. He had two specific developments in mind while making the comment: The first was the 2008 financial crisis, which hardly any economists, other than Raghuram Rajan and Nouriel Roubini, had predicted; the second was that in the six months after the Brexit referendum in June 2016, the UK economy had performed far better than what most economists, including those in the Bank of England, had forecasted. The former spectacularly demonstrated how the most sophisticated models for measuring credit risks failed when you need them the most. As for its impact on output, the Dynamic Stochastic General Equilibrium models of the macroeconomy used by most central banks ignore the financial sector and the impact it can have on the economy. In a way, this is strange when most crises in the last four decades have had their origins in the financial sector. Is it one more indication of how modern economics has become model-driven rather than reaching conclusions on the basis of empirical analysis? It is often forgotten that the results of mathematical models are only as reliable as the assumptions on which the models are based.
 
Coming to the more general question of the use and overuse of mathematical models in economics, their general acceptance in the profession goes back to the 1950s and 60s, and the first model of general equilibrium in markets free of external interference, named after Kenneth Arrow and Gerard Debreu. In fact, the Arrow-Debreu model made “the mathematical formulation of economic theory not only common and desirable, but essential” (Prof Sudhir Shah of the Delhi School of Economics). Not only this, one suspects that very often this methodology has been used to propagate a particular neoliberal, laissez faire model of the economy. (The Nobel Factor, a recent book by Avner Offer and Gabriel Soderberg, reviewed in this paper last Saturday, argues that the Nobel Prize in economics was instituted for propagating a neoliberal political agenda.) What is often forgotten is that Arrow himself had made clear that his “conclusions about the workings of competitive markets held true only under ideal — that is to say unrealistic — assumptions” (Michael M Weinstein in The New York Times). Arrow himself described “the idea that the market could solve all problems… patently false”.
 
To be sure, there are some signs that the standard methodology and the objectives of economic policy are being questioned by an increasing number of commentators and scholars. In one recently published book, The Econocracy: The Perils of Leaving Economics to the Experts by Joe Earle, Cahal Moran and Zach Ward-Perkins, the student authors argue how today’s economic courses seem unconnected to real issues. They also question the assumption of rationality in economic agents, which is the base of all mathematical formulations — as does the relatively new discipline of behavioural economics. In The Reformation in Economics: A Deconstruction and Reconstruction of Economic Theory, Philip Pilkington argues the dangers of mathematicising economic arguments. In Economism: Bad Economics and the Rise of Inequality, James Kwak focuses on another aspect, namely wealth and income inequalities, often ignored by macroeconomists. Neoliberal economics justifies inequalities as representing the differing contribution of individuals to society. If present trends continue, inequalities could become the big issue of economics in the next couple of decades.

The author is chairman, A V Rajwade & Co Pvt Ltd; avrajwade@gmail.com