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Kenneth Arrow enriched the toolkit for analysis of decision-making in face of risk

Numerous tributes to Kenneth Arrow’s intellectual contributions have already appeared. Is another one justified?

Kenneth Arrow, Nobel prize, Social Choice and Individual Values, Competitive Analysis, Lionel McKenzie, real economy, economy, law of one price, Robert Merton, Stephen Ross, Fischer Black, Myron Scholes
Numerous tributes to Kenneth Arrow’s intellectual contributions have already appeared. Is another one justified?
 Kenneth Arrow, Nobel prize, Social Choice and Individual Values, Competitive Analysis, Lionel McKenzie, real economy, economy, law of one price, Robert Merton, Stephen Ross, Fischer Black, Myron Scholes
Numerous tributes to Kenneth Arrow’s intellectual contributions have already appeared. Is another one justified?

Numerous tributes to Kenneth Arrow’s intellectual contributions have already appeared. Is another one justified? That might well have been a question asked if Arrow had received a second Nobel prize after sharing the one with John Hicks in 1972. The answer, in both contexts, is affirmative. Arrow made seminal contributions to economics, but three stand out for their impact and audacity of ambition, each marked by a book that either contained or extended his original work.

The landmark Social Choice and Individual Values initiated the vast literature investigating the formal properties of all procedures for aggregating individual preferences into a social preference, not merely various voting mechanisms, although they are the leading examples of such procedures. The celebrated ‘impossibility theorem’ proved that the utopian programme of perfecting social institutions (in this case, preference aggregation procedures) has logical limits, and thus some normative values must be traded-off against others. Following this theorem, results of this type have appeared in many different contexts in economics.

The second, General Competitive Analysis (co-authored with Frank Hahn), surveyed the progress in general equilibrium theory (the study of simultaneous operation of all markets, not just a few at a time) since the contributions of Arrow, Gerard Debreu and Lionel McKenzie. This work had deep intellectual roots in economics (going back to Adam Smith via Leon Walras, Vilfredo Pareto and Francis Edgeworth) and settled various fundamental and vexing questions that had bedevilled all earlier generations of economists. It enabled economists to confidently use the so-called Arrow-Debreu model for myriad applications, eg, the study of international trade, public finance, financial markets and even macroeconomic growth models.

The earlier tributes have stressed the above two contributions and there seems little point in going over that ground again. So, I would like to draw attention to Arrow’s seminal contributions in the area of risk-bearing and finance, partly contained in Essays in the Theory of Risk-bearing. Of his contributions, it is fair to say that this work had the most direct and quantifiable impact on the way the world works because it bridged the gulf between economics and finance. On one hand, it provided economic foundations for financial theory and practice. It forced economists, traditionally obsessed with the deep structure of the ‘real economy’, and therefore often contemptuous of financial markets as a mere ‘nominal veil’ engaged in the trading of numbers in books of account, to recognise the crucial role of this nominal veil in any economy.

Arrow integrated financial markets into formal economic theory by bringing them within the ambit of general equilibrium theory (the second contribution discussed above). His work demonstrated the fundamental role of financial assets in facilitating the efficient allocation of risk in an economy. Efficient allocation of risk in an Arrow-Debreu world requires a complete set of ‘contingent claims markets’. But, actual economies feature very few contingent claims markets, certainly not a complete set. Why? Does this absence necessarily condemn us to inefficient allocation of risk?

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Arrow answered these questions with the fundamental and elegant insight that trading of an appropriate small set of financial assets can fully replicate the effects of trading a much larger complete set of contingent claims. So, the absence of the latter is explained by the existence of the former. In other words, financial markets are indeed a gambling den, but one that serves a crucial social purpose and is indispensable for an economy that has to efficiently allocate risk.

This insight, combined with the ‘law of one price’ (identical items must command the same price as differences imply arbitrage profits that will be competed away), is the bedrock of modern finance. When the law of one price is combined in sophisticated ways with the possibility of frequent trading of financial assets, we arrive at modern asset pricing theory and financial engineering practice initiated by Robert Merton, Stephen Ross, Fischer Black, Myron Scholes and many others, which enables a mere handful of financial assets to do the work of a vastly greater number of contingent claims.

Apart from this work on the economic role of financial markets, Arrow also greatly enriched the tool-kit for any analysis of decision-making in the face of risk. An essential item in this kit is the notion of risk aversion, formulated independently and simultaneously by Arrow and John Pratt. The sheer originality of this work may be gauged from the simple fact that Pratt’s paper on the subject, published in the most prestigious Economics journal Econometrica, contains no references (an almost unheard-of event in academic writing) other than a footnote acknowledging Arrow’s Stanford lecture notes on a related subject!

Apart from Arrow’s various specific contributions to economics, his meta-contribution in terms of professional style, rhetoric and methodology also deserves recognition and comment. The work of Arrow, Gerard Debreu and others made the mathematical formulation of economic theory not only common and desirable, but essential. The language and discipline imposed by mathematical methods has been enormously fruitful for the economics discipline, not merely for forcing greater clarity and precision, but also for enabling the recognition and analysis of substantive new problems that could not even be properly formulated without the mathematical language.

– Sudhir A Shah
The author is professor, Delhi School of Economics, University of Delhi

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