Uncertainty, Expectations, and Financial Instability

Reviving Allais's Lost Theory of Psychological Time

Eric Barthalon

• Publisher: Columbia University Press
• Year: 2014
• eBook ISBN: 9780231538305
• Topic: Economics
• Subtopic: Investments & Securities
• Index: Economics

Eric Barthalon applies the neglected theory of psychological time and memory decay of Nobel Prize–winning economist Maurice Allais (1911–2010) to model investors' psychology in the present context of recurrent financial crises. Shaped by the behavior of the demand for money during episodes of hyperinflation, Allais's theory suggests economic agents perceive the flow of clocks' time and forget the past at a context-dependent pace: rapidly in the presence of persistent and accelerating inflation and slowly in the event of the opposite situation. Barthalon recasts Allais's work as a general theory of "expectations" under uncertainty, narrowing the gap between economic theory and investors' behavior.

Barthalon extends Allais's theory to the field of financial instability, demonstrating its relevance to nominal interest rates in a variety of empirical scenarios and the positive nonlinear feedback that exists between asset price inflation and the demand for risky assets. Reviewing the works of the leading protagonists in the expectations controversy, Barthalon exposes the limitations of adaptive and rational expectations models and, by means of the perceived risk of loss, calls attention to the speculative bubbles that lacked the positive displacement discussed in Kindleberger's model of financial crises. He ultimately extrapolates Allaisian theory into a pragmatic approach to investor behavior and the natural instability of financial markets. He concludes with the policy implications for governments and regulators. Balanced and coherent, this book will be invaluable to researchers working in macreconomics, financial economics, behavioral finance, decision theory, and the history of economic thought.

PART ONE

The Progressive Emergence of Expectations in Economic Theory

CHAPTER ONE

Expectations Before the Rational Expectations Revolution

HINTS OR even statements about time, uncertainty, and expectations are present in the writings of early economists. In 1755, Cantillon, for example, defined the farmer as “an undertaker who promises to pay to the Landowner … a fixed sum of money … without assurance of the profit he will derive from this enterprise.”¹

He reinforced his point by saying that “the price of the Farmer’s produce depends naturally upon … unforeseen circumstances, and consequently he conducts the enterprise of his farm at an uncertainty.”

In the same vein, Cantillon defined merchants as “undertakers [who] pay a certain price following that of the place where they purchase it, to resell wholesale or retail at an uncertain price” and stated that competition between them is such that it is impossible for them to ever know “how long their customers will buy of them.”

As Cantillon sought to refute the already widely held view according to which low interest rates are the consequence of an abundant supply of money and argued, instead, that what matters is the balance between the supply of and the demand for loanable funds, he explicitly referred to the profit expectations held by the borrowers:² “everybody had become an Undertaker in the South Sea scheme and wanted to borrow money to buy Shares, expecting to make an immense profit out of which it would be easy to pay this high rate of Interest rate.”³

But it is certainly in his chapter on the augmentation and diminution of coins in denomination that Cantillon proved the most farsighted and perceptive as regards the role of expectations in economics. Decided by the Sovereign, changes in the nominal denomination of species were all monetary policy was about in those days and had actually been since Solon and the Roman Republic. Contracts—like loans—were denominated in money of account, but payments were made in species, which were defined by their weight: for example, in 1714, in France, 1 écu, that is, 1 ounce of silver, was worth 5 Livres Tournois. Resources-strapped states had found very early on that an increase in the nominal value of coins, that is, a devaluation of the money of account (what we would call inflation nowadays), was a way for them to ease their financial strains.

In this fascinating chapter, Cantillon discusses both the short- and long-term effects of decreases and increases in the nominal denomination of coins, depending on whether these changes are made “suddenly without warning” or phased in over a period of time. His discussion implicitly considers there is a diversity of expectations in the marketplace, some undertakers being less “able and accredited” than others.

However perceptive Cantillon’s insights may be, they do not constitute per se a conscious theory of time, uncertainty, and expectations. For quite a long time—that is, almost a hundred and fifty years—economists continued to mention expectations in passing, as if they did not fully realize the central role of expectations in dynamic economic analysis, which involves the discussion of how economic adjustments are brought about through time.

Until the formulation of the rational expectations hypothesis between 1960 and 1975, there was no formal academic debate about the nature and role of expectations. As a result, the major contributions of the first half of the twentieth century often give the impression that they were presented without any reference to one another. Despite this apparent lack of structured debate, three trends emerged:

• Some authors—Wicksell, Knight, Keynes, Hayek, Hicks—progressively put expectations at the center of the stage, implicitly considered them to be adaptive, while suggesting at the same time that expectations belonged to the realm of the incalculable, namely, human psychology.

• Other authors—Fisher, Cagan, Allais—dedicated their efforts to quantify the supposedly incalculable by proposing expectations models liable to be confronted with empirical data.

• Inspired by an analysis of the shortcomings and inconsistencies of these efforts, the rational expectations hypothesis proposed that economic agents form their expectations rationally, that is, by using “the” one and only correct (neoclassical) model of the economy. While this hypothesis has always failed to convince a large body of academics and practitioners, it has become the paradigm in policy-making circles.

1.1 Expectations Are Important, but They Belong to the Realm of the Incalculable

Knut Wicksell, John Maynard Keynes, Frank Knight, and Friedrich Hayek have been the first economists to stress the importance of expectations explicitly, as regards cyclical fluctuations, be it in economic activity or in financial markets.

Wicksell used the word “expectation” as early as 1898, as he made a distinction between “the natural rate of interest on capital” and “the rate of interest on loans”:⁴

For reasons connected with the conception of subjective value, the probability that an entrepreneur will make a profit must always be somewhat greater than the probability that he will make a loss. For otherwise his “moral expectation” would be negative. In many cases, however, the entrepreneurs’ gambling spirit will prevent this rule from applying to their behavior.⁵

Wicksell pushed expectations at the forefront of dynamic economic analysis in discussing further the cumulative inflationary (or deflationary) effect of a discrepancy between the market rate of interest and the natural rate of interest.⁶ He starts by distinguishing “present prices” and “future prices calculated at present [expected prices].” He also makes a clear distinction between “situations in which a rise in price can be foreseen with more or less certainty” and “the element of speculation which necessarily enters into all business transactions.” In that second situation, “the normal assumption is that present prices will remain constant.” But according to Wicksell,

if the market rate [of interest] falls below the marginal productivity of waiting [the natural rate of interest], entrepreneurs, even with current prices as the foundation of their calculation of future prices, will be able to pay a somewhat higher price. In this way, the present price level will be raised indirectly and therefore the future price level also.⁷

However concise this very last sentence may be, it is an expectation model, albeit a very crude one. In Wicksell’s model, expectations are determined by the outcome observed in the previous period, and a change in current prices is assumed to change expected prices in the same direction and in the same proportion.⁸ Wicksell’s central proposition of cumulative instability is entirely dependent on his assumption that people expect future prices to rise at least as fast as current prices.

Nowadays, Knight is essentially remembered for having forcefully shown that uncertainty is the source of entrepreneurial profit in an economy where entrepreneurs compete for acquiring productive services.⁹ In chapter 8 of Risk, Uncertainty and Profit, there is, however, much more than this fundamental contribution. This chapter is presented by Knight as an “inquiry into the nature and function of knowledge.” In a very Socratic tone, Knight claims that “we must know ourselves as well as the world.” Knight reinforces his point with a provocative statement: “In spite of rash statements by over-ardent devotees of the new science of ‘behavior,’ it is preposterous to suppose that it will ever supersede psychology or the theory of knowledge.”

However, says Knight, and this is the whole problem, “the universe may not be ultimately knowable.” Yet, we have to act and to make decisions. The question is then: on the basis of which knowledge? Foreshadowing Keynes by a few years, Knight is keen to stress how limited or fragile our knowledge is and how little we know about the way we acquire it:

At present we are concerned only to emphasize the fact that knowledge is in a sense variable in degree and that the practical problem may relate to the degree of knowledge rather than to its presence or absence in toto … The essence of the situation is action according to opinion, of greater or less foundation and value, neither entire ignorance nor complete and perfect information, but partial knowledge.

Of course, successful adaptations on our part to a “world of change” require some forward-looking consciousness. But these adjustments take time, and this is precisely where the difficulties lie:

An explanation of the readjustment necessarily runs in terms of stimulus and reaction, in this temporal order. Yet in our own experience we know that we do not react to past stimulus, but to the “image” of a future state of affairs … However successful mechanistic science may be in explaining the reaction in terms of a past cause, it will still be irresistibly convenient for common sense to think of it as prompted by a future situation present to consciousness. The role of consciousness is to give the organism this “knowledge” of the future.

Needless to say, it is not only convenient, but also reassuring for us, confronted as we are with uncertainty, to think of our response to past stimulus as if it were a forward-looking consciousness. But how does consciousness work? Frustration is palatable in Knight’s answer:

The ordinary decisions of life are made on the basis of “...

Table of contents

• Cover 
• Title Page
• Copyright
• Dedication
• Contents 
• List of Tables
• List of Figures
• Preface
• Acknowledgments
• Epigraph
• Introduction
• Glossary of Mathematical Symbols in Order of Appearance
• Part 1: The Progressive Emergence of Expectations in Economic Theory
• Part 2: Allais’s Theory of “Expectations” Under Uncertainty
• Part 3: Transposing the HRL Formulation to Financial Markets: Preliminary Steps
• Part 4: The HRL Formulation and Financial Instability
• Appendix A: How to Compute Zn and zn
• Appendix B: Nominal Interest Rates and the Perceived Rate of Nominal Growth
• Appendix C: Proofs
• Appendix D: Comparison Between the Kalman Filter and Allais’s HRL Algorithm
• Appendix E: A Note on the Theory of Intertemporal Choice
• Appendix F: Allais’s Cardinal Utility Function
• Notes
• Bibliography
• Index