How Expectations and Uncertainty Affect the Economy — An Interview with Eric Barthalon

Uncertainty, Expectations, and Financial Instability

The following is an interview with Eric Barthalon, author of Uncertainty, Expectations, and Financial Instability: Reviving Allais’s Lost Theory of Psychological Time.

Question: What is your book about?

Eric Barthalon: Uncertainty, Expectations and Financial Instability is about what we call “expectations” and the pro-cyclical responses they trigger. I argue that, under uncertainty, we infer the future largely from our experience of the past, and I show how Allais’s lost theory of psychological time gives an operational and testable content to this intuition or hypothesis.

Q: What exactly do you mean by uncertainty?

EB: When we throw four dices repeatedly, we cannot tell the outcome of each throw, but experience as well as mathematics tell us very precisely what we should expect: there will not be many instances where the sum of the four dices is either 4 or 24; most of the throws will yield a result close to 14. This is a situation of “known unknowns” or risk, in which it would be insane to expect a throw to yield either a 2 or a 30, and—even if the first throws are not close to 14—it would be equally insane not to expect the average of the throws to converge toward 14. In such risky situations, our expectations should be identical to the model’s forecasts. This is the very definition of rational expectations.

In contrast, as highlighted by Knight, uncertainty refers to situations where the distribution of potential outcomes is not known and is unstable. Most of the situations we encounter in the real world are uncertain, rather than risky: they are made of “unknown unknowns”. Therefore, a theory of expectations under uncertainty, a theory explaining how we learn in an uncertain world is a key building block of economic theory.

Q: Which are the key insights that one can find in your book?

EB: Usual disclaimer to the contrary notwithstanding, the first of them is that persistent past performance is seen as the guide of choice to future performance: in other words, “expectations” spring from memory.

The second key insight is that, unlike in a standard adaptive expectations model, the duration of memory (or the elasticity of “expectations”) is context-dependent: it varies with respect to the present value of past returns. Bull markets have a short memory; deflationary “expectations” are inelastic. The elasticity of expectations with respect to actual outcomes varies between 1 in hyperinflation or bubble episodes, and 0 in deflation or bear markets. In other words, deflationary “expectations” are like quick sands, while exuberant expectations are inherently unstable.

The third key insight is that the demand for risky assets or speculative finance rises with respect to past performances. More specifically, the demand curve for risky assets is upward sloping, but non-linear and bounded.

The fourth insight is that the perceived risk of loss (i.e. the present value of past drawdowns) emboldens investors further when it is low, and restrains them when it is high.

Altogether, the first three insights explain endogenous financial instability. The fourth one suggests that attempts to dampen volatility ultimately increases it.

Q: What is psychological time and what role does it play in Allais’s theory of memory?

Every one of us regularly experiences that clock’s time seems to flow sometimes rapidly, when a lot happens per day, hour or second, and sometimes slowly, when little or nothing happens. Some experiences, like progress or a page-turner, always seem to end too quickly; in contrast, other experiences, like decline or a traffic jam, never seem to come to an end. Literature is replete with examples of our versatile relationship with clock’s time.

Research on hyperinflation episodes led Allais to observe this phenomenon in monetary economics, too. He was testing the assumption that people’s behavior, their demand for money, is influenced by sequences of past inflation rates. Looking at a diversity of hyperinflationary episodes, Allais found out that the higher the average inflation rate during a given episode, the shorter the length of the sequence that best explained people’s behavior, as if the duration of their memory shrunk or their rate of memory decay increased. Furthermore, accelerating hyperinflation, which fills or saturates units of calendar time with larger and larger increases in prices, seemed to force past inflation rates out of people’s memory at an increasing rate.

Having observed that forgetting does not unfold at a constant pace in calendar time, but seems to vary according to some natural law, Allais conjectured first, that there exists a psychological time scale along which people measure the flow of calendar time; second, that the rate of memory decay is constant along this scale of reference. He went much further than that by proposing a mathematical formalization of the relationship between the psychological and the calendar time scales. Allais did not have financial markets in mind when he constructed his theory of psychological time and memory, but my book shows that his formalization is compatible with many aspects of financial behavior.

As Allais’s theory of psychological time and memory was born in monetary dynamics but involves fundamental aspects of human psychology, I would not be surprised if research proved its relevance in fields in which it has not been applied yet.

Q: You’re a practitioner. How did you come to write a book which looks rather academic?

EB: Very early on, my involvement in the asset management industry has given me many opportunities to observe market participants’ behavior and to doubt that it was properly described by the rational expectations hypothesis. What I saw rather looked as a pronounced propensity to extrapolate past trends and to respond pro-cyclically to them.

Later on, I became aware of Allais’s theory of psychological time and conjectured that, given the generality of its psychological assumptions, it might provide a framework to formalize my intuition. But, for this to happen, I had first to explain Allais to myself and to test whether his theory was compatible with empirical data. In the course of this exercise, I realized that Allais’s theory of psychological time addresses many of the issues raised by the many prominent thinkers who have qualms about rational expectations.

Expectations are a very important issue because the validity of many theoretical propositions and policy recommendations ultimately depends on assumptions made, more or less explicitly, about their nature. We cannot afford to miss a single opportunity to enrich the debate with fresh propositions.

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