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This chapter examines the microfoundations of Maurice Allais's theory of monetary dynamics, with particular emphasis on his hereditary, relativist, and logistic (HRL) formulation of the demand for money. According to the HRL formulation, the ratio of desired money-to-aggregate nominal spending is a logistic decreasing function of the present value of past growth rates in nominal spending. Allais assumed that the demand for money was a function of nominal growth “expectations” and that “expectations” were formed adaptively and could be represented by an exponential average of the sequence of historic rates of nominal growth. He observed that exponential averages were good at fitting empirical data on average over whole samples, but were struggling with the different phases of inflationary processes. Allais modeled this observed variability of the elasticity of “expectations” by formulating three psychological assumptions: the hereditary assumption, the relativist assumption, and the logistic assumption. The chapter discusses these three assumptions and the elasticities in the HRL formulation before concluding with an analysis of how the HRL formulation quantifies the perceived flow of calendar time.

This chapter focuses on the simultaneous testing of the compatibility of both the HRL formulation of the demand for money and the fundamental equation of monetary dynamics (FEMD) with empirical data. Maurice Allais's HRL formulation of the demand for money and the FEMD complement each other and are in practice interdependent. Through the coefficient of psychological expansion, the HRL formulation links the sequence of rates of growth in nominal spending and relative desired balances, while the FEMD shows how the gap between effective and desired balances determines growth in nominal spending. Yet, appealing as these complementarity and interdependence may be from a theoretical point of view, they remain to be confronted with empirical data. This chapter first reviews early tests of the HRL formulation of the demand for money before discussing Allais's joint testing of the HRL formulation and the FEMD using the U.S. economy of 1918–1941 as the data set. It also considers the insights and assumptions that behavioral finance could or should borrow from Allais's monetary dynamics.

This chapter illustrates the dynamic properties of the HRL formulation by means of a detailed numerical example based on the hyperinflation observed in Zimbabwe between 2000 and 2008. It first presents the results of dynamic equilibrium and dynamic disequilibrium simulations. It shows that the perceived rate of inflation converged asymptotically toward the instantaneous rate of inflation. This asymptotic convergence happens because the rate of memory decay grows exponentially and the elasticity of the perceived rate of inflation with respect to the instantaneous rate of inflation converges toward unity. The duration of the memory of inflation is also computed, along with the distribution of forecasting errors in the HRL formulation. Finally, the chapter examines how the HRL formulation sheds light on what Charles P. Kindleberger calls “some historical puzzles in macroeconomic behavior”.

This chapter describes a few simple models that explain financial behavior by the perceived returns on financial assets and thereby provide evidence of positive feedback from past returns to the demand for risky assets. These models bring to light nonlinear relationships between perceived returns and observed investors' behavior. The chapter presents a few examples that are particularly relevant with respect to the dynamics of financial instability. The discussion begins with some empirical evidence of a positive feedback from past equity returns into the demand for equities. As this demand exhibits a nonlinear pattern that is similar to the one found by Maurice Allais in his HRL formulation of the supply of money, the findings are compared with those of Allais. The chapter concludes with a discussion of the policy implications of positive feedback.

This chapter focuses on the psychological importance of downside risk by presenting Maurice Allais's paradox and by contrasting how Allais and prospect theory have interpreted this paradox. It also considers whether the HRL formulation can be used to model how financial market participants form “expectations” of the dispersion of returns under uncertainty. The chapter begins with a brief overview of expected utility theory, with particular emphasis on the Saint Petersburg paradox and how it was resolved by Daniel Bernoulli in 1738. It then considers the Allais paradox and its conflicting interpretations, including prospect theory. It also offers a critique of prospect theory and goes on to discuss Allais's interpretation of his paradox, paying special attention to his invariant cardinal utility function. The chapter concludes with an assessment of the utility of a risky prospect.

This chapter examines how time can be introduced in the assessment of downside risk, that is, how Maurice Allais's paradox and his theory of psychological time can be combined into the perceived risk of loss. It illustrates the relevance of the perceived risk of loss by analyzing the pricing of some financial instruments. It considers whether the perceived risk of loss can explain the pricing of some financial assets and plays a role in the inception of financial bubbles. It also asks whether institutional or demographic factors might justify the claim made by the HRL formulation that collective human psychology is on average constant through time and space. It suggests that major bubbles tend to be heralded by a fall in the perceived risk of loss to unprecedented levels. The chapter concludes by discussing potential connections between the perceived risk of loss and moral hazard.

This book concludes by summarizing the key arguments in the form of a comparison of the HRL formulation with the rational expectations hypothesis (REH). It explains what makes Maurice Allais's contribution original, important, and modern. To start with, many of the rational expectations theorists' criticisms of standard adaptive expectations do not apply to the HRL formulation. The HRL formulation is much more sophisticated and much more rational than the standard adaptive expectations model tolerated by the REH advocates when economic variables are interdependent. Furthermore, the variability of the rate of memory decay is endogenous both to economic agents and to the environment they are responding to. Parsimony, nonlinearity and time variability of the gain, unequal weighting of past observations according to a well-specified and stable law of forgetting, absence of patterns in forecasting errors—these are the features that make Allais's HRL formulation worth the consideration of economists wishing to explore or to revisit the unsettled and important question of “expectations” formation.