The role of non-ergodicity in asset pricing, wealth dynamics, and income dynamics: Theoretical results and empirical applications

Abstract

How does randomness affect the evolution of an economy? The bedrock to answering this question lies in the ergodic hypothesis. Mathematically, the hypothesis tells us that an observable (e.g, the return of an asset or the growth rate of our wealth) is ergodic if its time average is equal to its expected value. Philosophically, if the hypothesis is valid, it means that randomness does not affect the dynamics of the system. That is, every asset traded on a stock market will exhibit similar prices over time, and in the long run investors will be indifferent about their investment decisions. Also, it will be irrelevant to track economic inequality, as the economy will not discriminate between individuals on the basis of their history: everyone will experience wealth and poverty during their life.

A growing body of literature, however, questions the validity of the ergodic hypothesis in economics. Despite a decade of important advances on bridging the gap between theory and applications, it remains unclear how the randomness induced by non-ergodicity is manifested in economic systems. In this document, we expand the literature by developing frameworks for studying the role of non-ergodicity in asset pricing, wealth dynamics, and income dynamics. The framework for modelling asset prices can be used to predict empirical option values and offers a computationally inexpensive and efficiently tractable solution for tracking the non-ergodic dynamics of asset prices. The framework for non-ergodic wealth dynamics can be used to infer which part of the population is able to live a wealthy life. The framework for income dynamics can be used to understand whether socio-economic policies for redistributing income work in the long run. These results are used to provide the first measurements of economic mobility in the Macedonian economy. A shared feature of these frameworks is that they unify results from previous research into comprehensive methodologies that can easily address the question of ergodicity. By practically implementing the frameworks, the puzzles besetting the current economic formalism can be resolved in a natural and empirically testable way. Namely, they can be applied in various economics domains: from tailoring optimal investment strategies up to designing essential policy interventions.