The Two Growth Rates of the Economy

TL;DR

This paper explores the difference between ensemble-average and time-average growth rates in economics, highlighting their implications for measuring economic growth and income inequality, and emphasizing the importance of considering both in policymaking.

Contribution

It introduces ergodicity economics to distinguish between ensemble and time averages, providing a new perspective on growth measurement and income inequality analysis.

Findings

Ensemble-average growth rate exceeds the time-average in multiplicative income processes.

The difference between the two growth rates measures income inequality.

Time-average growth rate is unaffected by income mobility.

Abstract

Economic growth is measured as the rate of relative change in gross domestic product (GDP) per capita. Yet, when incomes follow random multiplicative growth, the ensemble-average (GDP per capita) growth rate is higher than the time-average growth rate achieved by each individual in the long run. This mathematical fact is the starting point of ergodicity economics. Using the atypically high ensemble-average growth rate as the principal growth measure creates an incomplete picture. Policymaking would be better informed by reporting both ensemble-average and time-average growth rates. We analyse rigorously these growth rates and describe their evolution in the United States and France over the last fifty years. The difference between the two growth rates gives rise to a natural measure of income inequality, equal to the mean logarithmic deviation. Despite being estimated as the average of individual income growth rates, the time-average growth rate is independent of income mobility.