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The Two Growth Rates of the Economy (2009.10451v1)

Published 22 Sep 2020 in econ.GN and q-fin.EC

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.

Citations (3)

Summary

  • The paper introduces the concept of ensemble-average and time-average growth rates to reveal how GDP per capita can misrepresent individual economic experiences.
  • It employs ergodicity economics to quantify the 'ergodicity gap,' linking divergent growth measures to rising income inequality.
  • Empirical analysis of US and French data demonstrates that larger gaps signal the need for more equitable economic policies.

Analysis of Dual Growth Rates in Economic Performance

The paper "The Two Growth Rates of the Economy" offers a nuanced examination of economic growth rates, emphasizing the differentiation between ensemble-average and time-average growth rates. These two measures of growth are grounded in the principles of ergodicity economics, which assesses the ergodic nature of stochastic economic processes. This perspective acknowledges that stochastic processes with random multiplicative growth produce a significant discrepancy between ensemble-average growth, typically equated with GDP per capita, and time-average growth, which reflects individual economic trajectories over time.

The research identifies that GDP per capita—often used as a benchmark for national economic performance—tends to exaggerate economic prosperity because it aligns with the ensemble-average growth rate, thereby failing to account for the typical economic experience of individuals. This ensemble-average growth condenses the economic activity of an entire community into a single metric, often inflating the apparent economic success due to its plutocratic nature, wherein each individual's growth weighs according to their income. In contrast, the time-average growth rate, akin to the growing average income of an individual, offers a democratic measure reflecting equal individual weights.

A seminal contribution of the research is establishing the critical link between these two growth rates and income inequality. The authors propose using the difference between the ensemble-average growth rate and time-average growth rate as an inequality measure, coined the "ergodicity gap." This is mathematically represented as the mean logarithmic deviation (MLD), a measure traditionally used in inequality metrics like the Theil index. The multiplicative nature of growth and the unequal distribution of income growth rates underpin this gap, positing that if economic growth does not equitably translate into individual income increases, observed through a larger ergodicity gap, inequality inevitably rises.

Practical implications of these findings are significant. Policymakers are caught between leveraging GDP at a macroeconomic planning level and addressing citizens' lived experiences through individual income trajectories. The authors illustrate this dilemma by analyzing data from the United States and France over five decades. In the United States, the ensemble-average growth significantly outpaced time-average growth post-1980, highlighting rising inequality and a divergence in perceived economic prosperity. In France, by comparison, the gap between the two growth rates remained minimal, suggesting a more uniform distribution of economic growth benefits and potentially more effective redistributive mechanisms or economic policies.

The theoretical and empirical analyses in this paper underscore the importance of comprehensive economic indicators. The GDP per capita may reflect the productive capability of a nation, yet it risks misrepresenting individual economic viability unless accompanied by measures like the DDP per capita and the resulting ergodicity gap. Addressing these metrics offers clearer insights into economic inequality and fosters more informed policy interventions.

Future extensions of this work could involve exploring the dynamics of reallocation mechanisms or policy interventions that bridge the identified gap in ensemble-average and time-average growth. Moreover, examining these effects in various economic systems could yield practical insights into globally applicable policies to mitigate inequality.

Ultimately, integrating ensemble- and time-average assessments into economic reporting provides a multidimensional view of economic growth, vital for crafting policies that both foster economic productivity and uphold economic equity. This paper's findings impel a reevaluation of how economic success is measured and how socioeconomic policies are informed by these measurements.