A note on wealth in a volatile economy

TL;DR

This paper demonstrates that in stochastic capital accumulation models, an additional term must be considered to accurately measure genuine wealth, revealing how volatility influences accounting prices and wealth dynamics.

Contribution

It introduces a new term in wealth estimation for stochastic economies and analyzes its effects on accounting prices and wealth under different utility elasticities.

Findings

The value function decreases with volatility.

Volatility affects accounting prices.

The new term negatively impacts wealth changes.

Abstract

I show that if the capital accumulation dynamics is stochastic a new term, in addition to that given by accounting prices, has to be introduced in order to derive a correct estimate of the genuine wealth of an economy. In a simple model with multiplicative accumulation dynamics I show that: 1) the value function is always a decreasing function of volatility 2) the accounting prices are affected by volatility 3) the new term always gives a negative contribution to wealth changes. I discuss results for models with constant elasticity utility functions. When the elasticity of marginal utility is larger than one, accounting prices increase with volatility whereas when it is less than one accounting prices decrease with volatility. These conclusions are not altered when adopting optimal saving rates.