Income and Poverty in a Developing Economy

TL;DR

This paper develops a stochastic agent-based model for income distribution in developing economies, capturing both individual effort and trading effects, and validates it with Indian survey data to define a robust poverty index.

Contribution

It introduces a Langevin-based model with multiplicative noise for income distribution and derives a Fokker-Planck equation, providing a new theoretical framework validated by real-world data.

Findings

High earners follow a power-law income distribution.

Low income groups exhibit Levy distribution characteristics.

Model accurately fits Indian survey data across multiple years.

Abstract

We present a stochastic agent-based model for the distribution of personal incomes in a developing economy. We start with the assumption that incomes are determined both by individual labour and by stochastic effects of trading and investment. The income from personal effort alone is distributed about a mean, while the income from trade, which may be positive or negative, is proportional to the trader's income. These assumptions lead to a Langevin model with multiplicative noise, from which we derive a Fokker-Planck (FP) equation for the income probability density function (IPDF) and its variation in time. We find that high earners have a power-law income distribution while the low income groups have a Levy IPDF. Comparing our analysis with the Indian survey data (obtained from the world bank website) taken over many years we obtain a near-perfect data collapse onto our model's equilibrium IPDF. The theory quantifies the economic notion of "given other things". Using survey data to relate the IPDF to actual food consumption we define a poverty index, which is consistent with traditional indices, but independent of an arbitrarily chosen "poverty line" and therefore less susceptible to manipulation.