Low-Level Equilibrium and Fractional Poverty Traps

For more than 200 years development and agricultural economists have sought to understand the dynamic relationships between population growth, land utilization, and agricultural productivity. Originating with Malthus, numerous scholars have pushed representations of low and high-level equilibrium traps. More recently the literature has explored asset dynamics and fractal poverty traps. In this paper we advance these models by introducing risk into a dynamic growth model using the stochastic calculus and Ito’s Lemma. This approach does two important things. First it moves the discussion away from the idea of a stable short run equilibrium, to one in which the long-run economic attractor is an unknowable point in probability space. On this latter point we are able to show, via Monte Carlo simulation, that population growth is fractional and persistent with Hurst coefficient of around 7.0, while other measures such as output per capita are dynamically fractional with Hurst coefficients in the neighborhood of 0.3 to 0.4. This leads us to believe that poverty traps ought not be measured in a small time scale, but rather a longer time scale reflecting the frequency, duration, and intensity of below-subsistence excursion patterns. We make our case by simulating the Chines agricultural economy between about 1400 and 1900.