A Stochastic Growth Model of a Poorly Developed Country with Natural Disasters

This paper proposes a dynamic model in which natural disasters affect the accumulation of private wealth, public spending, and output in an economy that is intended to capture salient features of developing countries. The central object of the analysis is the stationary distribution of key macroeconomic variables that emerges in the presence of recurrent, stochastic disasters. Within this framework, we derive analytic characterizations of the stationary distributions of private wealth, government spending, and GDP, and study how their shapes and tails depend on both disaster risk and institutional parameters. Natural disasters affect the economy via two channels. First, the effects on production are transmitted through a demand channel by altering the consumption-savings trade-off of households and thus the proportion of capital that can be invested in capital accumulation. Second, natural disaster shocks also activate a supply channel: they destroy capital and alter the way in which public spending influences total factor productivity. The stationary distributions of capital stock and public expenditure exhibit unusual characteristics such as Pareto laws and upper Gamma distributions. Our stylized model describes key mechanisms in developing countries and allows us to investigate the factors that enhance economic resilience to shocks, as well as those that may render their effects persistent.