Big shocks versus small shocks in a dynamic stochastic economy with many interacting agents

This paper investigates the conditions under which a dynamic, stochastic macroeconomic model with many interacting agents will exhibit the ‘small shocks, large shocks’ property that is often said to characterize observed time series: small shocks have a transient impact on the system, whereas a sufficiently large shock will change its trajectory forever. An example is analyzed where the steady state distribution of output has a unique mode if the variance of labor productivity is sufficiently high; but has two modes, each with its own basin of attraction, if the variance falls below a critical value. An unanticipated exogenous shock can have a long lasting impact if it moves the economy into the basin of attraction of a different output mode. A general result is derived showing that the invariant measure of output can have multiple modes if each firm's probability of producing increases appropriately as the number of other firms producing rises.