Monte Carlo simulation of macroeconomic risk with a continuum of agents: the general case

In large random economies with heterogeneous agents, a standard stochastic framework presumes a random macro state, combined with idiosyncratic micro shocks. This can be formally represented by a random process consisting of a continuum of random variables that are conditionally independent given the macro state. However, this process satisfies a standard joint measurability condition only if there is essentially no idiosyncratic risk at all. Based on iteratively complete product measure spaces, we characterize the validity of the standard stochastic framework via Monte Carlo simulation as well as event-wise measurable conditional probabilities. These general characterizations also allow us to strengthen some earlier results related to exchangeability and independence. Parts of this work were done while Yeneng Sun was visiting Stanford University in July 2003, March–May 2005 and July 2006, and while Peter Hammond was visiting the National University of Singapore in March–April 2004. An early version was presented at the World Congress of the Econometric Society in 2005.