Conditional Exact Law of Large Numbers and Asymmetric Information Economies with Aggregate Uncertainty

TL;DR

This paper extends the exact law of large numbers to models with macro and micro shocks under conditional independence, demonstrating that efficient allocations in asymmetric information economies can be made incentive compatible.

Contribution

It generalizes the law of large numbers to conditional independence settings and shows that efficient allocations can be incentive compatible in complex economies.

Findings

Extended law of large numbers to macro-micro shocks

Efficient allocations can be incentive compatible under asymmetric information

Applicable to economies with infinitely many states

Abstract

A stochastic model with a continuum of economic agents often involves shocks at both macro and micro levels. This can be formalized by a continuum of random variables that are conditionally independent given the macro level shocks. Based on the framework of a Fubini extension, the results on the exact law of large numbers and its converse for a con- tinuum of independent random variables in [14] are extended to the setting with conditional independence given general macro states. As an illustrative application, it is shown that any ex ante efficient allocation in an asymmetric information economy with general aggre- gate uncertainty has a (utility) equivalent allocation that is incentive compatible, which generalizes the corresponding results in [15] to the case with infinitely many states.