Aggregate precautionary savings: when is the third derivative irrelevant?

When are aggregate precautionary savings positive? We address this question in the context of a general equilibrium model where infinitely-lived agents receive idiosyncratic labor endowment shocks, hold a risk-free asset to smooth consumption and face a liquidity constraint, We prove that (1) the steady-state capital stock is always larger in any equilibrium with idiosyncratic shocks and a liquidity constraint than without idiosyncratic shocks (i.e. aggregate precautionary savings are positive) as long as consumers are risk averse and (2) aggregate precautionary savings occurs if and only if the liquidity constraint binds for some agents. (C) 2001 Elsevier Science B.V. All rights reserved.