The Zilcha criterion for dynamic inefficiency

This paper reexamines the condition <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$E\{\ln r\} > \ln $</EquationSource> </InlineEquation> (1 + n), which Zilcha (1991) presents as a necessary and sufficient condition for dynamic inefficiency of stationary allocations in overlapping generation models with stochastic production. We show that this condition is necessary but not sufficient for a stationary allocation to be dynamically inefficient by Zilcha’s definition. We also show that there is a narrow but widely studied class of specifications in which the Zilcha test is both necessary and sufficient for dynamic inefficiency of stationary competitive equilibrium allocations. Outside this class, however, counterexamples can be constructed relatively easily. Copyright Springer-Verlag Berlin/Heidelberg 2005