The Zilcha criterion for dynamic inefficiency

Abstract

This paper reexamines the condition $E\{\ln r\} > \ln $ (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 2005Dynamic inefficiency, Zilcha criterion.,

The Zilcha criteria for dynamic inefficiency reconsidered

“…They come to the conclusion that the general characterization of dynamic inefficiency in stochastic nonstationary economies, the main result in Zilcha (1990), is (1) stated and (2) proved incorrectly and offer a corrected version of this characterization. Contrary to the first claim, we show in this note that the dynamic inefficiency characterization given in Zilcha (1990) is stated correctly and is indeed equivalent to the corrected statement given in Rangazas and Russell (2005).…”

“…The Cass-type argument given by Zilcha proves only a weaker result, namely that inefficiency holds if and only if a uniform boundedness condition holds. 1 This is shown in Rangazas and Russell (2005). Our result shows that this uniform boundedness condition holds if and only if Zilcha's original characterization for nonstationary economies is valid.…”

“…We reconsider necessary and sufficient conditions for dynamic inefficiency given in Zilcha (J Econ Theory 52: 364-379, 1990, J Econ Theory 55:1-16, 1991 and a critique by Rangazas and Russell (2005). First, we show that the characterization given in Zilcha (1990) for nonstationary economies is correct and correct Zilcha's proof.…”

“…In a recent paper, Rangazas and Russell (2005) criticize Zilcha's characterizations for dynamic inefficiency in overlapping generations models. They come to the conclusion that the general characterization of dynamic inefficiency in stochastic nonstationary economies, the main result in Zilcha (1990), is (1) stated and (2) proved incorrectly and offer a corrected version of this characterization.…”

“…However, as pointed out by Rangazas and Russell (2005), the proof offered by Zilcha (1990) is incorrect. The Cass-type argument given by Zilcha proves only a weaker result, namely that inefficiency holds if and only if a uniform boundedness condition holds.…”