Stochastic growth: asymptotic distributions

Summary. This note studies conditions under which sequences of state variables generated by discrete-time stochastic optimal accumulation models have law of large numbers and central limit properties. Productivity shocks with unbounded support are considered. Instead of restrictions on the support of the shock, an “average contraction” property is required on technology. Received: August 27, 2001; revised version: January 9, 2002 RID="*" ID="*"The author thanks John Creedy and Rabee Tourky for helpful comments, and the Economic Theory Center, University of Melbourne for financial support.     

Endogenous inequality and fluctuations in a two-country model

We study a two-country version of Matsuyama's [K. Matsuyama, Financial market globalization, symmetry-breaking, and endogenous inequality of nations, Econometrica 72 (2004) 853-884] world economy model. As in Matsuyama's model, symmetry-breaking can be observed, and symmetry-breaking generates endogenously determined levels of inequality. In addition, we show that when the countries differ in population size, their interaction through credit markets may lead to persistent endogenous fluctuations.     

Parametric continuity of stationary distributions

For Markovian economic models, long-run equilibria are typically identified with the stationary (invariant) distributions generated by the model. In this paper we provide new sufficient conditions for continuity in the map from parameters to these equilibria. Several existing results are shown to be special cases of our theorem. This paper has benefitted from the helpful comments of Kevin Reffett, Rabee Tourky, an anonymous referee and participants at the 13th European Workshop on General Equilibrium Theory, Venice 2004. The second author is grateful for financial support from Australian Research Council Grant DP0557625.     

On geometric ergodicity of the commodity pricing model

We provide a simple proof of geometric ergodicity for Samuelson's (1971) commodity pricing model. The proof yields a rate of convergence to the stationary distribution stated in terms of model primitives. We also provide a rate of convergence for prices to the stationary price process, and for the joint distribution of the state process to the stationary state process.     

Some stability results for Markovian economic semigroups

The present paper studies existence, uniqueness and stability of stationary equilibrium distributions in a class of stochastic dynamic models common to economic analysis. We provide applications to a heterogeneous agent model and two nonlinear multisector time series models with unbounded state space.     

Equilibrium storage with multiple commodities

This paper introduces a multisector model of commodity markets with storage, where equilibrium is defined by profit maximization, arbitrage and market clearing conditions. We then solve for the decentralized equilibrium via a corresponding dynamic program. We also describe the dynamics of the model, establishing geometric ergodicity, a Law of Large Numbers and a Central Limit Theorem.     

Stochastic Optimal Growth with Unbounded Shock

This paper considers a neoclassical optimal growth problem where the shock that perturbs the economy in each time period is potentially unbounded on the state space. Sufficient conditions for existence, uniqueness, and stability of equilibria are derived in terms of the primitives of the model using recent techniques from the field of perturbed dynamical systems. Journal of Economic Literature Classification Numbers: C61, C62, O41.     

Stochastic optimal growth with nonconvexities

This paper studies optimal investment and dynamic behavior in stochastically growing economies. We assume neither convex technology nor bounded support of the productivity shocks. A number of basic results concerning the investment policy and the Ramsey–Euler equation are established. We also prove a fundamental dichotomy pertaining to optimal growth models perturbed by standard econometric shocks: either an economy is globally stable or it is globally collapsing to the origin.