Continuous State Dynamic Programming via Nonexpansive Approximation

This paper studies fitted value iteration for continuous state dynamic programming using nonexpansive function approximators. A number of nonexpansive approximation schemes are discussed. The main contribution is to provide error bounds for approximate optimal policies generated by the value iteration algorithm.Dynamic Programming; Approximation

Random Dynamical Systems with Multiplicative Noise

The paper considers random economic systems generating nonlinear time series on the positive half-ray R+. Using Liapunov techniques, new conditions for existence, uniqueness and stability of stationary equilibria are obtained. The conditions generalize earlier results from the mathematical literature, and extend to models outside the scope of existing economic methodology. An application to the stochastic growth problem with increasing returns is given.

ASYMPTOTIC STATISTICAL PROPERTIES OF THE NEOCLASSICAL OPTIMAL GROWTH MODEL

The standard one-sector stochastic optimal growth model is shown to be not just ergodic but geometrically ergodic. In addition, it is proved that the time series generated by the optimal path satisfy the Law of Large Numbers and the Central Limit Theorem.

CONVERGENCE, PATH DEPENDENCE AND THE NATURE OF STOCHASTIC EQUILIBRIA: A TERATOLOGY OF GROWTH METHODS

This paper establishes global stability for a class of stochastic increasing returns accumulation models. The nature of the unique stochastic steady state is investigated. It is found that the models generate highly path dependent time series over long horizons. The findings demonstrate that the standard stability concept used in stochastic growth theory is satisfied by models which contradict our intuitive association of globally stability with unique, history-independent outcomes for each set of economic fundamentals. At the same time, the analysis provides a principled theoretical framework for integrating increasing returns models more closely with the cross-country income data.

Computing the Distributions of Economic Models Via Simulation

This paper studies the convergence properties of a Monte Carlo algorithm for computing distributions of state variables when the underlying model is a Markov chain with absolutely continuous transition probabilities. We show that the L1 error of the estimator always converges to zero with probability one. In addition, rates of convergence are established for L1 and integral mean squared errors. The algorithm is shown to have many applications in economics.

Computing the Distributions of Economic Models Via Simulation

This paper studies a Monte Carlo algorithm for computing distributions of state variables when the underlying model is a Markov process. It is shown that the L1 error of the estimator always converges to zero with probability one, and often at a parametric rate. A related technique for computing stationary distributions is also investigated.Distributions, Markov processes, simulation.

Continuous State Dynamic Programming Via Nonexpansive Approximation

This paper studies fitted value iteration for continuous state dynamic programming using nonexpansive function approximators. A number of nonexpansive approximation schemes are discussed. The main contribution is to provide error bounds for approximate optimal policies generated by the value iteration algorithm.

Computable Bounds for Extreme Event Probabilities in Stochastic Economic Models

The paper introduces a multiplicative drift condition for evaluating stochastic economic models. The drift condition is shown to permit computation of quantitative bounds for extreme event probabilities in terms of the model primitives. By way of illustration, the technique is applied to a simple threshold autoregression model of exchange rates.

Necessary and Sufficient Conditions for Stability of Finite State Markov Chains

This note considers finite state Markov chains which overlap supports. While the overlapping supports condition is known to be necessary and sufficient for stability of these chains, the result is typically presented in a more general context. As such, one objective of the note is to provide an exposition, along with simple proofs corresponding to the finite case. Second, the note provides an additional equivalent condition which should be useful in applications.

NECESSARY AND SUFFICIENT CONDITIONS FORSTABILITY OF FINITE STATE MARKOV CHAINS

This note considers finite state Markov chains which overlap supports. While the overlapping supports condition is known to be necessary and sufficient for stability of these chains, the result is typically presented in a more general context. As such, one objective of the note is to provide an exposition, along with simple proofs corresponding to the finite case. Second, the note provides an additional equivalent condition which should be useful in applications.