COMPUTABLE STATIONARY MARKOV EQUILIBRIA IN NON-OPTIMAL GENERAL EQUILIBRIUM ECONOMIES

DAMIAN PIERRI

Conferencia; Econometric Society Meeting, Toulouse; 2014

This paper derives a Markovian representation for a wide range of sequential non-optimal economies with infinite horizons. It also proves the existence of an invariant measure and a law of large numbers for any stochastic process obtained from this recursive structure. The results build on the seminal paper of Duffie et. al. (1994) and provides the first known proof of an invariant measure for a spotless time homogeneous Markov equilibrium (THME). The paper introduces a new equilibrium notion, called computable stationary Markov equilibria (CSME), which is defined as a spotless THME endowed with an invariant measure. The theoretical structure derived in this paper, composed by a CSME and a law of large numbers, can be seen as a general framework which allows computing, simulating and empirically evaluating non-optimal economies. In particular, it is shown that the recursive equilibrium algorithm in Feng. et. al. (2013) and the Markovian algorithm in Kubler and Schmedders (2003) can be used to approximate a CSME. Then, the law of large numbers guarantees the convergence of (almost) all numerical simulations to the exact steady state of the model, which is characterized by an invariant measure. Finally, the paper presents a calibration procedure which guarantees that the empirically relevant set of parameters actually reflects the long run behavior of the model