Some Stability Results for Markovian Economic Semigroups

The paper studies existence, uniqueness and stability of stationary equilibrium distributions in a class of stochastic dynamic models common to economic analysis. The stability conditions provided are suitable for treating multi-sector models and nonlinear time series models with unbounded state.Markov processes, asymptotic stability, semigroups

Evaluating Asset Pricing Implications of DSGE Models

This paper conducts an econometric evaluation of structural macroeconomic asset pricing models. A one-sector dynamic stochastic general equilibrium model (DSGE) with habit formation and capital adjustment costs is considered. Based on the log-linearized DSGE model, a Gaussian probability model for the joint distribution of aggregate consumption, investment, and a vector of asset returns R(t) is specified. We facilitate the stochastic discount factor M(t) representation obtained from the DSGE model and impose the no-arbitrage condition E[M(t)R(t)|t-1]=1. In addition to the full general equilibrium model, we also consider consumption and production based partial equilibrium specifications, and a more general reference model. To evaluate the various asset pricing models we compute posterior model probabilities and loss function based measures of model adequacy.

Memoria, equilibrios múltiples y crisis en países emergentes

We present a new Generalized Markov Equilibrium (GME) approach to studying sudden stops and financial crises in emerging countries in the canonical small open economy model with equilib-rium price-dependent collateral constraints. Our approach to characterizing and computing stochastic equilibrium dynamics is global, encompasses recursive equilibrium as a special case, yet allows for a much more flexible approach to modeling memory in such models that are known to have multiple equilibrium. We prove the existence of ergodic GME selections from the set of sequential competitive equilibrium, and show that at the same time ergodic GME selectors can replicate all the observed phases of the macro crises associated with a sudden stop (boom, collapse, spiralized recession, recov-ery) while still being able to capture the long-run stylized behavior of the data. We also compute stochastic equilibrium dynamics associated with stationary and nonstationary GME selections, and we find that: a) the ergodic GME selectors generate stochastic dynamics that are less financially constrained with respect to stationary non-ergodic paths; and, b) non-stationary GME selections ex-hibit a great range of fluctuations in macroeconomic aggregates compared to the stationary selections. From a theoretical perspective, we prove the existence of both sequential competitive equilibrium and (minimal state space) recursive equilibrium, as well as provide a complete theory of robust recursive equilibrium comparative statics in deep parameters. Consistent with recent results in the literature, relative to the set of recursive equilibrium, we find 2 stationary equilibrium: one with high/over borrowing, the other with low/under borrowing. These equilibrium are extremal and “self-fulfilling” under rational expectations. The selection among these equilibria depend on observable variables and not on sunspots.Presentamos un nuevo equilibrio generalizado de Markov (GME) para estudiar crisis de balanza de pagos en economías emergentes que sufren fricciones financieras en la forma de restricciones de colateral. Nuestro enfoque permite caracterizar y computar los equilibrios dinámicos y estocásticos en forma global, comprende a otros equilibrios recursivos (como los de espacio de esta mínimo) y representa una forma flexible de modelar “memoria” en estas economías que suelen tener equilibrios múltiples. Probamos la existencia de un GME ergódico cómo una selección del equilibrio secuencial el cual a su vez puede replicar tanto todas las fases de una crisis de balanza de pagos cómo los hechos estilizados de largo plazo. Computamos el equilibrio ergódico, estacionario y no estacionario. Encontramos que el equilibrio ergódico tiene trayectorias del consumo más suaves y que el no estacionario puede replicar un gran rango de crisis de balanza de pagos. Desde una perspectiva teórica, probamos la existencia del equilibrio secuencial y recursivo en espacio de estados mínimos, como así también resultados de estática comparativa robusta. En línea con la literatura, encontramos 2 tipos de equilibrios estacionarios: uno con alto y el otro con bajo endeudamiento. Estos equilibrios son auto-validantes en expectativas racionales y no requieren de manchas solares para su coordinación

Memory, multiple equilibria and emerging market crises

We present a new Generalized Markov Equilibrium (GME) approach to studying sudden stops and financial crises in emerging countries in the canonical small open economy model with equilibrium price-dependent collateral constraints. Our approach to characterizing and computing stochastic equilibrium dynamics is global, encompasses recursive equilibrium as a special case, yet allows for a much more flexible approach to modeling memory in such models that are known to have multiple equilibrium. We prove the existence of ergodic GME selections from the set of sequential competitive equilibrium, and show that at the same time ergodic GME selectors can replicate all the observed phases of the macro crises associated with a sudden stop (boom, collapse, spiralized recession, recovery) while still being able to capture the long-run stylized behavior of the data. We also compute stochastic equilibrium dynamics associated with stationary and nonstationary GME selections, and we find that a) the ergodic GME selectors generate stochastic dynamics that are less financially constrained with respect to stationary non-ergodic paths, b) non-stationary GME selections exhibit a great range of fluctuations in macroeconomic aggregates compared to the stationary selections. From a theoretical perspective, we prove the existence of both sequential competitive equilibrium and (minimal state space) recursive equilibrium, as well as provide a complete theory of robust recursive equilibrium comparative statics in deep parameters. Consistent with recent results in the literature, relative to the set of recursive equilibrium, we find 2 stationary equilibrium: one with high/over borrowing, the other with low/under borrowing. These equilibrium are extremal and “selffulfilling” under rational expectations. The selection among these equilibria depend on observable variables and not on sunspots

Existence and Uniqueness of Equilibrium in Nonoptimal Unbounded Infinite Horizon Economies

In applied work in macroeconomics and finance, nonoptimal infinite horizon economies are often studied in the the state space is unbounded. Important examples of such economies are single vector growth models with production externalities, valued fiat money, monopolistic competition, and/or distortionary government taxation. Although sufficient conditions for existence and uniqueness of Markovian equilibrium are well known for the compact state space case, no similar sufficient conditions exist for unbounded growth. This paper provides such a set of sufficient conditions, and also present a computational algorithm that will prove asymptotically consistent when computing Markovian equilibrium

Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk

We present a new approach to studying equilibrium dynamics in a class of stochastic games with a continuum of players with private types and strategic complementarities. We introduce a suitable equilibrium concept, called Markov Stationary Nash Distributional Equilibrium (MSNDE), prove its existence, and determine comparative statics of equilibrium paths and the steady state invariant distributions to which they converge. Finally, we provide numerous applications of our results including: dynamic models of growth with status concerns, social distance, and paternalistic bequest with endogenous preference for consumption

Differential information in large games with strategic complementarities

We study equilibrium in large games of strategic complementarities (GSC) with differential information. We define an appropriate notion of distributional Bayesian Nash equilibrium and prove its existence. Furthermore, we characterize order-theoretic properties of the equilibrium set, provide monotone comparative statics for ordered perturbations of the space of games, and provide explicit algorithms for computing extremal equilibria. We complement the paper with new results on the existence of Bayesian Nash equilibrium in the sense of Balder and Rustichini (J Econ Theory 62(2):385–393, 1994) or Kim and Yannelis (J Econ Theory 77(2):330–353, 1997) for large GSC and provide an analogous characterization of the equilibrium set as in the case of distributional Bayesian Nash equilibrium. Finally, we apply our results to riot games, beauty contests, and common value auctions. In all cases, standard existence and comparative statics tools in the theory of supermodular games for finite numbers of agents do not apply in general, and new constructions are required