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Working Paper
Reliably Computing Nonlinear Dynamic Stochastic Model Solutions: An Algorithm with Error Formulas
This paper provides a new technique for representing discrete time nonlinear dynamic stochastic time invariant maps. Using this new series representation, the paper augments the usual solution strategy with an additional set of constraints thereby enhancing algorithm reliability. The paper also provides general formulas for evaluating the accuracy of proposed solutions. The technique can readily accommodate models with occasionally binding constraints and regime switching. The algorithm uses Smolyak polynomial function approximation in a way which makes it possible to exploit a high degree of ...
Working Paper
Equilibrium with Mutual Organizations in Adverse Selection Economies
An equilibrium concept in the Debreu (1954) theory-of-value tradition is developed for a class of adverse selection economies and applied to the Spence signaling and Rothschild-Stiglitz (1976) adverse selection environments. The equilibrium exists and is optimal. Further, all equilibria have the same individual type utility vector. The economies are large with a finite number of types that maximize expected utility on an underlying commodity space. An implication of the analysis is that the invisible hand works for this class of adverse selection economies.
Working Paper
Monetary Policy and Macroeconomic Stability Revisited
A large literature with canonical New Keynesian models has established that the Fed's policy change from a passive to an active response to inflation led to U.S. macroeconomic stability after the Great Inflation of the 1970s. We revisit this view by estimating a staggered price model with trend inflation using a Bayesian method that allows for equilibrium indeterminacy and adopts a sequential Monte Carlo algorithm. {{p}} The model empirically outperforms a canonical New Keynesian model and demonstrates an active response to inflation even in the Great Inflation era, during which the U.S. ...
Working Paper
Global Dynamics in a Search and Matching Model of the Labor Market
We study global and local dynamics of a simple search and matching model of the labor market. We show that the model can be locally indeterminate or have no equilibrium at all, but only for parameterizations that are empirically implausible. In contrast to the local results, we show that the model exhibits chaotic and periodic dynamics for reasonable parameter values both in backward and forward time. In contrast to earlier work, we establish these results analytically without placing numerical restrictions on the parameters.
Working Paper
Inflation Gap Persistence, Indeterminacy, and Monetary Policy
Empirical studies have documented that the persistence of the gap between inflation and its trend declined after the Volcker disinflation. Previous research into the source of the decline has offered competing views while sidestepping the possibility of equilibrium indeterminacy. This paper examines the source by estimating a medium-scale DSGE model using a Bayesian method that allows for indeterminacy. The estimated model shows that the Fed's change from a passive to an active policy response to the inflation gap or a decrease in firms' probability of price change can fully account for the ...
Report
Optimal target criteria for stabilization policy
This paper considers a general class of nonlinear rational-expectations models in which policymakers seek to maximize an objective function that may be household expected utility. We show how to derive a target criterion that is 1) consistent with the model?s structural equations, 2) strong enough to imply a unique equilibrium, and 3) optimal, in the sense that a commitment to adjust the policy instrument at all dates so as to satisfy the target criterion maximizes the objective function. The proposed optimal target criterion is a linear equation that must be satisfied by the projected paths ...
Report
Constructing Pure-Exchange Economies with Many Equilibria
We develop a restart algorithm based on Scarf’s (1973) algorithm for computing approximate Brouwer fixed points. We use the algorithm to compute all of the equilibria of a general equilibrium pure-exchange model with four consumers, four goods, and 15 equilibria. The mathematical result that motivates the algorithm is a fixed-point index theorem that provides a sufficient condition for uniqueness of equilibrium and a necessary condition for multiplicity of equilibria. Examining the structure of the model with 15 equilibria provides us with a method for constructing higher dimensional models ...
Report
Risk Loving and Fat Tails in the Wealth Distribution
We study the dynamic properties of the wealth distribution in an overlapping generations model with warm-glow bequests and heterogeneous attitudes towards risk. Some dynasties of agents are risk averters, and others are risk lovers. Agents can invest in two types of Lucas trees. The two types of trees are symmetric in the sense that one type has a high return in states where the other has a return of zero. This symmetry allows risk averters to perfectly ensure their future income and eliminates aggregate uncertainty in the model. Furthermore, risk lovers take extreme portfolio positions, ...
Journal Article
Closing Small and "Sufficiently" Large Open Economies with Different Asset Structures
There are two important dimensions that matter when we write down a model economy of a country that is open to international financial markets. The first one is its size, and the second one is its asset market structure. Small open economies are price takers so the analysis happens in partial equilibrium, while countries that are “sufficiently" large can affect international prices and the analysis happens in general equilibrium. The second important dimension is the asset market structure. If markets are complete there is full risk sharing, while if markets are incomplete there is not. In ...
Working Paper
A Generalized Approach to Indeterminacy in Linear Rational Expectations Models
We propose a novel approach to deal with the problem of indeterminacy in Linear Rational Expectations models. The method consists of augmenting the original state space with a set of auxiliary exogenous equations to provide the adequate number of explosive roots in presence of indeterminacy. The solution in this expanded state space, if it exists, is always determinate, and is identical to the indeterminate solution of the original model. The proposed approach accommodates determinacy and any degree of indeterminacy, and it can be implemented even when the boundaries of the determinacy region ...