Some Implications of Uncertainty and Misperception for Monetary Policy
When choosing a strategy for monetary policy, policymakers must grapple with mismeasurement of labor market slack, and of the responsiveness of price inflation to that slack. Using stochastic simulations of a small-scale version of the Federal Reserve Board?s principal New Keynesian macroeconomic model, we evaluate representative rule-based policy strategies, paying particular attention to how those strategies interact with initial conditions in the U.S. as they are seen today and with the current outlook. To do this, we construct a current relevant baseline forecast, one that is loosely ...
The market resources method for solving dynamic optimization problems
We introduce the market resources method (MRM) for solving dynamic optimization problems. MRM extends Carroll?s (2006) endogenous grid point method (EGM) for problems with more than one control variable using policy function iteration. The MRM algorithm is simple to implement and provides advantages in terms of speed and accuracy over Howard?s policy improvement algorithm. Codes are available.
A Matter of Perspective: Mapping Linear Rational Expectations Models into Finite-Order VAR Form
This paper considers the characterization of the reduced-form solution of a large class of linear rational expectations models. I show that under certain conditions, if a solution exists and is unique, it can be cast in finite-order VAR form. I also investigate the conditions for the VAR form to be stationary with a well-defined residual variance-covariance matrix in equilibrium, for the shocks to be recoverable, and for local identification of the structural parameters for estimation from the sample likelihood. An application to the workhorse New Keynesian model with accompanying Matlab ...
Model Averaging and Persistent Disagreement
The authors consider the following scenario: Two agents construct models of an endogenous price process. One agent thinks the data are stationary, the other thinks the data are nonstationary. A policymaker combines forecasts from the two models using a recursive Bayesian model averaging procedure. The actual (but unknown) price process depends on the policymaker?s forecasts. The authors find that if the policymaker has complete faith in the stationary model, then beliefs and outcomes converge to the stationary rational expectations equilibrium. However, even a grain of doubt about ...
Computing Equilibria of Stochastic Heterogeneous Agent Models Using Decision Rule Histories
This paper introduces a general method for computing equilibria with heterogeneous agents and aggregate shocks that is particularly suitable for economies with private information. Instead of the cross-sectional distribution of agents across individual states, the method uses as a state variable a vector of spline coefficients describing a long history of past individual decision rules. Applying the computational method to a Mirrlees RBC economy with known analytical solution recovers the solution perfectly well. This test provides considerable confidence on the accuracy of the method.
Finite-Order VAR Representation of Linear Rational Expectations Models: With Some Lessons for Monetary Policy
This paper considers the characterization via finite-order VARs of the solution of a large class of linear rational expectations (LRE) models. I propose a unified approach that uses a companion Sylvester equation to check the existence and uniqueness of a solution to the canonical (first-order) LRE model in finite-order VAR form and a quadratic matrix equation to characterize it decoupling the backward- and forward-looking aspects of the model. I also investigate the fundamentalness of the shocks recovered. Solving LRE models by this procedure is straightforward to implement, general in its ...
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 ...
A Portfolio-Balance Approach to the Nominal Term Structure
Explanations of why changes in the relative quantities of safe debt seem to affect asset prices often appeal informally to a ?portfolio balance? mechanism. I show how this type of effect can be incorporated in a general class of structural, arbitrage-free asset-pricing models using a numerical solution method that allows for a wide range of nonlinearities. I consider some applications in which the Treasury market is isolated, investors have mean-variance preferences, and the short-rate process is truncated at zero. Despite its simplicity, a version of this model incorporating inflation can ...
Optimal Monetary Policy Regime Switches
An economy that switches between high and low growth regimes creates incentives for the monetary authority to change its rule. As lower growth tends to produce lower real interest rates, the monetary authority has an incentive to increase the inflation target and increase the degree of inertia in setting rates in an attempt to keep the nominal rate positive. An optimizing monetary authority therefore responds to permanently lower growth by slightly increasing both the inflation target and inertia; focusing solely on the inflation target ignores a key margin of adjustment. With repeated growth ...
Rational Inattention via Ignorance Equivalence
We introduce the concept of the ignorance equivalent to effectively summarize the payoff possibilities in a finite Rational Inattention problem. The ignorance equivalent is a unique fictitious action that is weakly preferable to all existing learning strategies and yet generates no new profitable learning opportunities when added to the menu of choices. We fully characterize the relationship between the ignorance equivalent and the optimal learning strategies. Agents with heterogeneous priors self-select their own ignorance equivalent, which gives rise to an expected-utility analogue of the ...