Abstract: This paper introduces random versions of successive approximations and multigrid algorithms for computing approximate solutions to a class of finite and infinite horizon Markovian decision problems (MDPs). We prove that these algorithms succeed in breaking the “curse of dimensionality ” for a subclass of MDPs known as discrete decision processes (DDPs). 1

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We examine optimal and other monetary policies in a linear-quadratic setup with a relatively general form of model uncertainty, so-called Markov jump-linear-quadratic systems extended to include forward-looking variables and unobservable “modes. ” The form of model uncertainty our framework encompasses includes: simple i.i.d. model deviations; serially correlated model deviations; estimable regime-switching models; more complex structural uncertainty about very different models, for instance, backward- and forward-looking models; time-varying centralbank judgment about the state of model uncertainty; and so forth. We provide an algorithm for finding the optimal policy as well as solutions for arbitrary policy functions. This allows us to compute and plot consistent distribution forecasts—fan charts—of target variables and instruments. Our methods hence extend certainty equivalence and “mean forecast targeting ” to more general certainty non-equivalence and “distribution forecast targeting.” JEL Classification: E42, E52, E58

This paper shows how to formulate and compute robust Ramsey (aka Stackelberg) plans for linear models with forward looking private agents. The leader and the followers share a common approximating model and both have preferences for robust decision rules because both doubt the model. Since their preferences differ, the leader’s and followers ’ decision rules are fragile to different misspecifications of the approximating model. We define a Stackelberg equilibrium with robust decision makers in which the leader and follower have different worst-case models despite sharing a common approximating model. To compute a Stackelberg equilibrium we formulate a Bellman equation that is associated with an artificial singleagent robust control problem. The artificial Bellman equation contains a description of implementability constraints that include Euler equations that describe the worst-case analysis of the followers. As an example, the paper analyzes a model of a monopoly facing a competitive fringe.

A dynamic stochastic general-equilibrium (DSGE) model with real and nominal rigidities succeeds in capturing some key nominal features of U.S. business cycles. Monetary policy is specified following the developments in the structural vector autoregression (VAR) literature. Four shocks, including both technology and monetary policy shocks, affect the economy. Interaction between real and nominal rigidities is essential to reproduce the liquidity effect of monetary policy. The model is estimated by maximum likelihood on U.S. data. The model's fit is as good as that of an unrestricted first-order VAR and that the estimated model produces reasonable impulse responses and second moments. An increase of interest rates predicts a decrease of output two to six quarters in the future. This feature of U.S. business cycles has never been captured by previous research with DSGE models. Lastly, the policy implications are discussed.

How informative are unrestricted VARs about how particular economic models respond to preference, technology, and information shocks? 1 In the simplest possible setting, this paper provides a check for whether a theoretical model has the property in population that it is possible to infer economic shocks and impulse responses to them from the innovations and the impulse responses associated with a vector autoregression (VAR). We revisit an invertibility issue that is known to cause a potential problem for interpreting VARs, and present a simple check for its presence. 2 We illustrate our check in the context of a permanent income model for which it can be applied by hand.

This paper shows how to compute robust Ramsey (aka Stackelberg) plans for linear models with forward looking private agents. We formulate a Bellman equation for the robust plan. We describe robust filtering for when some of the forcing variables (like potential GDP or trend growth) are not observed, and how the decision problem interacts with the filtering problem. We use a ‘new synthesis’ macro model of Woodford as an example.

We provide a user’s guide to “exotic ” preferences: nonlinear time aggregators, departures from expected utility, preferences over time with known and unknown probabilities, risksensitive and robust control, “hyperbolic ” discounting, and preferences over sets (“temptations”). We apply each to a number of classic problems in macroeconomics and finance, including consumption and saving, portfolio choice, asset pricing, and Pareto optimal allocations.

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This paper presents and estimates a variant of Hansen and Sargent's (1988) real business cycle model with straight time and overtime. The model presented has only one latent variable, the state of technology, yet it does a better job propagating and magnifying shocks than the labor hoarding models which incorporate unobserved effort. This model, as well as a version of Burnside, Eichenbaum and Rebelo's (1993) labor hoarding model, is estimated using maximum likelihood. The maximum likelihood parameter estimates are compared to those using GMM. Key words: Business cycle fluctuations; Dynamic general equilibrium; Shock propagation; Maximum likelihood JEL classification: E32; C51 I thank John Cochrane, Charles Evans, Robert Lucas, David Marshall, Ellen McGrattan, Ned Prescott, Argia Sbordone, Thomas Tallarini and Mark Watson for helpful conversations. I thank Martin Eichenbaum, Lars Hansen and Thomas Sargent for their encouragement, support and comments. This paper has benefitted from ...