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86
Using Randomization to Break the Curse of Dimensionality
 Econometrica
, 1997
"... 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 ” fo ..."
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Cited by 122 (0 self)
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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
A Joint Econometric Model of Macroeconomic and Term Structure Dynamics
 Journal of Econometrics
, 2006
"... In 2004 all publications will carry a motif taken from the €100 banknote. This paper can be downloaded without charge from ..."
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Cited by 111 (3 self)
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In 2004 all publications will carry a motif taken from the €100 banknote. This paper can be downloaded without charge from
Comparing Dynamic Equilibrium Models to Data: A Bayesian Approach
, 2002
"... This paper studies the properties of the Bayesian approach to estimation and comparison of dynamic equilibrium economies. Both tasks can be performed even if the models are nonnested, misspecified, and nonlinear. First, we show that Bayesian methods have a classical interpretation: asymptotically ..."
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Cited by 93 (14 self)
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This paper studies the properties of the Bayesian approach to estimation and comparison of dynamic equilibrium economies. Both tasks can be performed even if the models are nonnested, misspecified, and nonlinear. First, we show that Bayesian methods have a classical interpretation: asymptotically, the parameter point estimates converge to their pseudotrue values, and the best model under the KullbackLeibler distance will have the highest posterior probability. Second, we illustrate the strong small sample behavior of the approach using a wellknown application: the U.S. cattle cycle. Bayesian estimates outperform maximum likelihood results, and the proposed model is easily compared with a set of BVARs.
2007a, Monetary policy with model uncertainty: distribution forecast targeting, unpublished manuscript
"... We examine optimal and other monetary policies in a linearquadratic setup with a relatively general form of model uncertainty, socalled Markov jumplinearquadratic systems extended to include forwardlooking variables and unobservable “modes. ” The form of model uncertainty our framework encompas ..."
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Cited by 72 (19 self)
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We examine optimal and other monetary policies in a linearquadratic setup with a relatively general form of model uncertainty, socalled Markov jumplinearquadratic systems extended to include forwardlooking variables and unobservable “modes. ” The form of model uncertainty our framework encompasses includes: simple i.i.d. model deviations; serially correlated model deviations; estimable regimeswitching models; more complex structural uncertainty about very different models, for instance, backward and forwardlooking models; timevarying 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 nonequivalence and “distribution forecast targeting.” JEL Classification: E42, E52, E58
Robust control of forwardlooking models
 Journal of Monetary Economics
, 2003
"... 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 pre ..."
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Cited by 60 (0 self)
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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 worstcase 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 worstcase analysis of the followers. As an example, the paper analyzes a model of a monopoly facing a competitive fringe.
Exotic Preferences for Macroeconomists
 In NBER Macroeconomics Annual 2004
, 2005
"... 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 num ..."
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Cited by 32 (9 self)
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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.
DSGE Models in a DataRich Environment
 NBER WORKING PAPERS 12772, NATIONAL BUREAU OF ECONOMIC RESEARCH, INC
, 2005
"... Standard practice for the estimation of dynamic stochastic general equilibrium (DSGE) models maintains the assumption that economic variables are properly measured by a single indicator, and that all relevant information for the estimation is summarized by a small number of data series. However, rec ..."
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Cited by 27 (0 self)
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Standard practice for the estimation of dynamic stochastic general equilibrium (DSGE) models maintains the assumption that economic variables are properly measured by a single indicator, and that all relevant information for the estimation is summarized by a small number of data series. However, recent empirical research on factor models has shown that information contained in large data sets is relevant for the evolution of important macroeconomic series. This suggests that conventional model estimates and inference based on estimated DSGE models are likely to be distorted. In this paper, we propose an empirical framework for the estimation of DSGE models that exploits the relevant information from a datarich environment. This framework provides an interpretation of all information contained in a large data set, and in particular of the latent factors, through the lenses of a DSGE model. The estimation involves Bayesian MarkovChain MonteCarlo (MCMC) methods extended so that the estimates can, in some cases, inherit the properties of classical maximum likelihood estimation. We apply this estimation approach to a stateoftheart DSGE monetary model. Treating theoretical concepts of the model – such as output, inflation and employment – as partially observed, we show that the information from a large set of macroeconomic indicators is important for accurate estimation of the model. It also allows us to improve the forecasts of important economic variables.
Monetary Policy in a Stochastic Equilibrium Model with Real and Nominal Rigidities
, 1996
"... A dynamic stochastic generalequilibrium (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 bot ..."
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Cited by 24 (1 self)
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A dynamic stochastic generalequilibrium (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 firstorder 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.
Knowing the forecast of others
 Review of Economic Dynamics, Vol
, 2004
"... ABSTRACT. We apply recursive methods to obtain a finite dimensional and recursive representation of an equilibrium of one of Townsend’s models of ‘forecasting the forecasts of others’. The equilibrium has the property that decision makers make common forecasts of the hidden state variable whose pres ..."
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Cited by 21 (2 self)
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ABSTRACT. We apply recursive methods to obtain a finite dimensional and recursive representation of an equilibrium of one of Townsend’s models of ‘forecasting the forecasts of others’. The equilibrium has the property that decision makers make common forecasts of the hidden state variable whose presence motivates them to pay attention to prices in other markets. Thus, the model has too few sources of randomness to put decision makers into a situation where they should form ‘higher order beliefs ’ (i.e., beliefs about others ’ beliefs). In Townsend’s model, they know the beliefs of others because they share them. We attain our finitedimensional recursive representation by applying methods of Pearlman, Currie, and Levine (1986). Key Words: Forecasting the forecasts of others, higher order beliefs, pooling