We estimate a dynamic stochastic general equilibrium (DSGE) model for the US economy. The model incorporates many types of real and nominal frictions: sticky nominal price and wage setting, habit formation in consumption, investment adjustment costs, variable capital utilisation and fixed costs in production. It also contains many types of shocks including productivity, labour supply, investment, preference, cost-push and monetary policy shocks. Using Bayesian estimation techniques, the relative importance of the various frictions and shocks in explaining the US business cycle are empirically investigated. We also show that this model is able to outperform standard VAR and BVAR models in out-of-sample prediction.

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Shocks and frictions in US business cycles: A Bayesian DSGE approach

Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

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Differential Equations and Dynamical Systems

Econometric policy evaluation: A critique

We propose and axiomatize a model of preferences over acts such that the decision maker evaluates acts according to the expectation (over a set of probability measures) of an increasing transformation of an act's expected utility. This expectation is calculated using a subjective probability over the set of probability measures that the decision maker thinks are relevant given her subjective information. A key feature of our model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective information, and ambiguity attitude, a characteristic of the decision maker's tastes. We show that attitudes towards risk are characterized by the shape of the von Neumann-Morgenstern utility function, as usual, while attitudes towards ambiguity are characterized by the shape of the increasing transformation applied to expected utilities. We show that the negative exponential form of this transformation is the special case of constant ambiguity aversion. Ambiguity itself is defined behaviorally and is shown to be characterized by properties of the subjective set of measures. This characterization of ambiguity is formally related to the definitions of subjective ambiguity advanced by Epstein-Zhang (2001) and Ghirardato-Marinacci (2002). One advantage of this model is that the well-developed machinery for dealing with risk attitudes can be applied as well to ambiguity attitudes. The model is also distinct from many in the literature on ambiguity in that it allows smooth, rather than kinked, indifference curves. This leads to different behavior and improved tractability, while still sharing the main features (e.g., Ellsberg's Paradox, etc.). The Maxmin EU model (e.g., Gilboa and Schmeidler (1989)) with a given set of measures may be seen as an extreme case of our model with infinite ambiguity aversion. Two illustrative applications to portfolio choice are offered.

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A Smooth Model of Decision Making under Ambiguity

In recent years, simple policy rules have received attention as a means to a more transparent and effective monetary policy. Often, however, the analysis is based on unrealistic assumptions about the timeliness of data availability. This permits rule specifications that are not operational and ignore difficulties associated with data revisions. This paper examines the magnitude of these informational problems using Taylor's rule as an example. I demonstrate that the real-time policy recommendations differ considerably from those obtained with the ex post revised data and are revised substantially even a year after the relevant quarter. Further, I show that estimated policy reaction functions obtained using the ex post revised data can yield misleading descriptions of historical policy. Using Federal Reserve staff forecasts I show that in the 1987-1992 period simple forward-looking specifications describe policy better than comparable Taylor-type specifications, a fact that is largely obscured when the analysis is based on the ex post revised data.

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Monetary Policy Rules Based on Real-Time Data

http://www.tomsargent.com/research/triple47.pdf

Robust control and model misspecification

We use a micro-founded macroeconometric modeling framework to investigate the design of monetary policy when the central bank faces uncertainty about the true structure of the economy. We apply Bayesian methods to estimate the parameters of the baseline specification using postwar U.S. data and then determine the policy under commitment that maximizes household welfare. We find that the performance of the optimal policy is closely matched by a simple operational rule that focuses solely on stabilizing nominal wage inflation. Furthermore, this simple wage stabilization rule is robust to uncertainty about the model parameters and to various assumptions regarding the nature and incidence of the innovations. However, the characteristics of optimal policy are very sensitive to the specification of the wage-contracting mechanism, thereby highlighting the importance of additional research regarding the structure of labor markets and wage determination.

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Monetary Policy under Uncertainty in Micro-Founded Macroeconometric Models

We study how decision-makers’ concerns about robustness affect prices and quantities in a stochastic growth model.In the model economy, growth rates in technology are altered by infrequent large shocks and continuous small shocks.An investor observes movements in the technology level but cannot perfectly distinguish their sources.Instead the investor solves a signal extraction problem.We depart from most of the macroeconomics and finance literature by presuming that the investor treats the specification of technology evolution as an approximation.To promote a decision rule that is robust to model misspecification, an investor acts as if a malevolent player threatens to perturb the actual data-generating process relative to his approximating model.We study how a concern about robustness alters asset prices.We show that the dynamic evolution of the risk-return trade-off is dominated by movements in the growth-state probabilities and that the evolution of the dividend-price ratio is driven primarily by the capital-technology ratio. This article shows how decision-makers’ concerns about model misspecification can affect prices and quantities in a dynamic economy.We use the familiar stochastic growth model of Brock and Mirman (1972) and Merton (1975) as a laboratory.Technology is specified as a continuous-time hidden Markov model (HMM), inducing investors to make inferences about the growth rate.They form their opinions about the growth rate from current and past observations of technology that are clouded by concurrently evolving small shocks modeled as Brownian motions.We show how investors’ desire to make their decision rules robust to misspecification of the evo

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Robustness and Pricing with Uncertain Growth

Working Paper 2004-22 September 2004 Abstract: The authors use a Bayesian Markov chain Monte Carlo algorithm to estimate a model that allows temporary gaps between a true expectational Phillips curve and the monetary authority's approximating nonexpectational Phillips curve. A dynamic programming problem implies that the monetary authority's inflation target evolves as its estimated Phillips curve moves. The authors' estimates attribute the rise and fall of post-World War II inflation in the United States to an intricate interaction between the monetary authority's beliefs and economic shocks. Shocks in the 1970s altered the monetary authority's estimates and made it misperceive the tradeoff between inflation and unemployment. That misperception caused sharp rise in inflation in the 1970s. The authors' estimates indicate that policy makers updated their beliefs continuously. By the 1980s, policy makers' beliefs about the Phillips curve had changed enough to account for Fed chairman Paul Volcker's conquest of U.S. inflation in the early 1980s. JEL classification: E3, E5 Key words: updating beliefs, policy evaluation, self-confirming equilibrium, Nash inflation, Ramsey outcomes I. INTRODUCTION Today, many statesmen and macroeconomists believe that inflation can largely be determined by a government monetary authority. Then why did the Federal Reserve Board preside over high US inflation during the late 1960s and the 1970s? And why, under Paul Volcker, did it rapidly bring inflation down during the early 1980s? This paper answers these questions by estimating a model that features a particular process that makes a procession of economic shocks induce the monetary authority to alter its model of inflation-unemployment dynamics, the Phillips curve. At each date t, the monetary authority updates its beliefs about the Phillips curve and then recomputes a first-period action recommended by a "Phelps problem", a discounted dynamic programming problem that minimizes the expected value of a discounted quadratic loss function of inflation and unemployment. (1) The monetary authority pursues the same objectives at each date, using the same structural model, with only its estimates of that model changing over time. (2) This model of the systematic part of inflation puts the monetary authority's beliefs about the Phillips curve front and center. (3) We assume that the monetary authority's model of the Phillips curve deviates in two subtle but important ways from what it would be in a rational expectations model (e.g., Kydland and Prescott (1977)). The first deviation is that, while the true Phillips curve is like Kydland and Prescott's, we assume that the monetary authority omits the public's expected rate of inflation from its Phillips curve. By itself, this omission need not prevent the outcomes of our model from coinciding with those of Kydland and Prescott's, nor need it imply that the government's model is wrong in a way that could be detected from even an infinite sample. Whether the monetary authority's model is wrong in a statistically detectable way depends on how we allow the monetary authority to reestimate the parameters of its model. In particular, if the monetary authority were to believe that the coefficients of its Phillips curve are constant over time, then its estimates would converge to ones that support a self-confirming equilibrium (SCE). After convergence, its estimated Phillips curve would correctly describe occurrences along the SCE path for inflation and unemployment. Such an after-convergence version of our model has little hope of explaining the rise and fall of US inflation: that model would have inflation fluctuating randomly around a constant SCE level that coincides with Kydland and Prescott's time consistent suboptimal (i.e., excessive) level. (4) This outcome motivates our second subtle deviation from a rational expectations equilibrium. …

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Shocks and Government Beliefs: The Rise and Fall of American Inflation

Recently there has been a great deal of interest in studying monetary policy under model uncertainty. We develop new methods to analyze dierent sources of uncertainty in one coherent structure, which is useful for policy decisions. We show how to estimate the size of the uncertainty based on time series data, and how to incorporate this uncertainty in choosing policy. In particular, we develop a new approach for modeling uncertainty called model error modeling. The approach imposes additional structure on the errors of an estimated model, and builds a statistical description of the uncertainty around the model. We develop both parametric and nonparametric specifications of this approach, and use them to estimate uncertainty in a small model of the US economy. We then use our estimates to compute Bayesian and minimax robust policy rules, which are designed to perform well in the face of uncertainty.

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Noah Williams

Papers

Robust control and model misspecification

Monetary Policy under Uncertainty in Micro-Founded Macroeconometric Models

Robustness and Pricing with Uncertain Growth

Shocks and Government Beliefs: The Rise and Fall of American Inflation

Modeling model uncertainty