"Learning and the Role of Macroeconomic Factors in the Term Structure" (with Thomas Laubach and John C. Williams).

**Abstract: **Models of the term structure based on only observable variables have had limited success in explaining movements in longer-term interest rates. A key assumption in much of this literature is that agents know all the parameters describing the model of the economy, and that these parameters are fixed for all time. In this paper, we relax both of these assumptions and assume instead that agents regularly re-estimate the parameters of their models--both those determining the point forecasts and those describing economic volatility--based on incoming data. In this way, we allow for the real-time problem of pricing assets based on properly dated information sets. In addition, we allow for discounting of past data reflecting a concern on the part of agents for undetectable structural change in the economy. We find that the learning model with discounting does a much better job at explaining longer-term yields than an equivalent model with constant coefficients estimated over the full sample; in particular, the deviations from the pure expectations hypothesis are much smaller, on average, with our learning model. We then estimate the model term premia imposing an affine arbitrage-free structure. We show that incorporating learning improves the in-sample fit and forecasting performance of the model. Learning also implies time variation in the real-time estimates of macroeconomic volatility that is absent in standard macroeconomic models with constant coefficients. We find that these shifts in estimates of macroeconomic volatility help explain movements in term premia over the past half century. More generally, our analysis highlights the importance of taking into account the information sets of investors in understanding the determinants of bond prices.

JEL Codes: D83, D84, G12

Keywords: affine term structure models, learning, structural change.

Version date: September 11, 2007. Click here for a PDF of this, our first good draft.

"Real-time Model Uncertainty in the United States: 'Robust' policies put to the test"

**Abstract:** We exploit 30 versions of the Board of Governor's FRB/US model, that differ by vintage; 4 per year since the model's inception in 1996. The surprisingly substantive model changes incurred over a relatively short period of time imply that the policies that were optimal *ex ante*, were considerably less so *ex post*. This situation provides a rare opportunity to test in a real-world setting proposed methods for designing policies that are purportedly robust to parameter and model uncertainty. We also examine rules that are robust in the sense of attempting to encompass the range of models represented by the historical range of specifications.

JEL Classifications: E37, E5, C5, C6.

Keywords: monetary policy, model uncertainty, robust policies, real time.

The paper is about to be substantially revised; please check back here later.

"Robustifying Learnability" (with Peter von zur Muehlen) originally Finance and Economics Discussion Series no. 2005-58.

**Abstract:** In recent years, the learnability of rational expectations equilibria (REE) and the determinacy of economic models have rightfully joined the usual performance criteria among the sought-after goals of policy design. There have been some important contributions to the literature, outlining useful features of policies in general and monetary policy rules in particular that facilitate learning. An omitted topic has been a treatment of policy design for learnability under model uncertainty. This paper provides such a treatment. We examine the design of simple rules to maximize the set of perceived laws of motion (agents' initially misspecified model) that converge on a unique REE. We compare the features of these rules with those that maximize economic performance in the true model, and we measure the performance cost of maximizing learnability. Contains cool full-colour pictures.

Version date: February 2008. Click here to get the revised and extended version.

JEL Classifications: C6, E5.

Keywords: monetary policy, learning, E-stability, determinacy, robust policies.

"The Great Inflation and the Great Moderation" (with Peter von zur Muehlen) manuscript in progress.

**Abstract:** In the late 1960s and into the 1970s, the United States experienced a burst of inflation--the Great Inflation in the words of Delong (1997)--the origins of which seemed hard to uncover. Then, in the 1980s, it all went away, replaced not only by lower inflation, but a remarkably less volatile economy; the Great Moderation, according to Stock and Watson (2003). Straightforward explanations for either of these phenomena have been hard to come by. Typically, one must either appeal to a number of proximate causes, or to happenstance. This paper advances the idea that the Fed simply got the model wrong. We assume that the true model is a variant of the canonical New Keynesian business cycle model, but the Fed estimates a reduced-form VAR, consistent with common practice over the period. We find that a central bank, learning its model by variants of recursive least squares learning, and choosing optimal policies conditional on its beliefs would have allowed indeterminancy. We calibrate the resulting sunspots using empirical results from Leduc *et al.* (2003) and show that the "resonance frequency" of prediction errors generated by the model is consistent with those from their empirical results. The Volcker disinflation is then seen as a bold stroke that to rule out sunspot equilibria and restore the stability of inflation expectations. An implication of this is that the observed higher volatility of the economy in the 1970s than today is really a manifestation of having mistakenly assumed away sunspots which shows up as fundamental shocks during the earlier period.

JEL classifications: C5, E5.

Keywords: monetary policy, learning, indeterminacy, sunspots, control problems.

"Time Variation in the Phillips Curve and the Sacrifice Ratio in Real Time and *Ex Post*" (with Dave Reifschneider) Draft in Progress.

**Abstract:** The debate on the persistence of inflation in the United States turns, in part, on apparent time variation in the Phillips curve on the one hand and on whether one conditions on a break in the trend rate of inflation on the other. Because of the colinearity of the data and the absence of a agreed upon specification, the conclusions one draws from the data depends on the priors one brings to the issue. This paper approaches the issue in a different way than most others by examining explicitly the time variation in the Phillips curve using both ex post and real-time data. We also exploit archives of the FRB/US model to see whether the conclusions one might draw in single-equation reduced-form analyses would differ from those from a full-model real-time analysis. We conclude that while one might argue on the basis of ex post fitting of reduced-form equations that the Phillips curve is time invariant, approaching the question from a real-time perspective renders a different verdict.

JEL Classification: C22, C5, E31.

Keywords: Phillips curve, sacrifice ratio, time-varying parameters, real time, econometric inference.