This chapter examines the concept of inflation persistence in macroeconomic theory. It begins with a definition of persistence, emphasizing the difference between reduced-form and structural persistence. It then examines a number of empirical measures of reduced-form persistence, considering the possibility that persistence has changed over time. The chapter then examines the theoretical sources of persistence, distinguishing “intrinsic ” from “inherited” persistence, and deriving a number of analytical results on persistence. It summarizes the implications for persistence from the literatures on “stickyinformation” models, learning and so-called trend inflation models, providing some new results throughout.

We examine whether the U.S. rate of price inflation has become harder to forecast and, to the extent that it has, what changes in the inflation process have made it so. The main finding is that the univariate inflation process is well described by an unobserved component trend-cycle model with stochastic volatility or, equivalently, an integrated moving average process with time-varying parameters. This model explains a variety of recent univariate inflation forecasting puzzles and begins to explain some multivariate inflation forecasting puzzles as well. Key words: Phillips curve, trend-cycle model, moving average, great moderation JEL codes: C53, E37 *We thank Jonas Fisher for bringing several of the issues discussed in this paper to our attention in a 1999 conversation, Luca Benati for (more recent) helpful suggestions, and Matthew Shapiro, Robert Gordon, and two anonymous referees for helpful comments on an earlier draft. Replications files for the results in this paper can be downloaded from

New Keynesian Phillips Curves (NKPC) have been extensively used in the analysis of monetary policy, but yet there are a number of issues of concern about how they are estimated and then related to the underlying macroeconomic theory. The first is whether such equations are identified. To check identification requires specifying the process for the forcing variables (typically the output gap) and solving the model for inflationintermsoftheobservables. Inpractice,theequationisestimatedby GMM, relying on statistical criteria to choose instruments. This may result in failure of identification or weak instruments. Secondly, the NKPC is usually derived as a part of a DSGE model, solved by log-linearising around a steady state and the variables are then measured in terms of deviations from the steady state. In practice the steady states, e.g. for output, are usually estimated by some statistical procedure such as the Hodrick-Prescott (HP) filter that might not be appropriate. Thirdly, there are arguments that other variables, e.g. interest rates, foreign inflation and foreign output gaps should enter the Phillips curve. This paper examines these three issues and argues that all three benefit from a global perspective. The global perspective provides additional instruments to alleviate the weak instrument problem, yields a theoretically consistent measure of the steady state and provides a natural route for foreign inflation or output gap to enter the NKPC. Keywords: Global VAR (GVAR), identification, New Keynesian Phillips Curve, Trend-Cycle decomposition.

This paper uses a structurally estimated macroeconometric model, denoted the MC model, to evaluate inflation targeting in the United States. Various interest rate rules are tried with differing weights on inflation and output, and various optimal control problems are solved using differing weights on inflation and output targets. Price-level targeting is also considered. The results show that 1) there are output costs to inflation targeting, especially for price shocks, 2) price-level targeting is dominated by inflation targeting, 3) the estimated interest rate rule of the Fed (in Table 4) is consistent with the Fed placing equal weights on inflation and unemployment in a loss function, 4) the estimated interest rate rule does a fairly good job at lowering variability, and 5) considerable economic variability is left after the Fed has done its best. Overall, the results suggest that the Fed should continue to behave as it has in the past.

Abstract: We use the inflation premium—the difference between nominal and real interest rates—as a proxy for expected inflation in the context of the New Keynesian Phillips Curve. Using data from inflation-indexed and nominal bonds we estimate a forward-looking Phillips curve for the United Kingdom over the period 1985-2004. The proposed model describes UK inflation dynamics considerably better than does the standard hybrid New Keynesian Phillips Curve under the assumption of rational expectations. In contrast with the findings in the rest of the literature we find that there still exists a tradeoff between inflation and the stance of the real economy, regardless of the empirical measure used. This relationship also persists in the period since the UK adopted inflation targeting as a framework for monetary policy.

Replacing rational expectations by recursive learning schemes complicates the dynamics of economic models. We show that when such models are used for structural inference, conventional asymptotic theory does not necessarily apply. In the context of two prototypical structural models with learning, we show that: (i) estimators of the structural parameters exhibit large biases and nonnormality; and (ii) t-statistics are nonpivotal, and t-tests are seriously size distorted. These features are attributable to a violation of ergodicity and to weak identification. We show that valid inference can be conducted using a generalized Anderson-Rubin statistic with appropriate choice of instruments. As an application we study a New Keynesian Phillips curve with learning.

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Replacing rational expectations by adaptive learning algorithms complicates the dynamics of economic models. Identification of the structural parameters is improved under learning relative to rational expectations, but it deteriorates when learning converges to rational expectations. Learning also induces persistent dynamics, and this makes the distribution of estimators and test statistics non-standard. We show that valid inference can be conducted using the Anderson-Rubin statistic with appropriate choice of instruments. Application of this method to the new Keynesian Phillips curve with US data provides evidence against constant gain least squares learning.

The relationship between in‡ation and the output gap can be modeled simply and e¤ectively by including an unobserved random walk component in the model. The dynamic properties match the stylized facts and the random walk component satis…es the properties normally required for core in‡ation. The model may be generalized to as to include a term for the expectation of next period’s output, but it is shown that this is di ¢ cult to distinguish from the original speci…cation. The model is …tted as a single equation and as part of a bivariate model that includes an equation for GDP. Fitting the bivariate model highlights some new aspects of unobserved components modeling. Single equation and bivariate models tell a similar story: an output gap two per cent above trend is associated with an annual in‡ation rate that is one percent above core in‡ation.

We develop methods for testing that an econometric model is underidentified and for estimating the nature of the failed identification. We adopt a generalized-method-of moments perspective in a possibly non-linear econometric specification. If, after attempting to replicate the structural relation, we find substantial evidence against the overidentifying restrictions of an augmented model, this is evidence against underidentification of the original model. To diagnose how identification might fail, we study the estimation of a one-dimensional curve that gives the parameter configurations that provide the greatest challenge to identification, and we illustrate this calculation in an empirical example. 1