Measuring Inflation Expectations Uncertainty Using High‐Frequency Data

Inflation expectations play a key role in determining future economic outcomes. The associated uncertainty provides a direct gauge of how well‐anchored the inflation expectations are. We construct a model‐based measure of inflation expectations uncertainty by augmenting a standard unobserved components model of inflation with information from noisy and possibly biased measures of inflation expectations obtained from financial markets. This new model‐based measure of inflation expectations uncertainty is more accurately estimated and can provide valuable information for policymakers. Using U.S. data, we find significant changes in inflation expectations uncertainty during the Great Recession.     

Nowcasting U.S. Headline and Core Inflation

Forecasting future inflation and nowcasting contemporaneous inflation are difficult. We propose a new and parsimonious model for nowcasting headline and core inflation in the U.S. consumer price index and price index for personal consumption expenditures that relies on relatively few variables. The model's nowcasting accuracy improves as information accumulates over a month or quarter, outperforming statistical benchmarks. In real‐time comparisons, the model's headline inflation nowcasts substantially outperform those from the Blue Chip consensus and the Survey of Professional Forecasters. Across all four inflation measures, the model's nowcasting accuracy is comparable to that of the Federal Reserve Board's Greenbook.     

Estimation of a forward-looking monetary policy rule: A time-varying parameter model using ex post data

In this paper, we consider estimation of a time-varying parameter model for a forward-looking monetary policy rule, by employing ex post data. A Heckman-type (1976. The common structure of statistical models of truncation, sample selection, and limited dependent variables and a simple estimator for such models. Annals of Economic and Social Measurement 5, 475-492) two-step procedure is employed in order to deal with endogeneity in the regressors. This allows us to econometrically take into account changing degrees of uncertainty associated with the Fed's forecasts of future inflation and GDP gap when estimating the model. Even though such uncertainty does not enter the model directly, we achieve efficiency in estimation by employing the standardized prediction errors for inflation and GDP gap as bias correction terms in the second-step regression. We note that no other empirical literature on monetary policy deals with this important issue. Our empirical results also reveal new aspects not found in the literature previously. That is, the history of the Fed's conduct of monetary policy since the early 1970s can in general be divided into three subperiods: the 1970s, the 1980s, and the 1990s. The conventional division of the sample into pre-Volcker and Volcker-Greenspan periods could mislead the empirical assessment of monetary policy.     

Measuring Inflation Anchoring and Uncertainty: A U.S. and Euro Area Comparison

We use several U.S. and euro‐area surveys of professional forecasters to estimate a dynamic factor model of inflation featuring time‐varying uncertainty. We obtain survey‐consistent distributions of future inflation at any horizon, both in the U.S. and the euro area. Equipped with this model, we propose a novel measure of the anchoring of inflation expectations that accounts for inflation uncertainty. Our results suggest that following the Great Recession, inflation anchoring improved in the United States, while mild de‐anchoring occurred in the euro area. As of our sample end, both areas appear to be almost equally anchored.     

Inflation Dynamics in the U.S.: Global but Not Local Mean Reversion

A stylized fact of U.S. inflation dynamics is one of extreme persistence and possible unit root behavior. If so, the implications for macroeconomics and monetary policy are somewhat unpalatable. Our econometric analysis proposes a parsimonious univariate representation of the inflation process for the last 60 years, the nonlinear exponential smooth autoregressive. The empirical results confirm a number of the key features such as global stationarity, local unit root behavior, and lower persistence in the post-1983 period than in the pre-1983 period. We compare the forecasting ability of our model with that of competing univariate models and find that the nonlinear model outperforms the linear autoregressive model in the pre-1983 period and the random walk in the post-1983 period at short horizons.     

The Taylor Rule and Forecast Intervals for Exchange Rates

In this paper, we examine the Meese–Rogoff puzzle from a different perspective: out‐of‐sample interval forecasting. While most studies in the literature focus on point forecasts, we apply semiparametric interval forecasting to a group of exchange rate models. Forecast intervals for 10 OECD exchange rates are generated and the performance of the empirical exchange rate models are compared with the random walk. Our contribution is twofold. First, we find that in general, exchange rate models generate tighter forecast intervals than the random walk, given that their intervals cover out‐of‐sample exchange rate realizations equally well. Our results suggest a connection between exchange rates and economic fundamentals: economic variables contain information useful in forecasting distributions of exchange rates. We also find that the benchmark Taylor rule model performs better than the monetary, PPP and forward premium models, and its advantages are more pronounced at longer horizons. Second, the bootstrap inference framework proposed in this paper for forecast interval evaluation can be applied in a broader context, such as inflation forecasting.     

Why Has U.S. Inflation Become Harder to Forecast?

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.     

A New Model of Inflation,Trend Inflation,and Long‐Run Inflation Expectations

This paper develops a bivariate model of inflation and a survey‐based long‐run forecast of inflation that allows for the estimation of the link between trend inflation and the long‐run forecast. Thus, our model allows for the possibilities that long‐run forecasts taken from surveys can be equated with trend inflation, that the two are completely unrelated, or anything in between. Using a variety of inflation measures and survey‐based forecasts for several countries, we find that long‐run forecasts can provide substantial help in refining estimates and fitting and forecasting inflation. It is less helpful to simply equate trend inflation with the long‐run forecasts.     

An Inflation‐Predicting Measure of the Output Gap in the Euro Area

Using a small Bayesian dynamic factor model of the euro area, we estimate the deviations of output from its trend that are consistent with the behavior of inflation. We label these deviations the output gap. In order to pin down the features of the model, we evaluate the accuracy of real‐time inflation forecasts from different model specifications. The version that forecasts inflation best implies that after the 2011 sovereign debt crisis, the output gap in the euro area has been much larger than the official estimates. Versions featuring a secular stagnation‐like slowdown in trend growth, and hence a small output gap after 2011, do not adequately capture the inflation developments.     

Real Wage Rigidities and the New Keynesian Model

Most central banks perceive a trade‐off between stabilizing inflation and stabilizing the gap between output and desired output. However, the standard new Keynesian framework implies no such trade‐off. In that framework, stabilizing inflation is equivalent to stabilizing the welfare‐relevant output gap. In this paper, we argue that this property of the new Keynesian framework, which we call the divine coincidence, is due to a special feature of the model: the absence of nontrivial real imperfections. We focus on one such real imperfection, namely, real wage rigidities. When the baseline new Keynesian model is extended to allow for real wage rigidities, the divine coincidence disappears, and central banks indeed face a trade‐off between stabilizing inflation and stabilizing the welfare‐relevant output gap. We show that not only does the extended model have more realistic normative implications, but it also has appealing positive properties. In particular, it provides a natural interpretation for the dynamic inflation–unemployment relation found in the data.     

Trend Inflation and the Nature of Structural Breaks in the New Keynesian Phillips Curve

We show that with a unit root in inflation, the new Keynesian Phillips curve (NKPC) implies an unobserved components model with a stochastic trend component and an inflation gap. Our empirical results suggest that with an increase in trend inflation during the Great Inflation, the response of inflation to real economic activity decreases and the persistence of the inflation gap increases due to an increase in the persistence of the unobserved stationary component. These results are in line with the predictions of Cogley and Sbordone ( 2008 ), who show that the coefficients of the NKPC are functions of time‐varying trend inflation.     

Robustness and U.S. Monetary Policy Experimentation

We study how a concern for robustness modifies a policymaker's incentive to experiment. A policymaker has a prior over two submodels of inflation‐unemployment dynamics. One submodel implies an exploitable trade‐off, the other does not. Bayes' law gives the policymaker an incentive to experiment. The policymaker fears that both submodels and his prior probability distribution over them are misspecified. We compute decision rules that are robust to misspecifications of each submodel and of the prior distribution over submodels. We compare robust rules to ones that Cogley, Colacito, and Sargent (2007) computed assuming that the models and the prior distribution are correctly specified. We explain how the policymaker's desires to protect against misspecifications of the submodels, on the one hand, and misspecifications of the prior over them, on the other, have different effects on the decision rule.     

What Makes the Output–Inflation Trade‐Off Change? The Absence of Accelerating Deflation in Japan

It is standard to model the output–inflation trade-off as a linear relationship with a time-invariant slope. We assess empirical evidence for two sets of theories that allow for endogenous variation in the slope of the short-run Phillips curve. At an empirical level, we examine why large negative output gaps in Japan in the late 1990s did not lead to accelerating deflation but instead coincided with stable, albeit moderately negative inflation. Our results suggest that this episode is most convincingly interpreted as reflecting a gradual flattening of the Phillips curve. We find that this flattening is best explained by models with endogenous price durations. These models imply that in any economy where trend inflation is substantially lower (or substantially higher) today than in past decades, time variation in the slope of the Phillips curve has become too important to ignore.     

Estimating Trend Inflation Based on Unobserved Components Model: Is It Correlated with the Inflation Gap?

Building on the work of Stock and Watson (2007), this paper empirically shows that a negative correlation between innovations to trend inflation and the inflation gap plays an important role in the dynamics of postwar U.S. inflation. Additional features that we incorporate in our model include regime‐switching inflation gap persistence and association between inflation and inflation uncertainty. The resulting estimate of trend inflation is smooth, and our model provides superior out‐of‐sample forecasts than Stock and Watson's (2007) unobserved components model with stochastic volatility or than Atkeson and Ohanian's (2001) random walk model does.     

New tests of the new-Keynesian Phillips curve

Lagged dependent variables typically play an important role in empirical models of inflation. Do these lags reflect backward-looking inflation expectations, or do they proxy for rational forward-looking expectations, as in the new-Keynesian Phillips curve? Galí and Gertler [1999. Inflation dynamics: a structural econometric analysis. Journal of Monetary Economics 44, 195-222] attempt to answer this question using GMM to estimate specifications incorporating both lagged and future inflation. They report small coefficients on lagged inflation and conclude that the new-Keynesian model provides a good first approximation to inflation dynamics. We show that these tests have low power against alternative backward-looking specifications, and demonstrate that their results are also consistent with a backward-looking Phillips curve. Using an alternative approach, we find that the new-Keynesian pricing model cannot explain the importance of lagged inflation in standard inflation regressions, and find that forward-looking terms play a very limited role in explaining inflation dynamics.     

Inflation Dynamics When Inflation Is Near Zero

We discuss the likely evolution of U.S. inflation in the near and medium terms on the basis of (i) past U.S. experience with very low levels of inflation, (ii) the most recent Japanese experience with negative inflation, and (iii) some preliminary U.S. micro evidence on downward nominal wage rigidity. Our findings question the view that stable long‐run inflation expectations and downward nominal wage rigidity will necessarily provide sufficient support to prices to avoid further declines in inflation. We show that an inflation model fitted on Japanese data over the past 20 years, which accounts for both short‐ and long‐run inflation expectations, matches the recent U.S. inflation experience quite well. While the model indicates that U.S. inflation might be subject to a lower bound, it does not rule out a prolonged period of low inflation or even mild deflation going forward. In addition, micro‐level data on wages suggest no obvious downward rigidity in the firm's wage bill, downward rigidity in individual wages notwithstanding. As a consequence, downward nominal wage rigidity may not be enough to offset deflationary pressures in the current situation.     

Comparing New Keynesian models of the business cycle: A Bayesian approach

The baseline New Keynesian model cannot replicate the observed persistence in inflation, output, and real wages for sensible parameter values. As a result, several extensions have been suggested to improve its fit to the data. We use a Bayesian approach to estimate and compare the baseline sticky price model of Calvo's [1983. Staggered prices in a utility maximizing framework. Journal of Monetary Economics 12, 383-398.] and three extensions. Our empirical results are as follows. First, we find that adding price indexation improves the fit of Calvo's [1983. Staggered prices in a utility maximizing framework. Journal of Monetary Economics 12, 383-398.] model. Second, models with both staggered price and wage setting dominate models with only price rigidities. Third, introducing wage indexation does not significantly improve the fit. Fourth, all model estimates suggest a high degree of price stickiness. Fifth, the estimates of labor supply elasticity are higher in models with both staggered price and wage contracts. Finally, the estimated inflation parameters of the Taylor rule are stable across models.     

Does Inflation Adjust Faster to Aggregate Technology Shocks than to Monetary Policy Shocks?

This paper studies U.S. inflation adjustment speed to aggregate technology shocks and to monetary policy shocks in a medium size Bayesian vector autoregression model. According to the model estimated on the 1959–2007 sample, inflation adjusts much faster to aggregate technology shocks than to monetary policy shocks. These results are robust to different identification assumptions and measures of aggregate prices. However, by separately estimating the model over the pre‐ and post‐1980 periods, this paper further shows that inflation adjusts much faster to technology shocks than to monetary policy shocks in the post‐1980 period, but not in the pre‐1980 period.     

Are Expected Inflation Rates and Expected Real Rates Negatively Correlated? A Long‐Run Test of the Mundell‐Tobin Hypothesis

Some empirical evidence suggests that the expected real interest and expected inflation rates are negatively correlated. This hypothesis of negative correlation is sometimes known as the Mundell‐Tobin hypothesis. In this article we reinvestigate this negative relation from a long‐term point of view using cointegration analysis. The data on the historical interest rate on T‐bills and the inflation rate indicate that the Mundell‐Tobin hypothesis does not hold in the long run for the United States, the United Kingdom, and Canada. We also obtain similar results using the real interest rate on index‐linked gilt traded in the United Kingdom.     

The economics of options-implied inflation probability density functions

Recently a market in options based on consumer price index inflation (inflation caps and floors) has emerged in the US. This paper uses quotes on these derivatives to construct probability densities for inflation. We study how these probability density functions respond to news announcements and find that the implied odds of deflation are sensitive to certain macroeconomic news releases. We also estimate empirical pricing kernels using these option prices along with time series models fitted to inflation. The options-implied densities assign considerably more mass to extreme inflation outcomes (either deflation or high inflation) than do their time series counterparts. This yields a U-shaped empirical pricing kernel, with investors having high marginal utility in states of the world characterized by either deflation or high inflation.