Modelling Inflation Volatility

This paper discusses estimation of US inflation volatility using time‐varying parameter models, in particular whether it should be modelled as a stationary or random walk stochastic process. Specifying inflation volatility as an unbounded process, as implied by the random walk, conflicts with priors beliefs, yet a stationary process cannot capture the low‐frequency behaviour commonly observed in estimates of volatility. We therefore propose an alternative model with a change‐point process in the volatility that allows for switches between stationary models to capture changes in the level and dynamics over the past 40 years. To accommodate the stationarity restriction, we develop a new representation that is equivalent to our model but is computationally more efficient. All models produce effectively identical estimates of volatility, but the change‐point model provides more information on the level and persistence of volatility and the probabilities of changes. For example, we find a few well‐defined switches in the volatility process and, interestingly, these switches line up well with economic slowdowns or changes of the Federal Reserve Chair. Moreover, a decomposition of inflation shocks into permanent and transitory components shows that a spike in volatility in the late 2000s was entirely on the transitory side and characterized by a rise above its long‐run mean level during a period of higher persistence. Copyright © 2015 John Wiley & Sons, Ltd.     

Asymmetric Quantile Persistence and Predictability: the Case of US Inflation

This article investigates the evidence of time‐variation and asymmetry in the persistence of US inflation. We compare the out‐of‐sample performance of different forecasting models and find that quantile forecasts from an Auto‐Regressive (AR) model with level‐dependent volatility are at least as accurate as the forecasts of the Quantile Auto‐Regressive model, in particular for the core inflation measures. Our results indicate that the persistence of core inflation has been relatively constant and high, but it declined for the headline inflation measures. We also find that the asymmetric persistence of inflation shocks can be mostly attributed to the positive relation between inflation level and its volatility.     

The dynamics of US inflation: Can monetary policy explain the changes?

We investigate the relationship between monetary policy and inflation dynamics in the US using a medium scale structural model. The specification is estimated with Bayesian techniques and fits the data reasonably well. Policy shocks account for a part of the decline in inflation volatility; they have been less effective in triggering inflation responses over time and qualitatively account for the rise and fall in the level of inflation. A number of structural parameter variations contribute to these patterns.     

Yield curve in an estimated nonlinear macro model

This paper estimates a sticky price macro model with US macro and term structure data using Bayesian methods. The model is solved by a nonlinear method. The posterior distribution of the parameters in the model is found to be bi-modal. The degree of nominal rigidity is high at one mode (“sticky price mode”) but is low at the other mode (“flexible price mode”). I find that the degree of nominal rigidity is important for identifying macro shocks that affect the yield curve. When prices are more flexible, a slowly varying inflation target of the central bank is the main driver of the overall level of the yield curve by changing long-run inflation expectations. In contrast, when prices are more sticky, a highly persistent markup shock is the main driver. The posterior probability of each mode is sensitive to the use of observed proxies for inflation expectations. Ignoring additional information from survey data on inflation expectations significantly reduces the posterior probability of the flexible price mode. Incorporating this additional information suggests that yield curve fluctuations can be better understood by focusing on the flexible price mode. Considering nonlinearities of the model solution also increases the posterior probability of the flexible price mode, although to a lesser degree than using survey data information.     

Assessing the Transmission of Monetary Policy Using Time‐varying Parameter Dynamic Factor Models*

This article extends the current literature which questions the stability of the monetary transmission mechanism, by proposing a factor‐augmented vector autoregressive (VAR) model with time‐varying coefficients and stochastic volatility. The VAR coefficients and error covariances may change gradually in every period or be subject to abrupt breaks. The model is applied to 143 post‐World War II quarterly variables fully describing the US economy. I show that both endogenous and exogenous shocks to the US economy resulted in the high inflation volatility during the 1970s and early 1980s. The time‐varying factor augmented VAR produces impulse responses of inflation which significantly reduce the price puzzle. Impulse responses of other indicators of the economy show that the most notable changes in the transmission of unanticipated monetary policy shocks occurred for gross domestic product, investment, exchange rates and money.     

Band or point inflation targeting? An experimental approach

We conduct laboratory experiments with human subjects to test the rationale of adopting a band versus point inflation targeting regime. Within the standard New Keynesian model, we evaluate the macroeconomic performances of both regimes according to the strength of shocks affecting the economy. We find that when the economy faces small uncorrelated shocks, the level of inflation as well as its volatility are significantly lower in a band targeting regime, while the output gap and interest rate levels and volatility are significantly lower in a point targeting regime with tolerance bands. However, when the economy faces large uncorrelated shocks, choosing the suitable inflation targeting regime is irrelevant because both regimes lead to comparable performances. These findings stand in contrast to those of the literature and question the relevance of clarifying a mid-point target within the bands, especially in emerging market economies more inclined to large and frequent shocks.     

Optimal univariate inflation forecasting with symmetric stable shocks

Monthly inflation in the United States indicates non-normality in the form of either occasional big shocks or marked changes in the level of the series. We develop a univariate state space model with symmetric stable shocks for this series. The non-Gaussian model is estimated by the Sorenson–Alspach filtering algorithm. Even after removing conditional heteroscedasticity, normality is rejected in favour of a stable distribution with exponent 1·83. Our model can be used for forecasting future inflation, and to simulate historical inflation forecasts conditional on the history of inflation. Relative to the Gaussian model, the stable model accounts for outliers and level shifts better, provides tighter estimates of trend inflation, and gives more realistic assessment of uncertainty during confusing episodes. © 1998 John Wiley & Sons, Ltd.     

Issue Information

Much research studies US inflation history with a trend‐cycle model with unobserved components, where the trend may be viewed as the Fed's evolving inflation target or long‐horizon expected inflation. We provide a novel way to measure the slowly evolving trend and the cycle (or inflation gap), by combining inflation predictions from the Survey of Professional Forecasters (SPF) with realized inflation. The SPF forecasts may be treated either as rational expectations (RE) or updating according to a sticky information (SI) law of motion. We estimate RE and SI state‐space models with stochastic volatility on samples of consumer price index and gross national product/gross domestic product deflator inflation and the associated SPF inflation predictions using a particle Metropolis–Markov chain Monte Carlo sampler. The trend converges to 2% and its volatility declines over time—two tendencies largely complete by the late 1990s.     

Risk shocks and housing supply: A quantitative analysis

This paper analyzes the role of stochastic uncertainty in a multi-sector housing model with financial frictions. We include time varying uncertainty (i.e. risk shocks) in the technology shocks that affect housing production and provide estimates of the time-series properties of risk shocks by using firm level productivity data. The analysis demonstrates that risk shocks to the housing production sector are a quantitatively important impulse mechanism for understanding housing price movements. Specifically, the model can match the volatility of housing prices observed in the data. It is also demonstrated that adjustment costs are important in replicating the contemporaneous correlation of housing prices with GDP and residential investment. Critically, bankruptcy costs act as an endogenous markup factor in housing prices and are an important determinant of house price volatility. However, in comparison to housing demand shocks, risk shocks have low explanatory power for real quantities.     

Inflation Volatility with Regime Switching

This paper presents a new approach to model U.S. inflation dynamics by allowing regime switching in an unobserved components stochastic volatility framework. We use a modified particle filter to construct likelihood and estimate the model using MLE. The number of regimes is determined based on a bootstrap. We find that a model with three regimes and regime‐dependent constant volatilities has superior performance. In addition, we show that since 2000:II, U.S. inflation has entered a regime with moderate volatility where most of the volatility comes from transitory shocks.     

Time‐varying yield curve dynamics and monetary policy

Monetary policy, the yield curve and the private sector behaviour of the US economy are modelled as a time‐varying structural vector autoregression. The monetary policy shocks of the early 1980s explain a large portion of the persistence of inflation and the level of the term structure. Changes in inflation expectations implied by the yield curve account for the persistence of the federal funds rate. Failures of the expectations hypothesis are rare, and coincided with the credibility building of Paul Volcker's Fed tenure at the beginning of the 1980s and the sequence of consecutive policy rate cuts around the time of the early 1990s recession. Copyright © 2009 John Wiley & Sons, Ltd.     

Bayesian counterfactual analysis of the sources of the great moderation

We use counterfactual experiments to investigate the sources of the large volatility reduction in US real GDP growth in the 1980s. Contrary to an existing literature that conducts counterfactual experiments based on classical estimation and point estimates, we consider Bayesian analysis that provides a straightforward measure of estimation uncertainty for the counterfactual quantity of interest. Using Blanchard and Quah's ( 1989 ) structural VAR model of output growth and the unemployment rate, we find strong statistical support for the idea that a counterfactual change in the size of structural shocks alone, with no corresponding change in the propagation of these shocks, would have produced the same overall volatility reduction as what actually occurred. Looking deeper, we find evidence that a counterfactual change in the size of aggregate supply shocks alone would have generated a larger volatility reduction than a counterfactual change in the size of aggregate demand shocks alone. We show that these results are consistent with a standard monetary VAR, for which counterfactual analysis also suggests the importance of shocks in generating the volatility reduction, but with the counterfactual change in monetary shocks alone generating a small reduction in volatility. Copyright © 2007 John Wiley & Sons, Ltd.     

Monetary policy regimes and the term structure of interest rates

US monetary policy is investigated using a regime-switching no-arbitrage term structure model that relies on inflation, output, and the short interest rate as factors. The model is complemented with a set of assumptions that allow the dynamics of the private sector to be separated from monetary policy. The monetary policy regimes cannot be estimated if the yield curve is ignored during estimation. Counterfactual analysis evaluates importance of regimes in policy and shocks for the great moderation. The low-volatility regime of exogenous shocks plays an important role. Monetary policy contributes by trading off asymmetric responses of output and inflation under different regimes.     

Fiscal news and macroeconomic volatility

This paper analyzes the contribution of anticipated capital and labor tax shocks to business cycle volatility in an estimated New Keynesian business cycle model. While fiscal policy accounts for about 15% of output variance at business cycle frequencies, this mostly derives from anticipated government spending shocks. Tax shocks, both anticipated and unanticipated, contribute little to the fluctuations of real variables. However, anticipated capital tax shocks do explain a sizable part of inflation fluctuations, accounting for up to 12% of its variance. In line with earlier studies, news shocks in total account for about 50% of output variance. Further decomposing this news effect, we find permanent total factor productivity news shocks to be most important. When looking at the federal level instead of total government, the importance of anticipated tax and spending shocks significantly increases, suggesting that fiscal policy at the subnational level typically counteracts the effects of federal fiscal policy shocks.     

LONG‐RUN RISKS IN THE TERM STRUCTURE OF INTEREST RATES: ESTIMATION

This paper estimates a model in which persistent fluctuations in expected consumption growth, expected inflation, and their time‐varying volatility determine asset price variation. The model features Epstein–Zin recursive preferences, which determine the market price of macro risk factors. Analysis of the US nominal term structure data from 1953 to 2006 shows that agents dislike high uncertainty and demand compensation for volatility risks. Also, the time variation of the term premium is driven by the compensation for inflation volatility risk, which is distinct from consumption volatility risk. The central role of inflation volatility risk in explaining the time‐varying term premium is consistent with other empirical evidence including survey data. In contrast, the existing long‐run risks literature emphasizes consumption volatility risk and ignores inflation‐specific time‐varying volatility. The estimation results of this paper suggest that inflation‐specific volatility risk is essential for fitting the time series of the US nominal term structure data. Copyright © 2012 John Wiley & Sons, Ltd.     

Labor market institutions and inflation volatility in the euro area

Despite having had the same currency for many years, EMU countries still have quite different inflation dynamics. In this paper we explore one possible reason: country specific labor market institutions, giving rise to different inflation volatilities. When unemployment insurance schemes differ, as they do in EMU, reservation wages react differently in each country to area-wide shocks. This implies that real marginal costs and inflation also react differently. We report evidence for EMU countries supporting the existence of a cross-country link over the cycle between labor market structures on the one side and real wages and inflation on the other. We then build a DSGE model that replicates the data evidence. The inflation volatility differentials produced by asymmetric labor markets generate welfare losses at the currency area level of approximately 0.3% of steady state consumption.     

News shocks and asset price volatility in general equilibrium

We study equity price volatility in general equilibrium with news shocks about future productivity and monetary policy. As West (1988) shows, in a partial equilibrium present discounted value model, news about the future cash flow reduces asset price volatility. We show that introducing news shocks in a canonical dynamic stochastic general equilibrium model may not reduce asset price volatility under plausible parameter assumptions. This is because, in general equilibrium, the asset cash flow itself may be affected by the introduction of news shocks. In addition, we show that neglecting to account for policy news shocks (e.g., policy announcements) can potentially bias empirical estimates of the impact of monetary policy shocks on asset prices.     

Structural evolution of the postwar U.S. economy

We consider a time-varying parameter vector autoregressive model with stochastic volatility and mixture innovations to study the empirical relevance of the Lucas critique for the postwar U.S. economy. The model allows blocks of parameters to change at endogenously estimated points of time. Contrary to the Lucas critique, there are large changes at certain points of time in the parameters associated with monetary policy that do not correspond to changes in “reduced-form” parameters for inflation or the unemployment rate. However, the structure of the U.S. economy has evolved considerably over the postwar period, with an apparent reduction in the late 1980s in the impact of monetary policy shocks on inflation, though not on the unemployment rate. Related, we find changes in the Phillips curve tradeoff between inflation and cyclical unemployment (measured as the deviation from the time-varying steady-state unemployment rate implied by the model) in the 1970s and especially since the mid-1990s.     

The asymmetric effects of uncertainty on inflation and output growth

We study the effects of growth volatility and inflation volatility on average rates of output growth and inflation for post‐war US data. Our results suggest that increased growth uncertainty is associated with significantly lower average growth, while higher inflation uncertainty is significantly negatively correlated with lower output growth and lower average inflation. Both inflation and growth display evidence of significant asymmetric response to positive and negative shocks of equal magnitude. Copyright © 2004 John Wiley & Sons, Ltd.     

Shifts in volatility driven by large stock market shocks

This paper presents an extension of the stochastic volatility model which allows for level shifts in volatility of stock market returns, known as structural breaks. These shifts are endogenously driven by large return shocks (innovations), reflecting large pieces of market news. These shocks are identified from the data as being bigger in absolute terms than the values of two threshold parameters of the model: one for the negative shocks and one for the positive shocks. The model can be employed to investigate different sources of stock market volatility shifts driven by market news, without relying on exogenous information. In addition to this, it has a number of interesting features which enable us to study the effects of large return shocks on future levels of market volatility. The above properties of the model are shown based on a study for the US stock market volatility.