Bayesian model comparison for time‐varying parameter VARs with stochastic volatility

We develop importance sampling methods for computing two popular Bayesian model comparison criteria, namely, the marginal likelihood and the deviance information criterion (DIC) for time‐varying parameter vector autoregressions (TVP‐VARs), where both the regression coefficients and volatilities are drifting over time. The proposed estimators are based on the integrated likelihood, which are substantially more reliable than alternatives. Using US data, we find overwhelming support for the TVP‐VAR with stochastic volatility compared to a conventional constant coefficients VAR with homoskedastic innovations. Most of the gains, however, appear to have come from allowing for stochastic volatility rather than time variation in the VAR coefficients or contemporaneous relationships. Indeed, according to both criteria, a constant coefficients VAR with stochastic volatility outperforms the more general model with time‐varying parameters.     

The response of asset prices to monetary policy shocks: Stronger than thought

Standard macroeconomic theory predicts rapid responses of asset prices to monetary policy shocks. Small‐scale vector autoregressions (VARs), however, often find sluggish and insignificant impact effects. Using the same high‐frequency instrument to identify monetary policy shocks, we show that a large‐scale dynamic factor model finds overall stronger and quicker asset price reactions compared to a benchmark VAR, both on euro area and US data. Our results suggest that incorporating a sufficiently large information set is crucial to estimate monetary policy effects.     

Macroeconomic forecasting and structural change

The aim of this paper is to assess whether modeling structural change can help improving the accuracy of macroeconomic forecasts. We conduct a simulated real‐time out‐of‐sample exercise using a time‐varying coefficients vector autoregression (VAR) with stochastic volatility to predict the inflation rate, unemployment rate and interest rate in the USA. The model generates accurate predictions for the three variables. In particular, the forecasts of inflation are much more accurate than those obtained with any other competing model, including fixed coefficients VARs, time‐varying autoregressions and the naïve random walk model. The results hold true also after the mid 1980s, a period in which forecasting inflation was particularly hard. Copyright © 2011 John Wiley & Sons, Ltd.     

Mind the Output Gap: The Disconnect of Growth and Inflation during Recessions and Convex Phillips Curves in the Euro Area

We develop a theoretical model that features a business cycle‐dependent relation between output, price inflation and inflation expectations, augmenting the model by Svensson (1997) with a nonlinear Phillips curve that reflects the rationale underlying the capacity constraint theory (Macklem, 1997). The theoretical model motivates our empirical assessment, based on a regime‐switching Phillips curve and a regime‐switching monetary structural VAR, employing different filter‐based, semi‐structural model‐based and Bayesian factor model‐implied output gaps. The analysis confirms the presence of a convex relationship between inflation and the output gap, meaning that the coefficient in the Phillips curve on the output gap recurringly increases during times of expansion and abates during recessions. Sign‐restricted monetary policy shocks based on a regime‐switching monetary SVAR reveal that expansionary monetary policy induces less pressure on inflation at times of weak as opposed to strong growth; thereby rationalizing relatively stronger expansionary policy, including unconventional volume‐based policy, during times of deep recession. A further augmented model shows that an effective euro exchange rate shock, too, implies business cycle state‐dependent responses, with more upward pressure on prices arising from unexpected currency depreciation at times of expansion than during recession phases.     

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.     

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.     

The puzzling effects of monetary policy in VARs: Invalid identification or missing information?

Standard vector autoregressions (VARs) often find puzzling effects of monetary policy shocks. Is this due to an invalid (recursive) identification scheme, or because the underlying small‐scale VAR neglects important information? I employ factor methods and external instruments to answer this question and provide evidence that the root cause is missing information. In particular, while a recursively identified dynamic factor model yields conventional monetary policy effects across the board, a small‐scale VAR identified via external instruments does not. Importantly, the discrepancy between both models largely disappears once the information set of the VAR is augmented via factors. This finding is comforting news for the recent monetary literature. Two leading empirical advances with different underlying assumptions—namely external instruments (applied to a factor‐augmented VAR) and dynamic factor models (identified recursively)—find very similar effects of monetary policy shocks, cross‐verifying each other.     

A Markov Switching Factor‐Augmented VAR Model for Analyzing US Business Cycles and Monetary Policy

This paper develops a Markov switching factor‐augmented vector autoregression to investigate the transmission mechanisms of monetary policy for distinct stages of the US business cycle. We assume that autoregressive parameters and covariance matrices of the error terms are regime dependent, driven by an unobserved Markov indicator. Endogenously determined transition probabilities are governed by an underlying probit model that features a large set of possible predictors. The empirical findings provide evidence for differences in the transmission of monetary policy shocks that mainly stem from heterogeneity in the responses of financial market quantities.     

Structural FECM: Cointegration in large‐scale structural FAVAR models

Starting from the dynamic factor model for nonstationary data we derive the factor‐augmented error correction model (FECM) and its moving‐average representation. The latter is used for the identification of structural shocks and their propagation mechanisms. We show how to implement classical identification schemes based on long‐run restrictions in the case of large panels. The importance of the error correction mechanism for impulse response analysis is analyzed by means of both empirical examples and simulation experiments. Our results show that the bias in estimated impulse responses in a factor‐augmented vector autoregressive (FAVAR) model is positively related to the strength of the error correction mechanism and the cross‐section dimension of the panel. We observe empirically in a large panel of US data that these features have a substantial effect on the responses of several variables to the identified permanent real (productivity) and monetary policy shocks.     

全球向量自回归模型的理论、方法及其应用

全球向量自回归模型(GVAR)是将经典VAR模型加以扩展,使其能够用于分析世界各国或各地区之间经济联系的一种新的模型方法。本文阐述GVAR模型的理论、方法及其在中国经济分析中的应用。基于包含33个国家的GVAR模型,本文实证分析了中国与世界经济的相互影响。通过一般冲击反应函数方法分析中国需求冲击、美国需求冲击、美国债券市场价格和国际油价变动等冲击对中国和其他国家经济增长以及通货膨胀的传导机制、影响强度、持续时间等。结果显示,中国需求冲击对美国、欧元区、日本等主要工业化国家有显著影响,同时中国经济也受到美国债券价格变动较强烈的冲击。     

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.     

On the informational role of term structure in the US monetary policy rule

This paper uses a structural approach based on the indirect inference principle to estimate a standard version of the new Keynesian monetary (NKM) model augmented with term structure using both revised and real-time data. The estimation results show that the term spread and policy inertia are both important determinants of the US estimated monetary policy rule whereas the persistence of shocks plays a small but significant role when revised and real-time data of output and inflation are both considered. More importantly, the relative importance of term spread and persistent shocks in the policy rule and the shock transmission mechanism drastically change when it is taken into account that real-time data are not well behaved.     

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.     

Decomposing the declining volatility of long-term inflation expectations

The level and volatility of survey-based measures of long-term inflation expectations have come down dramatically over the past several decades. To capture these changes in inflation dynamics, we embed both short- and long-term expectations into a medium-scale VAR model with stochastic volatility. The model estimates attribute most of the marked decline in the volatility of expectations to smaller shocks to long-run inflation expectations. According to our estimates, the volatility of shocks plummeted in the early to mid-1980s, moved to a somewhat higher level that prevailed for much of the 1990s, and then declined to and remained at very low levels.     

WAS THE GOLD STANDARD REALLY DESTABILIZING?

This paper investigates the extent to which the high macroeconomic volatility experienced in the classical Gold Standard era of US history can be attributed to the monetary policy regime per se as distinct from other shocks. For this purpose, we estimate a small dynamic stochastic general equilibrium model for the classical Gold Standard era. We use this model to conduct a counterfactual experiment to assess whether a monetary policy conducted on the basis of a Taylor rule characterizing the Great Moderation data would have led to different outcomes for macroeconomic volatility and welfare in the Gold Standard era. The counterfactual Taylor rule significantly reduces inflation volatility, but at the cost of higher real‐money and interest‐rate volatility. Output volatility is very similar. The end result is no welfare improvement. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Forecasting with High‐Dimensional Panel VARs

This paper develops methods for estimating and forecasting in Bayesian panel vector autoregressions of large dimensions with time‐varying parameters and stochastic volatility. We exploit a hierarchical prior that takes into account possible pooling restrictions involving both VAR coefficients and the error covariance matrix, and propose a Bayesian dynamic learning procedure that controls for various sources of model uncertainty. We tackle computational concerns by means of a simulation‐free algorithm that relies on analytical approximations to the posterior. We use our methods to forecast inflation rates in the eurozone and show that these forecasts are superior to alternative methods for large vector autoregressions.     

Combining Time Variation and Mixed Frequencies: an Analysis of Government Spending Multipliers in Italy

In this paper, we propose a time‐varying parameter vector autoregression (VAR) model with stochastic volatility which allows for estimation on data sampled at different frequencies. Our contribution is twofold. First, we extend the methodology developed by Cogley and Sargent (Drifts and volatilities: monetary policies and outcomes in the post WWII U.S. Review of Economic Studies 2005; 8 : 262–302) and Primiceri (Time varying structural vector autoregressions and monetary policy. Review of Economic Studies 2005; 72 : 821–852) to a mixed‐frequency setting. In particular, our approach allows for the inclusion of two different categories of variables (high‐frequency and low‐frequency) into the same time‐varying model. Second, we use this model to study the macroeconomic effects of government spending shocks in Italy over the 1988:Q4–2013:Q3 period. Italy—as well as most other euro area economies—is characterized by short quarterly time series for fiscal variables, whereas annual data are generally available for a longer sample before 1999. Our results show that the proposed time‐varying mixed‐frequency model improves on the performance of a simple linear interpolation model in generating the true path of the missing observations. Second, our empirical analysis suggests that government spending shocks tend to have positive effects on output in Italy. The fiscal multiplier, which is maximized at the 1‐year horizon, follows a U‐shape over the sample considered: it peaks at around 1.5 at the beginning of the sample; it then stabilizes between 0.8 and 0.9 from the mid 1990s to the late 2000s, before rising again to above unity during the recent crisis. Copyright © 2015 John Wiley & Sons, Ltd.     

Labor Market Dynamics: A Time‐Varying Analysis

This paper studies how key labour market stylized facts and the responses of labour market variables to technology shocks vary over the US postwar period. It uses a benchmark dynamic, stochastic, general equilibrium model enriched with labour market frictions and investment‐specific technological progress that enables a novel identification scheme based on sign restrictions on a SVAR with time‐varying coefficients and stochastic volatility. Key findings are: (i) the volatility in job finding and separation rates has declined over time, while their correlation varies across time; (ii) the job finding rate plays an important role for unemployment, and the two series are strongly negatively correlated over the sample period; (iii) the magnitude of the response of labour market variables to technology shocks varies across the sample period.