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.     

Steady‐state modeling and macroeconomic forecasting quality

Vector autoregressions (VARs) with informative steady‐state priors are standard forecasting tools in empirical macroeconomics. This study proposes (i) an adaptive hierarchical normal‐gamma prior on steady states, (ii) a time‐varying steady‐state specification which accounts for structural breaks in the unconditional mean, and (iii) a generalization of steady‐state VARs with fat‐tailed and heteroskedastic error terms. Empirical analysis, based on a real‐time dataset of 14 macroeconomic variables, shows that, overall, the hierarchical steady‐state specifications materially improve out‐of‐sample forecasting for forecasting horizons longer than 1 year, while the time‐varying specifications generate superior forecasts for variables with significant changes in their unconditional mean.     

Speculation in the Oil Market

The run‐up in oil prices since 2004 coincided with growing investment in commodity markets and increased price co‐movement among different commodities. We assess whether speculation in the oil market played a role in driving this salient empirical pattern. We identify oil shocks from a large dataset using a dynamic factor model. This method is motivated by the fact that a small‐scale vector autoregression is not informationally sufficient to identify the shocks. The main results are as follows. (i) While global demand shocks account for the largest share of oil price fluctuations, speculative shocks are the second most important driver. (ii) The increase in oil prices over the last decade is mainly driven by the strength of global demand. However, speculation played a significant role in the oil price increase between 2004 and 2008 and its subsequent collapse. (iii) The co‐movement between oil prices and the prices of other commodities is mainly explained by global demand shocks. Our results support the view that the recent oil price increase is mainly driven by the strength of global demand but that the financialization process of commodity markets also played a role. Copyright © 2014 John Wiley & Sons, Ltd.     

Real‐time forecast combinations for the oil price

Baumeister and Kilian (Journal of Business and Economic Statistics, 2015, 33(3), 338–351) combine forecasts from six empirical models to predict real oil prices. In this paper, we broadly reproduce their main economic findings, employing their preferred measures of the real oil price and other real‐time variables. Mindful of the importance of Brent crude oil as a global price benchmark, we extend consideration to the North Sea‐based measure and update the evaluation sample to 2017:12. We model the oil price futures curve using a factor‐based Nelson–Siegel specification estimated in real time to fill in missing values for oil price futures in the raw data. We find that the combined forecasts for Brent are as effective as for other oil price measures. The extended sample using the oil price measures adopted by Baumeister and Kilian yields similar results to those reported in their paper. Also, the futures‐based model improves forecast accuracy at longer horizons.     

Bayesian inference in a time varying cointegration model

There are both theoretical and empirical reasons for believing that the parameters of macroeconomic models may vary over time. However, work with time-varying parameter models has largely involved vector autoregressions (VARs), ignoring cointegration. This is despite the fact that cointegration plays an important role in informing macroeconomists on a range of issues. In this paper, we develop a new time varying parameter model which permits cointegration. We use a specification which allows for the cointegrating space to evolve over time in a manner comparable to the random walk variation used with TVP–VARs. The properties of our approach are investigated before developing a method of posterior simulation. We use our methods in an empirical investigation involving the Fisher effect.     

Commodity prices and fiscal policy design: Procyclical despite a rule

Recent studies offer evidence of reduced fiscal procyclicality to commodity price changes in resource‐rich countries—a feature commonly attributed to the adoption of fiscal policy rules. We revisit this issue and find that, by controlling for global activity shocks while allowing for time‐varying changes in both fiscal policy and the volatility of shocks, this finding does not hold. To show this we develop a time‐varying dynamic factor model, allowing for a multiple of shocks, stochastic volatility and time‐varying parameters, and estimate it on data for Norway, whose handling of resource wealth is often cited as exemplary.     

Efficient estimation of Bayesian VARMAs with time‐varying coefficients

Empirical work in macroeconometrics has been mostly restricted to using vector autoregressions (VARs), even though there are strong theoretical reasons to consider general vector autoregressive moving averages (VARMAs). A number of articles in the last two decades have conjectured that this is because estimation of VARMAs is perceived to be challenging and proposed various ways to simplify it. Nevertheless, VARMAs continue to be largely dominated by VARs, particularly in terms of developing useful extensions. We address these computational challenges with a Bayesian approach. Specifically, we develop a Gibbs sampler for the basic VARMA, and demonstrate how it can be extended to models with time‐varying vector moving average (VMA) coefficients and stochastic volatility. We illustrate the methodology through a macroeconomic forecasting exercise. We show that in a class of models with stochastic volatility, VARMAs produce better density forecasts than VARs, particularly for short forecast horizons.     

Macroeconomic Uncertainty and Oil Price Volatility

This paper shows that higher macroeconomic uncertainty causes higher oil price volatility. Regimes of low and high uncertainty are identified in a threshold VAR model in which the effects of structural oil demand and supply shocks are estimated. The results show that higher macroeconomic uncertainty, as measured by global industrial production volatility, significantly increases the sensitivity of oil prices to shocks in oil demand and supply. This occurs as uncertainty lowers the price elasticity of oil demand and supply. The difference in the estimated oil price elasticities is economically meaningful as the price impact of a similar change in oil production might double when it hits the economy in uncertain times. As such, varying uncertainty can explain why oil price volatility is typically higher during periods such as financial crises and recessions, and why oil price volatility changes over time more generally.     

Forecasting using variational Bayesian inference in large vector autoregressions with hierarchical shrinkage

Many recent papers in macroeconomics have used large vector autoregressions (VARs) involving 100 or more dependent variables. With so many parameters to estimate, Bayesian prior shrinkage is vital to achieve reasonable results. Computational concerns currently limit the range of priors used and render difficult the addition of empirically important features such as stochastic volatility to the large VAR. In this paper, we develop variational Bayesian methods for large VARs that overcome the computational hurdle and allow for Bayesian inference in large VARs with a range of hierarchical shrinkage priors and with time-varying volatilities. We demonstrate the computational feasibility and good forecast performance of our methods in an empirical application involving a large quarterly US macroeconomic data set.     

Global economy robust to higher oil,but EM vulnerable

• ? We do not envisage major central banks being pricked into deflationary action by the oil spike as there are limited concerns over a wage‐price spiral. But further rises — say to $100pb — would sour the global economy's ‘Goldilocks’ period. Vulnerable EM are the biggest concern; for some the impact is relatively large and could pile pressure on already‐strained domestic policies .
• ? A comparison with historical precedents is generally consoling. First, the price rise of 60% in the last year — though big — is only the sixth largest since 1973. Second, oil‐related global slowdowns have usually been associated with central bank hikes, which are less likely now than in past periods when inflation was less well anchored.
• ? Global implications: our baseline forecast of $80bp in H2 2018 may prompt a modest rise in non‐energy inflation and wages, and slightly weaker GDP growth. But we anticipate limited monetary policy responses. Concerns about the negative impact on activity are likely to trump fears of second‐round inflation effects.
• ? Model simulations: souring Goldilocks' porridge. Our $100pb oil simulations reveal a peak impact in 2020, knocking 0.7% off the level of global GDP. Inflation rises 1.2pp above our baseline by 2019.
• ? The recent association between strong oil and a strong dollar is unusual, but is probably not reflective of a fundamental change in the usual historic relationship (strong oil‐weak dollar).
• ? Simulations suggest EM oil importers endure the biggest hits via a (i) sharp terms of trade reversal; (ii) dollar strength; (iii) capital flows reversals; and (iv) recent reductions of oil price subsidies leaving consumers vulnerable to price increases. The most affected include already‐vulnerable economies Greece, Argentina and Turkey, as well as EM heavyweights China and India.

     

A sequential Monte Carlo approach to inference in multiple‐equation Markov‐switching models

Vector autoregressions with Markov‐switching parameters (MS‐VARs) offer substantial gains in data fit over VARs with constant parameters. However, Bayesian inference for MS‐VARs has remained challenging, impeding their uptake for empirical applications. We show that sequential Monte Carlo (SMC) estimators can accurately estimate MS‐VAR posteriors. Relative to multi‐step, model‐specific MCMC routines, SMC has the advantages of generality, parallelizability, and freedom from reliance on particular analytical relationships between prior and likelihood. We use SMC's flexibility to demonstrate that model selection among MS‐VARs can be highly sensitive to the choice of prior.     

The Government Spending Multiplier at the Zero Lower Bound: Evidence from the United States

We estimate state‐dependent government spending multipliers for the United States. We use a factor‐augmented interacted vector autoregression (FAIVAR) model. This allows us to capture the time‐varying monetary policy characteristics including the recent zero interest rate lower bound (ZLB) state, to account for the state of the business cycle and to address the limited information problem typically inherent in VARs. We identify government spending shocks by sign restrictions and use a government spending growth forecast series to account for the effects of anticipated fiscal policy. In our baseline specification, we find that government spending multipliers in a recession range from 3.56 to 3.79 at the ZLB. Away from the ZLB, multipliers in recessions range from 2.31 to 3.05. Several robustness analyses confirm that multipliers are higher, when the interest rate is lower and that multipliers in recessions exceed multipliers in expansions. Our results are consistent with theories that predict larger multipliers at the ZLB.     

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.     

Composite likelihood methods for large Bayesian VARs with stochastic volatility

Adding multivariate stochastic volatility of a flexible form to large vector autoregressions (VARs) involving over 100 variables has proved challenging owing to computational considerations and overparametrization concerns. The existing literature works with either homoskedastic models or smaller models with restrictive forms for the stochastic volatility. In this paper, we develop composite likelihood methods for large VARs with multivariate stochastic volatility. These involve estimating large numbers of parsimonious models and then taking a weighted average across these models. We discuss various schemes for choosing the weights. In our empirical work involving VARs of up to 196 variables, we show that composite likelihood methods forecast much better than the most popular large VAR approach, which is computationally practical in very high dimensions: the homoskedastic VAR with Minnesota prior. We also compare our methods to various popular approaches that allow for stochastic volatility using medium and small VARs involving up to 20 variables. We find our methods to forecast appreciably better than these as well.     

THE ROLE OF INVENTORIES AND SPECULATIVE TRADING IN THE GLOBAL MARKET FOR CRUDE OIL

We develop a structural model of the global market for crude oil that for the first time explicitly allows for shocks to the speculative demand for oil as well as shocks to flow demand and flow supply. The speculative component of the real price of oil is identified with the help of data on oil inventories. Our estimates rule out explanations of the 2003–2008 oil price surge based on unexpectedly diminishing oil supplies and based on speculative trading. Instead, this surge was caused by unexpected increases in world oil consumption driven by the global business cycle. There is evidence, however, that speculative demand shifts played an important role during earlier oil price shock episodes including 1979, 1986 and 1990. Our analysis implies that additional regulation of oil markets would not have prevented the 2003–2008 oil price surge. We also show that, even after accounting for the role of inventories in smoothing oil consumption, our estimate of the short‐run price elasticity of oil demand is much higher than traditional estimates from dynamic models that do not account for for the endogeneity of the price of oil. Copyright © 2013 John Wiley & Sons, Ltd.     

Upside/Downside spillovers between oil and Chinese stock sectors: From the global financial crisis to global pandemic

This paper examines the effects of the COVID-19 outbreak, recent oil price fall, and both global and European financial crises on dependence structure and asymmetric risk spillovers between crude oil and Chinese stock sectors. Using time-varying symmetric and asymmetric copula functions and the conditional Value at Risk measure, we provide evidence of positive tail dependence in most sectors using copula and conditional Value-at-Risk techniques. We can see the average dependence between oil and industries during the oil crisis. Moreover, we find strong evidence of bidirectional risk spillovers for all oil-sector pairs. The intensity of risk spillovers from oil to all stock sectors varies across sectors. The risk spillovers from sectors to oil are substantially larger than those from oil to sectors during COVID-19. Furthermore, the return spillover is time varying and sensitive to external shocks. The spillover strengths are higher during COVID-19 than financial and oil crises. Finally, oil do not exhibit neither hedge nor safe-haven characteristics irrespective of crisis periods.     

Markov Switching Oil Price Uncertainty

We investigate whether the United States economy responds negatively to oil price uncertainty and whether oil price shocks exert asymmetric effects on economic activity. In doing so, we relax the assumption in the existing literature that the data are governed by a single process, modifying the Elder and Serletis (2010) bivariate structural GARCH‐in‐Mean VAR to accommodate Markov regime switching in order to account for changing oil price dynamics over the sample period. We find evidence of asymmetries, against those macroeconomic theories that predict symmetries in the relationship between real aggregate economic activity and the real price of oil.     

基于小波变换和支持向量的国际原油价格预测

本文将小波分析与支持向量回归结合应用于国际原油价格预测,通过小波多尺度分析方法将油价时间序列分解为长期趋势和随机扰动项,然后采用支持向量回归对分解后的油价长期趋势进行预测。油价长期趋势的预测采用多因素预测方法,主要考虑市场供需基本面、库存、经济、投机等因素对石油价格走势的影响,建立多输入单输出的支持向量回归模型。实证研究表明,支持向量回归模型具有较高的预测性能,对原油价格长期趋势预测中,该方法比回归方法的预测精度高。     

VAR FORECASTING USING BAYESIAN VARIABLE SELECTION

This paper develops methods for automatic selection of variables in Bayesian vector autoregressions (VARs) using the Gibbs sampler. In particular, I provide computationally efficient algorithms for stochastic variable selection in generic linear and nonlinear models, as well as models of large dimensions. The performance of the proposed variable selection method is assessed in forecasting three major macroeconomic time series of the UK economy. Data‐based restrictions of VAR coefficients can help improve upon their unrestricted counterparts in forecasting, and in many cases they compare favorably to shrinkage estimators. Copyright © 2011 John Wiley & Sons, Ltd.