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This paper evaluates alternative indicators of global economic activity and other market fundamentals in terms of their usefulness for forecasting real oil prices and global petroleum consumption. We find that world industrial production is one of the most useful indicators that has been proposed in the literature. However, by combining measures from a number of di¤erent sources we can do even better. Our analysis results in a new index of global economic conditions and new measures for assessing future tightness of energy demand and expected oil price pressures. We illustrate their usefulness for quantifying the main factors behind the severe contraction of the global economy and the price risks faced by shale oil producers in early 2020.

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.

This paper proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility and exogenous predictors, as an equivalent high-dimensional static regression problem with thousands of covariates. Inference in this specification proceeds using Bayesian hierarchical priors that shrink the high-dimensional vector of coefficients either towards zero or time-invariance. Second, it introduces the frameworks of factor graphs and message passing as a means of designing efficient Bayesian estimation algorithms. In particular, a Generalized Approximate Message Passing (GAMP) algorithm is derived that has low algorithmic complexity and is trivially parallelizable. The result is a comprehensive methodology that can be used to estimate time-varying parameter regressions with arbitrarily large number of exogenous predictors. In a forecasting exercise for U.S. price inflation this methodology is shown to work very well., 89 pages; to appear in Journal of Business and Economic Statistics

Bayesian inference in economics is primarily perceived as a methodology for cases where the data are short, that is, not informative enough in order to be able to obtain reliable econometric estimates of quantities of interest. In these cases, prior beliefs, such as the experience of the decision-maker or results from economic theory, can be explicitly incorporated to the econometric estimation problem and enhance the desired solution. In contrast, in fields such as computing science and signal processing, Bayesian inference and computation have long been used for tackling challenges associated with ultra high-dimensional data. Such fields have developed several novel Bayesian algorithms that have gradually been established in mainstream statistics, and they now have a prominent position in machine learning applications in numerous disciplines. While traditional Bayesian algorithms are powerful enough to allow for estimation of very complex problems (for instance, nonlinear dynamic stochastic general equilibrium models), they are not able to cope computationally with the demands of rapidly increasing economic data sets. Bayesian machine learning algorithms are able to provide rigorous and computationally feasible solutions to various high-dimensional econometric problems, thus supporting modern decision-making in a timely manner.

We consider how an investor in the foreign exchange market can exploit predictive information by means of flexible Bayesian inference. Using a variety of vector autoregressive models, the investor is able, each period, to learn about important data features. The developed methodology synthesizes a wide array of established approaches for modeling exchange rate dynamics. In a thorough investigation of monthly exchange rate predictability for 10 countries, we find that using the proposed methodology for dynamic asset allocation achieves substantial economic gains out of sample. In particular, we find evidence for sparsity, fast model switching, and exploitation of the exchange rate cross-section.

As the amount of economic and other data generated worldwide increases vastly, a challenge for future generations of econometricians will be to master efficient algorithms for inference in empirical models with large information sets. This Chapter provides a review of popular estimation algorithms for Bayesian inference in econometrics and surveys alternative algorithms developed in machine learning and computing science that allow for efficient computation in high-dimensional settings. The focus is on scalability and parallelizability of each algorithm, as well as their ability to be adopted in various empirical settings in economics and finance.

This paper proposes a new, comprehensive Bayesian sampling scheme for inference in vector autoregressions (VARs) using sign restrictions. I build on a factor model decomposition of the reduced-form VAR disturbances, which are specified to be driven by a few common factors/shocks. The outcome is a computationally efficient algorithm that allows to jointly sample VAR parameters as well as decompositions of the covariance matrix satisfying desired sign or even zero restrictions. Unlike existing algorithms, the proposed framework allows to statistically test the plausibility of sign and other restrictions in VARs, for example, in situations where there is little guidance from economic theory about the effect of a certain shock. Using artificial and real data I show that the new algorithm works well and is multiple times more efficient than existing accept/reject algorithms for sign restrictions.

In a unified framework, we examine four sources of uncertainty in exchange rate forecasting models: (i) random variations in the data, (ii) estimation uncertainty, (iii) uncertainty about the degree of time-variation in coefficients, and (iv) uncertainty regarding the choice of the predictor. We find that models which embed a high-degree of coefficient variability yield forecast improvements at horizons beyond 1-month. At the 1-month horizon, and apart from the standard variance implied by unpredictable fluctuations in the data, the second and third sources of uncertainty listed above are key obstructions to predictive ability. The uncertainty regarding the choice of the predictors is negligible.

This paper proposes a simulation-free estimation algorithm for vector autoregressions (VARs) that allows fast approximate calculation of marginal parameter posterior distributions. We apply the algorithm to derive analytical expressions for independent VAR priors that admit a hierarchical representation and which would typically require computationally intensive posterior simulation methods. The benefits of the new algorithm are explored using three quantitative exercises. First, a Monte Carlo experiment illustrates the accuracy and computational gains of the proposed estimation algorithm and priors. Second, a forecasting exercise involving VARs estimated on macroeconomic data demonstrates the ability of hierarchical shrinkage priors to find useful parsimonious representations. We also show how our approach can be used for structural analysis and that it can successfully replicate important features of news-driven business cycles predicted by a large-scale theoretical model.

This paper studies the co-movement of global yield curve dynamics using a Bayesian hierarchical factor model augmented with macroeconomic fundamentals. Our data-driven approach is able to pin down the drivers of yield curve dynamics and produce plausible term premium estimates. We reveal the relative importance of global shocks through two transmission channels: policy and risk channels. Global inflation is the most important core macro fundamental affecting international yields, operating through a policy channel. Two identified global yield factors significantly influence global yield co-movements through a risk channel.

We estimate a large Bayesian time-varying parameter vector autoregressive (TVP-VAR) model of daily stock return volatilities for 35 U.S. and European financial institutions. Based on that model we extract a connectedness index in the spirit of Diebold and Yilmaz(2014)(DYCI).We show that the connectedness index from the TVP-VAR model captures abrupt turning points better than the one obtained from rolling-windows VAR estimates. As the TVP-VAR based DYCI shows more pronounced jumps during important crisis moments, it captures the intensification of tensions in financial markets more accurately and timely than the rolling-windows based DYCI. Finally, we show that the TVP-VAR based index performs better in forecasting systemic events in the American and European financial sectors as well.

This paper considers how an investor in the foreign exchange market can exploit predictive information by means of flexible Bayesian inference. Using a variety of different vector autoregressive models, the investor is able, each period, to revise past predictive mistakes and learn about important data features. The proposed methodology is developed in order to synthesize a wide array of established approaches for modelling exchange rate dynamics. In a thorough investigation of monthly exchange rate predictability for ten countries, we find that an investor using the proposed flexible methodology for dynamic asset allocation achieves significant economic gains out of sample relative to benchmark strategies. In particular, we find strong evidence for sparsity, fast model switching and exploiting the exchange rate cross-section.

This Chapter reviews econometric methods that can be used in order to deal with the challenges of inference in high-dimensional empirical macro models with possibly “more parameters than observations”. These methods broadly include machine learning algorithms for Big Data, but also more traditional estimation algorithms for data with a short span of observations relative to the number of explanatory variables. While building mainly on a univariate linear regression setting, I show how machine learning ideas can be generalized to classes of models that are interesting to applied macroeconomists, such as time-varying parameter models and vector autoregressions.

This paper proposes a variational Bayes algorithm for computationally efficient posterior and predictive inference in time-varying parameter (TVP) models. Within this context we specify a new dynamic variable/model selection strategy for TVP dynamic regression models in the presence of a large number of predictors. This strategy allows for assessing in individual time periods which predictors are relevant (or not) for forecasting the dependent variable. The new algorithm is evaluated numerically using synthetic data and its computational advantages are established. Using macroeconomic data for the US we find that regression models that combine time-varying parameters with the information in many predictors have the potential to improve forecasts of price inflation over a number of alternative forecasting models.

In this paper we model and predict the term structure of US interest rates in a data-rich and unstable environment. The dynamic Nelson–Siegel factor model is extended to allow the model dimension and the parameters to change over time, in order to account for both model uncertainty and sudden structural changes in one setting. The proposed specification performs better than several alternatives, since it incorporates additional macro-finance information during hard times, while it allows for more parsimonious models to be relevant during normal periods. A dynamic variance decomposition measure constructed from our model shows that parameter uncertainty and model uncertainty regarding different choices of predictors explain a large proportion of the predictive variance of bond yields.

This paper studies the co-movement of global yield curve dynamics using a Bayesian hierarchical factor model augmented with macroeconomic fundamentals. Our data-driven approach is able to pin down the drivers of yield curve dynamics and produce plausible term premium estimates. We reveal the relative importance of global shocks through two transmission channels: policy and risk channels. Global inflation is the most important core macro fundamental affecting international yields, operating through a policy channel. Two identified global yield factors significantly influence global yield co-movements through a risk channel.

We develop a novel, highly scalable estimation method for large Bayesian Vector Autoregressive models (BVARs) and employ it to introduce an “adaptive” version of the Minnesota prior. This flexible prior structure allows each coefficient of the VAR to have its own shrinkage intensity, which is treated as an additional parameter and estimated from the data. Most importantly, our estimation procedure does not rely on computationally intensive Markov Chain Monte Carlo (MCMC) methods, making it suitable for high-dimensional VARs with more predictors that observations. We use a Monte Carlo study to demonstrate the accuracy and computational gains of our approach. We further illustrate the forecasting performance of our new approach by applying it to a quarterly macroeconomic dataset, and find that it forecasts better than both factor models and other existing BVAR methods.

This paper compares the forecasting performance of models that have been proposed for forecasting in the presence of structural breaks. They differ in their treatment of the break process, the model applied in each regime and the out-of-sample probability of a break. In an extensive empirical evaluation, we demonstrate the presence of breaks and their importance for forecasting. We find no single model that consistently works best in the presence of breaks. In many cases, the formal modeling of the break process is important in achieving a good forecast performance. However, there are also many cases where rolling window forecasts perform well.

In this paper, we forecast EU-area inflation with many predictors using time-varying parameter models. The facts that time-varying parameter models are parameter-rich and the time span of our data is relatively short motivate a desire for shrinkage. In constant coefficient regression models, the Bayesian Lasso is gaining increasing popularity as an effective tool for achieving such shrinkage. In this paper, we develop econometric methods for using the Bayesian Lasso with time-varying parameter models. Our approach allows for the coefficient on each predictor to be: i) time varying, ii) constant over time or iii) shrunk to zero. The econometric methodology decides automatically which category each coefficient belongs in. Our empirical results indicate the benefits of such an approach.

This document contains supplementary material to the paper "On the Sources of Uncertainty in Exchange Rate Predictability". In part A we examine the ability of our models to generate economic value in a stylized asset portfolio management setting. We describe the criteria for such evaluation and the corresponding results. Part B presents figures on variance decomposition and other results associated with the BMA including time-varying coefficients at the 3-months forecasting horizon. Part C contains figures on the sources of prediction uncertainty for four currencies whose figures were omitted from the main text to conserve space (AUD, NOK, SEK, and CHF). Part D shows the recursive relative Root Mean Squared Forecast Error (RMSFE) for the Bayesian model averaging excluding and including time-varying coefficients. In part E we use predictive likelihoods to measure relative forecasting performance of the Bayesian model selection (BMS) excluding time-varying coefficients relative to BMS including time-varying coefficients. Part F reports results for additional robustness checks. We present the details regarding the estimation of the dynamic linear model that we consider in part G. Part H describes the data sources and the last part elaborates on the procedure to construct bootstrapped critical values for the DMW test.

We develop methods for Bayesian model averaging (BMA) or selection (BMS) in Panel Vector Autoregressions (PVARs). Our approach allows us to select between or average over all possible combinations of restricted PVARs where the restrictions involve interdependencies between and heterogeneities across cross-sectional units. The resulting BMA framework can find a parsi- monious PVAR specification, thus dealing with overparameterization concerns. We use these methods in an application involving the euro area sovereign debt crisis and show that our methods perform better than alternatives. Our findings contradict a simple view of the sovereign debt crisis which divides the euro zone into groups of core and peripheral countries and worries about financial contagion within the latter group.

Macroeconomists are increasingly working with large Vector Autoregressions (VARs) where the number of parameters vastly exceeds the number of observations. Existing approaches either involve prior shrinkage or the use of factor methods. In this paper, we develop an alternative based on ideas from the compressed regression literature. It involves randomly compressing the explanatory variables prior to analysis. A huge dimensional problem is thus turned into a much smaller, more computationally tractable one. Bayesian model averaging can be done over various compressions, attaching greater weight to compressions which forecast well. In a macroeconomic application involving up to 129 variables, we find compressed VAR\ methods to forecast as well or better than either factor methods or large VAR methods involving prior shrinkage.

In this paper we consider the determinants of regional disparities in unemployment rates for the UK regions at NUTS-II level. We use a mixture panel data model to describe unemployment differentials between heterogeneous groups of regions. The results indicate the existence of two clusters of regions in the UK economy, characterized by high and low unemployment rates, respectively. A major source of heterogeneity appears to be caused by the varying effect (between the two clusters) of the share of employment in the service sector, and we trace its origin to the fact that the high unemployment cluster is characterized by a higher degree of urbanization. © 2012 The Authors. Scottish Journal of Political Economy © 2012 Scottish Economic Society.

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. © Blackwell Publishing Ltd and the Department of Economics, University of Oxford 2012.

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. Databased restrictions of VAR coefficients can help improve upon their unrestricted counterparts in forecasting, and in many cases they compare favorably to shrinkage estimators.

This paper investigates global term structure dynamics using a Bayesian hierarchical factor model augmented with macroeconomic fundamentals. More than half of the variation in bond yields of seven advanced economies is due to global co-movement, which is mainly attributed to shocks to non-fundamentals. Global fundamentals, especially global inflation, affect yields through a ‘policy channel’ and a ‘risk compensation channel’, but the effects through two channels are offset. This evidence explains the unsatisfactory performance of fundamentals-driven term structure models. Our approach delineates asymmetric spillovers in global bond markets connected to diverging monetary policies. The proposed model is robust as identified factors has significant explanatory power of excess returns. The finding that global inflation uncertainty is useful in explaining realized excess returns does not rule out regime changing as a source of non-fundamental fluctuations.

This paper compares the forecasting performance of different models which have been proposed for forecasting in the presence of structural breaks. These models differ in their treatment of the break process, the model which applies in each regime and the out-of-sample probability of a break occurring. In an extensive empirical evaluation involving 60 macroeconomic quarterly and monthly time series, we demonstrate the presence of structural breaks and their importance for forecasting in the vast majority of cases. We find no single forecasting model consistently works best in the presence of structural breaks. In many cases, the formal modeling of the break process is important in achieving good forecast performance.\ud However, there are also many cases where simple, rolling window based forecasts perform well.

This paper models and predicts the term structure of US interest rates in a data rich environment. We allow the model dimension and parameters to change over time, accounting for model uncertainty and sudden structural changes. The proposed time-varying parameter Nelson-Siegel Dynamic Model Averaging (DMA) predicts yields better than standard benchmarks. DMA performs better since it incorporates more macro-finance information during recessions. The proposed method allows us to estimate plausible real-time term premia, whose countercyclicality weakened during the financial crisis.

Bayesian model averaging (BMA) methods are regularly used to deal with model uncertainty in regression models. This paper shows how to introduce Bayesian model averaging methods in quantile regressions, and allow for different predictors to affect different quantiles of the dependent variable. I show that quantile regression BMA methods can help reduce uncertainty regarding outcomes of future inflation by providing superior predictive densities compared to mean regression models with and without BMA.

This paper considers Bayesian variable selection in regressions with a large number of possibly highly correlated macroeconomic predictors. I show that by acknowledging the correlation structure in the predictors can improve forecasts over existing popular Bayesian variable selection algorithms.

We analyse the role of time-variation in coefficients and other sources of uncertainty in exchange rate forecasting regressions. Our techniques incorporate the notion that the relevant set of predictors and their corresponding weights, change over time. We find that predictive models which allow for sudden, rather than smooth, changes in coefficients significantly beat the random walk benchmark in out-of-sample forecasting exercise. Using an innovative variance decomposition scheme, we identify uncertainty in coefficients estimation and uncertainty about the precise degree of coefficients' variability, as the main factors hindering models' forecasting performance. The uncertainty regarding the choice of the predictor is small.

An expanding literature articulates the view that Taylor rules are helpful in predicting exchange rates. In a changing world however, Taylor rule parameters may be subject to structural instabilities, for example during the Global Financial Crisis. This paper forecasts exchange rates using such Taylor rules with Time Varying Parameters (TVP) estimated by Bayesian methods. In core out-of-sample results, we improve upon a random walk benchmark for at least half, and for as many as eight out of ten, of the currencies considered. This contrasts with a constant parameter Taylor rule model that yields a more limited improvement upon the benchmark. In further results, Purchasing Power Parity and Uncovered Interest Rate Parity TVP models beat a random walk benchmark, implying our methods have some generality in exchange rate prediction., Comment: 84 pages including additional appendix

In this paper, we forecast EU-area inflation with many predictors using time-varying parameter models. The facts that time-varying parameter models are parameter-rich and the time span of our data is relatively short motivate a desire for shrinkage. In constant coefficient regression models, the Bayesian Lasso is gaining increasing popularity as an effective tool for achieving such shrinkage. In this paper, we develop econometric methods for using the Bayesian Lasso with time-varying parameter models. Our approach allows for the coefficient on each predictor to be: i) time varying, ii) constant over time or iii) shrunk to zero. The econometric methodology decides automatically which category each coefficient belongs in. Our empirical results indicate the benefits of such an approach.

This paper proposes full-Bayes priors for time-varying parameter vector autoregressions (TVP-VARs) which are more robust and objective than existing choices proposed in the literature. We formulate the priors in a way that they allow for straightforward posterior computation, they require minimal input by the user, and they result in shrinkage posterior representations, thus, making them appropriate for models of large dimensions. A comprehensive forecasting exercise involving TVP-VARs of different dimensions establishes the usefulness of the proposed approach.

We use Bayesian factor regression models to construct a financial conditions index (FCI) for the U.S. Within this context we develop Bayesian model averaging methods that allow the data to select which variables should be included in the FCI or not. We also examine the importance of different sources of instability in the factors, such as stochastic volatility and structural breaks. Our results indicate that ignoring structural breaks in the loadings can be quite costly in terms of the forecasting performance of the FCI. Additionally, Bayesian model averaging can improve in specific cases the performance of the FCI, by means of discarding irrelevant financial variables during the estimation of the factor.

In this paper, we develop methods for estimation and forecasting in large time-varying parameter vector autoregressive models (TVP-VARs). To overcome computational constraints, we draw on ideas from the dynamic model averaging literature which achieve reductions in the computational burden through the use forgetting factors. We then extend the TVP-VAR so that its dimension can change over time. For instance, we can have a large TVP-VAR as the forecasting model at some points in time, but a smaller TVP-VAR at others. A final extension lies in the development of a new method for estimating, in a time-varying manner, the parameter(s) of the shrinkage priors commonly-used with large VARs. These extensions are operationalized through the use of forgetting factor methods and are, thus, computationally simple. An empirical application involving forecasting inflation, real output and interest rates demonstrates the feasibility and usefulness of our approach.

We use factor augmented vector autoregressive models with time-varying coefficients and stochastic volatility to construct a financial conditions index that can accurately track expectations about growth in key US macroeconomic variables. Time-variation in the models׳ parameters allows for the weights attached to each financial variable in the index to evolve over time. Furthermore, we develop methods for dynamic model averaging or selection which allow the financial variables entering into the financial conditions index to change over time. We discuss why such extensions of the existing literature are important and show them to be so in an empirical application involving a wide range of financial variables.

We use Bayesian factor regression models to construct a financial conditions index (FCI) for the U.S. Within this context we develop Bayesian model averaging methods that allow the data to select which variables should be included in the FCI or not. We also examine the importance of different sources of instability in the factors, such as stochastic volatility and structural breaks. Our results indicate that ignoring structural breaks in the loadings can be quite costly in terms of the forecasting performance of the FCI. Additionally, Bayesian model averaging can improve in specific cases the performance of the FCI, by means of discarding irrelevant financial variables during the estimation of the factor.

We forecast quarterly US inflation based on the generalized Phillips curve using econometric methods which incorporate dynamic model averaging. These methods not only allow for coe¢ cients to change over time, but also allow for the entire forecasting model to change over time. We find that dynamic model averaging leads to substantial forecasting improvements over simple benchmark regressions and more sophisticated approaches such as those using time varying coefficient models. We also provide evidence on which sets of predictors are relevant for forecasting in each period.

This paper builds on a simple unified representation of shrinkage Bayes estimators based on hierarchical Normal-Gamma priors. Various popular penalized least squares estimators for shrinkage and selection in regression models can be recovered using this single hierarchical Bayes formulation. Using 129 U.S. macroeconomic quarterly variables for the period 1959 – 2010 I exhaustively evaluate the forecasting properties of Bayesian shrinkage in regressions with many predictors. Results show that for particular data series hierarchical shrinkage dominates factor model forecasts, and hence it becomes a valuable addition to existing methods for handling large dimensional data.

This paper compares the forecasting performance of different models which have been proposed for forecasting in the presence of structural breaks. These models differ in their treatment of the break process, the parameters defining the model which applies in each regime and the out-of-sample probability of a break occurring. In an extensive empirical evaluation involving many important macroeconomic time series, we demonstrate the presence of structural breaks and their importance for forecasting in the vast majority of cases. However, we find no single forecasting model consistently works best in the presence of structural breaks. In many cases, the formal modeling of the break process is important in achieving good forecast performance. However, there are also many cases where simple, rolling OLS forecasts perform well.

Block factor methods offer an attractive approach to forecasting with many predictors. These extract the information in these predictors into factors reflecting different blocks of variables (e.g. a price block, a housing block, a financial block, etc.). However, a forecasting model which simply includes all blocks as predictors risks being over-parameterized. Thus, it is desirable to use a methodology which allows for different parsimonious forecasting models to hold at different points in time. In this paper, we use dynamic model averaging and dynamic model selection to achieve this goal. These methods automatically alter the weights attached to different forecasting models as evidence comes in about which has forecast well in the recent past. In an empirical study involving forecasting output growth and inflation using 139 UK monthly time series variables, we find that the set of predictors changes substantially over time. Furthermore, our results show that dynamic model averaging and model selection can greatly improve forecast performance relative to traditional forecasting methods.

The first three appendices contain details about the implementation of the estimation and forecasting of the structural break models named PPT and KP in the paper. These models are explained in Section 2 of the paper and information about the forecasting implementation of these models is presented in Section 4 of the paper. The fourth appendix contains tables that show detailed results that are summarized and discussed in Section 5 of the paper.