Model Uncertainty in Panel Vector Autoregressive Models.

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 parsimonious 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.

Term Structure Dynamics, Macro-Finance Factors and Model Uncertainty

This paper extends the Nelson-Siegel linear factor model by developing a flexible macro-finance framework for modeling and forecasting the term structure of US interest rates. Our approach is robust to parameter uncertainty and structural change, as we consider instabilities in parameters and volatilities, and our model averaging method allows for investors' model uncertainty over time. Our time-varying parameter Nelson-Siegel Dynamic Model Averaging (NS-DMA) predicts yields better than standard benchmarks and successfully captures plausible time-varying term premia in real time. The proposed model has significant in-sample and out-of-sample predictability for excess bond returns, and the predictability is of economic value.

Quantile forecasts of inflation under model uncertainty

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.

A note on model uncertainty in linear regression

We consider model selection uncertainty in linear regression. We study theoretically and by simulation the approach of Buckland and co-workers, who proposed estimating a parameter common to all models under study by taking a weighted average over the models, using weights obtained from information criteria or the bootstrap. This approach is compared with the usual approach in which the 'best' model is used, and with Bayesian model averaging. The weighted predictor behaves similarly to model averaging, with generally more realistic mean-squared errors than the usual model-selection-based estimator.

UK Macroeconomic Forecasting with Many Predictors: Which Models Forecast Best and When Do They Do So?

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.

What Belongs Where? Variable Selection for Zero-Inflated Count Models with an Application to the Demand for Health Care

This paper develops stochastic search variable selection (SSVS) for zero-inflated count models which are commonly used in health economics. This allows for either model averaging or model selection in situations with many potential regressors. The proposed techniques are applied to a data set from Germany considering the demand for health care. A package for the free statistical software environment R is provided.

Disentangling the effects of key innovations on the diversification of Bromelioideae (bromeliaceae).

The evolution of key innovations, novel traits that promote diversification, is often seen as major driver for the unequal distribution of species richness within the tree of life. In this study, we aim to determine the factors underlying the extraordinary radiation of the subfamily Bromelioideae, one of the most diverse clades among the neotropical plant family Bromeliaceae. Based on an extended molecular phylogenetic data set, we examine the effect of two putative key innovations, that is, the Crassulacean acid metabolism (CAM) and the water-impounding tank, on speciation and extinction rates. To this aim, we develop a novel Bayesian implementation of the phylogenetic comparative method, binary state speciation and extinction, which enables hypotheses testing by Bayes factors and accommodates the uncertainty on model selection by Bayesian model averaging. Both CAM and tank habit were found to correlate with increased net diversification, thus fulfilling the criteria for key innovations. Our analyses further revealed that CAM photosynthesis is correlated with a twofold increase in speciation rate, whereas the evolution of the tank had primarily an effect on extinction rates that were found five times lower in tank-forming lineages compared to tank-less clades. These differences are discussed in the light of biogeography, ecology, and past climate change.

Estimating Phillips Curves in Turbulent Times using the ECB’s Survey of Professional Forecasters

This paper uses forecasts from the European Central Bank's Survey of Professional Forecasters to investigate the relationship between inflation and inflation expectations in the euro area. We use theoretical structures based on the New Keynesian and Neoclassical Phillips curves to inform our empirical work. Given the relatively short data span of the Survey of Professional Forecasters and the need to control for many explanatory variables, we use dynamic model averaging in order to ensure a parsimonious econometric speci cation. We use both regression-based and VAR-based methods. We find no support for the backward looking behavior embedded in the Neo-classical Phillips curve. Much more support is found for the forward looking behavior of the New Keynesian Phillips curve, but most of this support is found after the beginning of the financial crisis.

Forecasting the European Carbon Market

In an effort to meet its obligations under the Kyoto Protocol, in 2005 the European Union introduced a cap-and-trade scheme where mandated installations are allocated permits to emit CO2. Financial markets have developed that allow companies to trade these carbon permits. For the EU to achieve reductions in CO2 emissions at a minimum cost, it is necessary that companies make appropriate investments and policymakers design optimal policies. In an effort to clarify the workings of the carbon market, several recent papers have attempted to statistically model it. However, the European carbon market (EU ETS) has many institutional features that potentially impact on daily carbon prices (and associated nancial futures). As a consequence, the carbon market has properties that are quite different from conventional financial assets traded in mature markets. In this paper, we use dynamic model averaging (DMA) in order to forecast in this newly-developing market. DMA is a recently-developed statistical method which has three advantages over conventional approaches. First, it allows the coefficients on the predictors in a forecasting model to change over time. Second, it allows for the entire fore- casting model to change over time. Third, it surmounts statistical problems which arise from the large number of potential predictors that can explain carbon prices. Our empirical results indicate that there are both important policy and statistical bene ts with our approach. Statistically, we present strong evidence that there is substantial turbulence and change in the EU ETS market, and that DMA can model these features and forecast accurately compared to conventional approaches. From a policy perspective, we discuss the relative and changing role of different price drivers in the EU ETS. Finally, we document the forecast performance of DMA and discuss how this relates to the efficiency and maturity of this market.

Regime-Switching Cointegration

We develop methods for Bayesian inference in vector error correction models which are subject to a variety of switches in regime (e.g. Markov switches in regime or structural breaks). An important aspect of our approach is that we allow both the cointegrating vectors and the number of cointegrating relationships to change when the regime changes. We show how Bayesian model averaging or model selection methods can be used to deal with the high-dimensional model space that results. Our methods are used in an empirical study of the Fisher effect.

UK Macroeconomic Forecasting with Many Predictors: Which Models Forecast Best and When Do They Do So?

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 model as evidence comes in about which has forecast well in the recent past. In an empirical study involving forecasting output 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.

Large Time-Varying Parameter VARs

In this paper we develop methods for estimation and forecasting in large timevarying parameter vector autoregressive models (TVP-VARs). To overcome computational constraints with likelihood-based estimation of large systems, we rely on Kalman filter estimation with forgetting factors. We also draw on ideas from the dynamic model averaging literature and extend the TVP-VAR so that its dimension can change over time. 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.

Regime-Switching Cointegration

We develop methods for Bayesian inference in vector error correction models which are subject to a variety of switches in regime (e.g. Markov switches in regime or structural breaks). An important aspect of our approach is that we allow both the cointegrating vectors and the number of cointegrating relationships to change when the regime changes. We show how Bayesian model averaging or model selection methods can be used to deal with the high-dimensional model space that results. Our methods are used in an empirical study of the Fisher e ffect.

Using VARs and TVP-VARs with Many Macroeconomic Variables

This paper discusses the challenges faced by the empirical macroeconomist and methods for surmounting them. These challenges arise due to the fact that macroeconometric models potentially include a large number of variables and allow for time variation in parameters. These considerations lead to models which have a large number of parameters to estimate relative to the number of observations. A wide range of approaches are surveyed which aim to overcome the resulting problems. We stress the related themes of prior shrinkage, model averaging and model selection. Subsequently, we consider a particular modelling approach in detail. This involves the use of dynamic model selection methods with large TVP-VARs. A forecasting exercise involving a large US macroeconomic data set illustrates the practicality and empirical success of our approach.

A New Index of Financial Conditions

We use factor augmented vector autoregressive models with time-varying coefficients to construct a financial conditions index. The time-variation in the 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 FCI 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.