On the time-varying relationship between EMU sovereign spreads and their determinants

We use a dynamic multipath general-to-specific algorithm to capture structural instability in the link between euro area sovereign bond yield spreads against Germany and their underlying determinants over the period January 1999 – August 2011. We offer new evidence suggesting a significant heterogeneity across countries, both in terms of the risk factors determining spreads over time as well as in terms of the magnitude of their impact on spreads. Our findings suggest that the relationship between euro area sovereign risk and the underlying fundamentals is strongly timevarying, turning from inactive to active since the onset of the global financial crisis and further intensifying during the sovereign debt crisis. As a general rule, the set of financial and macro spreads’ determinants in the euro area is rather unstable but generally becomes richer and stronger in significance as the crisis evolves.

Time Varying Dimension Models

Time varying parameter (TVP) models have enjoyed an increasing popularity in empirical macroeconomics. However, TVP models are parameter-rich and risk over-fitting unless the dimension of the model is small. Motivated by this worry, this paper proposes several Time Varying dimension (TVD) models where the dimension of the model can change over time, allowing for the model to automatically choose a more parsimonious TVP representation, or to switch between different parsimonious representations. Our TVD models all fall in the category of dynamic mixture models. We discuss the properties of these models and present methods for Bayesian inference. An application involving US inflation forecasting illustrates and compares the different TVD models. We find our TVD approaches exhibit better forecasting performance than several standard benchmarks and shrink towards parsimonious specifications.

Bayesian Inference in the 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 time varying parameter models which permit cointegration. Time-varying parameter VARs (TVP-VARs) typically use state space representations to model the evolution of parameters. In this paper, we show that it is not sensible to use straightforward extensions of TVP-VARs when allowing for cointegration. Instead we develop 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 a permanent/transitory variance decomposition for inflation.

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.

Model Switching and Model Averaging in Time- Varying Parameter Regression Models

This paper investigates the usefulness of switching Gaussian state space models as a tool for implementing dynamic model selecting (DMS) or averaging (DMA) in time-varying parameter regression models. DMS methods allow for model switching, where a different model can be chosen at each point in time. Thus, they allow for the explanatory variables in the time-varying parameter regression model to change over time. DMA will carry out model averaging in a time-varying manner. We compare our exact approach to DMA/DMS to a popular existing procedure which relies on the use of forgetting factor approximations. In an application, we use DMS to select different predictors in an in ation forecasting application. We also compare different ways of implementing DMA/DMS and investigate whether they lead to similar results.

Hierarchical Shrinkage in Time-Varying Parameter Models

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.

Time Variation in the Dynamics of Worker Flows: Evidence from the US and Canada

VAR methods have been used to model the inter-relationships between inflows and outfl ows into unemployment and vacancies using tools such as impulse response analysis. In order to investigate whether such impulse responses change over the course of the business cycle or or over time, this paper uses TVP-VARs for US and Canadian data. For the US, we find interesting differences between the most recent recession and earlier recessions and expansions. In particular, we find the immediate effect of a negative shock on both in ow and out flow hazards to be larger in 2008 than in earlier times. Furthermore, the effect of this shock takes longer to decay. For Canada, we fi nd less evidence of time-variation in impulse responses.

The Forward Premium Puzzle and The Euro

This paper evaluates the forward premium puzzle using the Euro exchange rate. Unlike previous studies, our analysis utilizes time-varying parameter methods and is based on two approaches for evaluation of the puzzle; the traditional approach analyzing the sensitivity of interest rate differentials to the forward premium, and the other looking into deviations from the covered interest rate parity (CIRP) condition. Then we provide evidence that the forward premium puzzle indeed became more prominent around the time of the recent crisis periods such as the Lehman Shock and the Euro crisis. This is also shown to be consistent with a deterioration in the CIRP.

Testing for Proportional Hazards with Unrestricted Univariate Unobserved Heterogeneity

We develop tests of the proportional hazards assumption, with respect to a continuous covariate, in the presence of unobserved heterogeneity with unknown distribution at the individual observation level. The proposed tests are specially powerful against ordered alternatives useful for modeling non-proportional hazards situations. By contrast to the case when the heterogeneity distribution is known up to …nite dimensional parameters, the null hypothesis for the current problem is similar to a test for absence of covariate dependence. However, the two testing problems di¤er in the nature of relevant alternative hypotheses. We develop tests for both the problems against ordered alternatives. Small sample performance and an application to real data highlight the usefulness of the framework and methodology.

Forecasting Inflation Using Dynamic Model Averaging

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 nd that dynamic model averaging leads to substantial forecasting improvements over simple benchmark regressions and more sophisticated approaches such as those using time varying coe¢ cient models. We also provide evidence on which sets of predictors are relevant for forecasting in each period.

Forecasting Inflation Using Dynamic Model Averaging

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 nd that dynamic model averaging leads to substantial forecasting improvements over simple benchmark regressions and more sophisticated approaches such as those using time varying coe¢ cient models. We also provide evidence on which sets of predictors are relevant for forecasting in each period.

Baysian Model Averaging, Learning and Model Selection

Agents have two forecasting models, one consistent with the unique rational expectations equilibrium, another that assumes a time-varying parameter structure. When agents use Bayesian updating to choose between models in a self-referential system, we find that learning dynamics lead to selection of one of the two models. However, there are parameter regions for which the non-rational forecasting model is selected in the long-run. A key structural parameter governing outcomes measures the degree of expectations feedback in Muth's model of price determination.

A New Model Of Trend Inflation

This paper introduces a new model of trend (or underlying) inflation. In contrast to many earlier approaches, which allow for trend inflation to evolve according to a random walk, ours is a bounded model which ensures that trend inflation is constrained to lie in an interval. The bounds of this interval can either be fixed or estimated from the data. Our model also allows for a time-varying degree of persistence in the transitory component of inflation. The bounds placed on trend inflation mean that standard econometric methods for estimating linear Gaussian state space models cannot be used and we develop a posterior simulation algorithm for estimating the bounded trend inflation model. In an empirical exercise with CPI inflation we find the model to work well, yielding more sensible measures of trend inflation and forecasting better than popular alternatives such as the unobserved components stochastic volatility model.

Stability of Growth Models with Generalised Lag Structures

This paper considers the lag structures of dynamic models in economics, arguing that the standard approach is too simple to capture the complexity of actual lag structures arising, for example, from production and investment decisions. It is argued that recent (1990s) developments in the the theory of functional differential equations provide a means to analyse models with generalised lag structures. The stability and asymptotic stability of two growth models with generalised lag structures are analysed. The paper concludes with some speculative discussion of time-varying parameters.

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.