Hierarchical shrinkage priors for dynamic regressions with many predictors

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.Forecasting; shrinkage; factor model; variable selection; Bayesian LASSO

Assessing the Transmission of Monetary Policy Shocks Using Dynamic Factor Models

This paper extends the current literature which questions the stability of the monetary transmission mechanism, by using a Dynamic Factor Model with time-varying parameters, which allows fast and efficient inference based on hundreds of explanatory variables. Different specifications are compared where the factor loadings, VAR coefficients and error covariances may change gradually in every period or be subject to small breaks. The model is applied to 157 post-World War II U.S. quarterly macroeconomic variables. The most notable changes were in the responses of real activity measures, prices and monetary aggregates, while other key indicators of the economy remained relatively unaffected.Structural FAVAR, time varying parameter model, monetary policy

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.Forecasting; variable selection; time-varying parameters; Bayesian vector autoregression

A new index of financial conditions

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 model’s 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

Machine Learning Macroeconometrics A Primer

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

Forecasting Inflation Using Dynamic Model Averaging

There is a large literature on forecasting inflation using the generalized Phillips curve (i.e. using forecasting models where inflation depends on past inflation, the unemployment rate and other predictors). The present paper extends this literature through the use of econometric methods which incorporate dynamic model averaging. These not only allow for coefficients to change over time (i.e. the marginal effect of a predictor for inflation can change), but also allows for the entire forecasting model to change over time (i.e. different sets of predictors can be relevant at different points in time). In an empirical exercise involving quarterly US inflation, we fi…nd that dynamic model averaging leads to substantial forecasting improvements over simple benchmark approaches (e.g. random walk or recursive OLS forecasts) and more sophisticated approaches such as those using time varying coefficient models.Option Pricing; Modular Neural Networks; Non-parametric Methods

On Regional Unemployment: An Empirical Examination of the Determinants of Geographical Differentials in the UK

This paper considers 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, characterised by high and low unemployment rates respectively. A major source of heterogeneity seems to be caused by the varying (between the two clusters) effect of the share of employment in the services sector, and we trace its origin to the fact that the “high unemployment” cluster is characterised by a higher degree of urbanization.distribution dynamics, regional labour markets, unemployment differentials

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.Bayesian, state space model, factor model, dynamic model averaging

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 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.Bayesian, State space model, Phillips curve