Forecasting with Medium and Large Bayesian VARs

This paper is motivated by the recent interest in the use of Bayesian VARs for forecasting, even in cases where the number of dependent variables is large. In such cases, factor methods have been traditionally used but recent work using a particular prior suggests that Bayesian VAR methods can forecast better. In this paper, we consider a range of alternative priors which have been used with small VARs, discuss the issues which arise when they are used with medium and large VARs and examine their forecast performance using a US macroeconomic data set containing 168 variables. We nd that Bayesian VARs do tend to forecast better than factor methods and provide an extensive comparison of the strengths and weaknesses of various approaches. Our empirical results show the importance of using forecast metrics which use the entire predictive density, instead of using only point forecasts.

Cohort effects within firms, and their implications for labour market outcomes and the business cycle

The project aims to achieve two objectives. First, we are analysing the labour market implications of the assumption that firms cannot pay similarly qualified employees differently according to when they joined the firm. For example, if the general situation for workers improves, a firm that seeks to hire new workers may feel it has to pay more to new hires. However, if the firm must pay the same wage to new hires and incumbents due to equal treatment, it would either have to raise the wage of the incumbents, or offer new workers a lower wage than the firm would do otherwise. This is very different from the standard assumption in economic analysis that firms are free to treat newly hired workers independently of existing hires. Second, we will use detailed data on individual wages to try to gauge whether (and to what extent) equity is a feature of actual labour markets. To investigate this, we are using two matched employer-employee panel datasets, one from Portugal and the other from Brazil. These unique datasets provide objective records on millions of workers and their firms over a long period of time, so that we can identify which firms employ which workers at each time. The datasets also include a large number of firm and worker variables.

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.

Large Bayesian VARMAs

Vector Autoregressive Moving Average (VARMA) models have many theoretical properties which should make them popular among empirical macroeconomists. However, they are rarely used in practice due to over-parameterization concerns, difficulties in ensuring identification and computational challenges. With the growing interest in multivariate time series models of high dimension, these problems with VARMAs become even more acute, accounting for the dominance of VARs in this field. In this paper, we develop a Bayesian approach for inference in VARMAs which surmounts these problems. It jointly ensures identification and parsimony in the context of an efficient Markov chain Monte Carlo (MCMC) algorithm. We use this approach in a macroeconomic application involving up to twelve dependent variables. We find our algorithm to work successfully and provide insights beyond those provided by VARs.