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.

Age, Life-satisfaction, and Relative Income – Insights from the UK and Germany

We first confirm previous results with the German Socio-Economic Panel by Layard et al. (2010), and obtain strong negative effects of comparison income. However, when we split the sample by age, we find quite different results for reference income. The effects on lifesatisfaction are positive and significant for those under 45, consistent with Hirschman’s (1973) ‘tunnel effect’, and only negative (and larger than in the full sample) for those over 45, when relative deprivation dominates. Thus for young respondents, reference income’s signalling role, indicating potential future prospects, can outweigh relative deprivation effects. Own-income effects are also larger for the older sample, and of greater magnitude than the comparison income effect. In East Germany the reference income effects are insignificant for all. With data from the British Household Panel Survey, we confirm standard results when encompassing all ages, but reference income loses significance in both age groups, and most surprisingly, even own income becomes insignificant for those over 45, while education has significant negative effects.