A state space approach for estimating VAR models for panel data with latent dynamic components

Abstract

Abstract: The econometric literature offers various modeling approaches for analyzing micro data in combination with time series of aggregate data. This paper discusses the estimation of a VAR model that allows unobserved heterogeneity across observation unit, as well as unobserved time-specific variables. The time-latent component is assumed to consist of a persistent and a transient term. By using a Helmert-type orthogonal transformation of the variables it is demonstrated that the likelihood function can be expressed on a state space form. The dimension of the state vector is low and independent of the time and cross section dimensions. This fact makes it convenient to employ an ECM algorithm for estimating the parameters of the model. An empirical application provides new insight into the problem of making forecasts for aggregate variables based on information from micro data. Keywords: State space models, panel vector autoregressions, random components, latent time series, maximum likelihood, Kalman filter, Helmert transformation, aggregation, prediction.