On vector autoregressive modeling in space and time

Despite the fact that it provides a potentially useful analytical tool, allowing for the joint modeling of dynamic interdependencies within a group of connected areas, until lately the VAR approach had received little attention in regional science and spatial economic analysis. While previous attempts at integrating vector autoregressions in a spatial econometric environment can be traced back, e.g., to the Lesage and Pan (1995) and Di Giacinto (2003, 2006) contributions, the recent article by Beenstock and Felsenstein (2007) is the first to provide a systematic treatment of the topic, by introducing the SpVAR model class. This paper aims at contributing further in this field by dealing with the issues of parameter identification and estimation and of structural impulse response analysis. In particular, the adaptation of the recursive identification scheme one of the common approaches in the time series VAR literature to a space-time environment is discussed. Parameter estimation, differently from Beenstock and Felsenstein, is subsequently based on the Full Information Maximum Likelihood (FIML) method, a standard approach in structural VAR analysis. Under a recursive identification scheme, the computation of FIML estimates is shown to simplify greatly, since in this case estimation can be carried out equation by equation. However, iterative optimization routines are required when the model includes simultaneous spatial lags of the endogenous variables. As a convenient tool to summarize the information conveyed by regional dynamic multipliers with a specific emphasis on the scope of spatial spillover effects, following the approach set forth in Di Giacinto (2006) a synthetic space-time impulse response (STIR) function is introduced. Confidence bands for the STIR estimates are also derived by implementing the bootstrap method. Finally, to provide a first test of the model's empirical performance, the paper presents an application to the analysis of the relationship between export dynamics and manufacturing sector productivity growth for the set of Italian NUTS3 regions.