Carlo Giannini

A traditional interpretation of macroeconomic fluctuations: The case of Italy

Abstract In this paper a structural VAR model is built for five Italian macroeconomic variables: real output, unemployment, prices, wages and money. A statistical analysis of the series shows that these are individually integrated and jointly cointegrated: three theoretically meaningful long-run relationships are identified. The main novelty in the paper is that the identification and estimation of the Structural model are achieved combining the short-run ‘Keynesian’ restrictions specified in Blanchard (1989) with constraints on the way deviations from long-run equilibria are loaded in each equation. Impulse responses and forecast error variance decompositions are computed, using the identified structural disturbances. Their results look consistent with the subsumed economic theory and display some largely expected features of the Italian economic facts during the last two decades.

From VAR models to Structural VAR models

In this chapter we introduce the philosophy, the basic concepts and definitions of VAR analysis (sections 1.1 and 1.2). After that, in section 1.3 we discuss the problems of VAR estimation and in section 1.4 we describe the possible uses of VAR models. Then in section 1.5 we start dealing with Structural VAR analysis, pointing out the main features of the different classes of Structural VAR models, their likelihood functions (section 1.6) and their differences with respect to the standard simultaneous equations models (section 1.7). We conclude this chapter by providing examples of Structural VARs taken from the applied econometric literature (section 1.8).

Model selection in Structural VAR analysis

In this chapter we explain how to use the dominance ordering and the likelihood dominance criteria introduced by Pollack and Wales (1991) as model selection devices in Structural VAR analysis1. In section 7.1 we recall the main aspects of model selection and we connect this issue directly to the Structural VAR framework. The next two sections are devoted to explaining the above mentioned model selection criteria.

The problem of non-fundamental representations

The validity of dynamic simulation results obtained from Structural VAR model has been very strongly criticised in two recent papers (Lippi and Reichlin, 1993 and 1994). The content of this criticism is closely connected to the existence and the relevance of non fundamental MA representations (see Hansen e Sargent, 1991, ch. 4). We start this chapter by describing the content of the Lippi and Reichlin criticism. Section 8.1 is devoted to explain the notion of non fundamental representation in time series models. Section 8.2 presents some examples of economic models generating non fundamental representations and section 8.3 connects the issue of the existence of non fundamental representations to Structural VAR analysis, presenting a new way to assess the relevance of these representations in particular applications. An applied example of this procedure is contained in section 8.4.

Two applications of Structural VAR analysis

In this chapter we present the results of two different applications of Structural VAR analysis, which are intended to provide the reader with some evidence of the way in which the techniques described in this book can be concretely applied.

Impulse response analysis and forecast error variance decomposition in SVAR modelling

In this chapter we explain how to use estimated Structural VAR models to perform dynamic simulations, via impulse response analysis (section 5.1) and forecast error variance decomposition (section 5.2). After presenting the asymptotic results which are used to obtain confidence bounds around the estimated coefficient, in section 5.3 we present some discussion about the reliability of these asymptotic results in small samples.

Long-run A-priori Information. Deterministic Components. Cointegration

In practical applications of Structural VAR Modeling, the most interesting theoretical constraints on the parameter space of matrices K, C, A and B probably come from some long-run considerations (see for example Blanchard and Quah (1989) for a very simple model of the C-class).