Econometric analysis of causality.

Summary We study the causality between time series from an econometric point of view. As such, we adopt the characterization proposed by Feigl (1953) who characterizes causality as a property, experimentally confirmed, of improved forecasting, in accordance with laws that define the economic frame of reference of the analysis. We approach the analysis of causality as an impulse analysis, considering two notions of impulse, deterministic and stochastic, characterized respectively as modifications of the initial conditions (or average characteristics of the dynamics) and canonical innovations. We show that causality, characterized in terms of improved forecasting at all horizons, (Lütkepohl (1990) can be analyzed by studying the propagation of deterministic impulses. We formalize precisely the notion of indirect unidirectional link and give a necessary and sufficient condition to exclude all direct and indirect causal links between two series extracted from a stationary VAR model. The effects of stochastic impulses are characterized, following the principles advocated by Sims (1980) and are associated with the characterization of causality in the sense of this author. When we study persistent causality between integrated series, we choose to analyze this property by developing a stochastic impulse analysis, because persistence is stochastic in nature. The formalization of persistent causality that we adopt can be interpreted in terms of improved forecasting over an infinite horizon, which allows us to finally propose a causal reading.