Causality and forecasting in incomplete systems

✍ Scribed by Guglielmo Maria Caporale; Nikitas Pittis

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 190 KB
• Volume: 16
• Category: Article
• ISSN: 0277-6693
• DOI: 10.1002/(sici)1099-131x(199711)16:6<425::aid-for657>3.0.co;2-9

✦ Synopsis

In this paper we examine how causality inference and forecasting within a bivariate VAR, consisting of yt and xt, are aected by the omission of a third variable, wt, which causes (a) none, (b) one, and (c) both variables in the bivariate system. We also derive conditions under which causality inference and forecasting are invariant to the selection of a bivariate or a trivariate model. The most general condition for the invariance of both causality and forecasting to model selection is shown to require the omitted variable not to cause any of the variables in the bivariate system, although it allows the omitted variable to be caused by the other two. We also show that the conditions for one-way causality inference to be invariant to model selection are not sucient to ensure that forecasting will also be invariant to the model selected. Finally, we present a numerical illustration of the potential losses, in terms of the variance of the forecast, as a function of the forecast horizon and for alternative parameter values Ðthey can be rather large, as the omission of a variable can make the incomplete model unstable.