Investigating Causal Relations by Econometric Models and Cross-spectral Methods

TLDR

Deciding the direction of causality between two related variables and detecting feedback can be difficult. The study proposes testable definitions of causality and feedback using simple two‑variable models and generalizes these results with the partial cross spectrum. The authors construct measures of causal lag and strength from simple two‑variable models and extend the approach using the partial cross spectrum. The study discusses apparent instantaneous causality, attributing it to slow recording or insufficient causal variables, and shows that the cross spectrum can be decomposed into two parts each corresponding to a single causal arm of a feedback situation.

Abstract

There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recording information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalisation of this result with the partial cross spectrum is suggested.