Recursiveness vs. interdependence in econometric models: A comprehensive analysis for the linear case

Summary

The paper gives an explicit solution to the problem of determining the causal structure of linear multi-equation econometric models.

In a deterministic context the paper establishes a decomposition of the coefficient matrix, weighting the right-hand side endogenous variables, into complementary terms highlighting the recursive and the interdependent mechanisms of the model.

In the Gaussian case, the article:

• a) proves that the stochastic specification is neutral with respect to the model's causal structure, under an uncorrelatedness hypothesis for the error terms;

• b) shows the mechanisms by which the disturbance correlation pattern may interfere with the underlying systematic connections among variables, possibly altering the system's causal structure;

• c) provides a decomposition of the coefficient matrix related to the systematic causal chains, which leads to detect the actual recursive links in a stochastic context, on the one hand, and the correlation-induced loops, on the other.