Simultaneous equation models (SEMs) are composed of relations which either represent unidirectional links, which entail a causal interpretation, or bidirectional links, due to feedback loops, which lead to the notion of interdependence. The issue is of prominent interest in several respects. Investigating the causal structure of a SEM, on the one hand, brings to light the theoretical assumptions behind the model and, on the other hand, pilots the choice of the befitting estimation method and of which policy to implement. This paper provides an operational method to distinguish causal relations from interdependent ones in SEMs, such as macro-econometric models, models in ecology, biology, demography, and so forth. It is shown that the causal structure of a system crucially rests on the feedback loops, which possibly affect the equations. These loops are associated to the non-null entries of the Hadamard product of matrices encoding the direct and indirect links among the SEM dependent variables. The effectiveness of feedbacks is verified with a Wald test based on the significance of the aforementioned non-null entries. An R package, SIRE (System of Interdependent/Recursive Equations), provides the operational completion of the methodological and analytic results of the paper. SIRE is applied to a macroeconomic model to illustrate how this type of analysis proves useful in clarifying the nature of the complex relations in SEMs.
- simultaneous equations model