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:
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a)
proves that the stochastic specification is neutral with respect to the model's causal structure, under an uncorrelatedness hypothesis for the error terms;
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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;
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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.
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References
Aigner D. andZellner, A., eds. (1988), Causality,A Supplement to the Journal of Econometrics.
Ancot J. P., ed. (1984),Analysing the Structure of Econometric Models, The Hague, Nijhoff.
Basilevsky A. (1983),Applied Matrix Algebra in the Statistical Sciences, North-Holland, New York.
Bentzel R. andHansen B. (1954), On recursiveness and interdependency in economic models,The Review of Economic Studies, 153–168.
Berman A. andPlemmons R. J. (1979)Non-negative Matrices in the Mathematical Sciences, Academic Press, New York.
Carlucci F. ed. (1985),Analisi della causalità e modelli economici, 2 voll. ISCO, Roma.
Dagum C. (1969), Structural permanence,Zeitschrift fur die Gesamte Staatswissenschaft, 211–235.
D'Azzo, J. J. andHoupis C. H. (1966),Feedback Control System Analysis and Synthesis, Mc-Graw Hill, New York.
Faliva M. (1983)Identificazione e stima nel modello lineare ed equazioni simultanee, Vita e Pensiero, Milano.
Faliva M. (1987),Econometria: Principi e metodi, UTET, Torino.
Faliva M. (1991), L'analisi dei modelli econometrici nell'ambito della teoria dei sistemi, in M. Faliva ed.Il ruolo dell'econometria nell'ambito delle scienze economiche, 115–126, Il Mulino, Bologna.
Faliva M. (1992), Causalità ed interdipendenza nei modelli econometrici multiequazionali,Atti della XXXVI Riunione Scientifica della Società Italiana di Statistica, 423–434, Pescara.
Fiedler M. (1986),Special Matrices and their Applications in Numerical Mathematics, Nijhoff, Dordrecht.
Gallo G. andCorsi P. (1986), Gli ordinamenti causali in econometria,Note di Informatica, IBM, Pisa.
Gilli M. (1984), CAUSOR-A program for the Analysis of Recursive and interdependent Causal Structures,Cahiers du Département d'Econométrie 84.03, Universitá de Genève.
Harary F. (1972),Graph Theory, Addison-Wesley, Reading Mass.
Harary F., Norman R. Z. andCartwright D. (1968),Introduction à la théorie des graphes orientés, Dunod, Paris.
Huggins, W. H. andEntwisle D. R. (1968),Introductory Systems and Designs, Blaidell, Waltham Mass.
Joreskog K. G. andWold H., eds., (1982),Systems under Indirect Observation, 2 voll., North-Holland, Amsterdam.
MacFarlane A. G. L. (1970),Dynamical System Models, Harrap, London.
Marimont R. B. (1969), System Connectivity and Matrix Properties,Bull. of Math. Biophysics, 255–274.
Mosbaek E. andWold H. (1970),Interdependent Systems: Structures and Estimation, North-Holland, Amsterdam.
Pasinetti L. (1965), Causalità ed interdipendenza nell'analisi econometrica e nella teoria economica,Ann. Univ. Cattolica, 233–250, Vita e Pensiero, Milano.
Shiryayev A. N. (1984),Probability, Springer-Verlag, New York.
Styan, G. P. N. (1973), Hadamard products and multivariate statistical analysis,Linear Algebra and its Applications, 217–240.
Wold H., ed. (1964a),Econometric Model Building, North-Holland, Amsterdam.
Wold H., ed. (1964b),La technique des modèles, Sciences Humaines, Monaco.
Zellner A. (1979), Causality and econometrics, in K. Brunner and A. H. Meltzer eds.,Three Aspects of Policy and Policy Making, 9–54, North-Holland, Amsterdam.
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A preliminary version of this article served as a basis for an invited lecture at the XXXVI Scientific Meeting of the Italian Statistical Society, held in Pescara in April 1992. The material includes the author's contributions to a research program partly supported by a C.N.R. (Italian Research Council) grant.
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Faliva, M. Recursiveness vs. interdependence in econometric models: A comprehensive analysis for the linear case. J. It. Statist. Soc. 1, 335–357 (1992). https://doi.org/10.1007/BF02589085
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DOI: https://doi.org/10.1007/BF02589085