The Dynamic Behaviour of Canadian Imports and the Linear-Quadratic Model: Evidence Based on the Euler Equation

Robert Amano and Tony Wirjanto ()

Staff Working Papers from Bank of Canada

Abstract: We examine the ability of the simple linear-quadratic model under rational expectations to explain dynamic behaviour of aggregate Canadian imports. In contrast to authors of previous studies who examine dynamic behaviour using the LQ model, we estimate the structural parameters using the Euler equation in a limited information framework that does not require an explicit solution for the model's control variables in terms of the exogenous forcing variables. In the first stage of our two-step methodology, we find statistically stable long-run elasticities of domestic activity and relative price to be about 1.5 and -0.5 over the sample period of estimation. In the second stage, we use the parameter estimates from the first stage and estimate the Euler equation. These empirical estimates imply that adjustment costs are about 9 to 13 times more important than disequilibrium costs. In sum, we find surprisingly encouraging evidence supporting the view that the LQ model is not inconsistent with the dynamic behaviour of Canadian aggregate imports. Dans le present article, les auteurs cherchent a etablir si le modele simple de forme quadratique lineaire peut, sous l'hypothese de rationalite des attentes, expliquer le comportement dynamique de l'ensemble des importations canadiennes. Contrairement aux auteurs d'etudes anterieures, axees sur la methode quadratique lineaire, ils estiment les parametres structurels a l'aide de l'equation d'Euler en utilisant une methode du maximum de vraisemblance a information limitee qui n'exige pas que les variables de controle du modele soient explicitement resolues en fonction des variables d'impulsion exogenes. Dans la premiere des deux etapes de leur methode, les auteurs trouvent des elasticites a long terme stables sur le plan statistique oscillant autour de 1,5 pour l'activite interieure et autour de -0,5 pour les prix relatifs sur l'ensemble de la periode consideree. Dans la deuxieme etape, ils estiment l'equation d'Euler en se fondant sur les estimations des parametres obtenues a la premiere etape. Ces estimations empiriques laissent supposer que les couts d'ajustement sont de 9 a 13 fois environ plus importants que les couts de desequilibre. Somme toute, ils trouvent des resultats etonnamment encourageants validant l'hypothese que le modele de forme quadratique lineaire peut servir a formaliser le comportement dynamique de l'ensemble des importations canadiennes.

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