Origin of cyclical fluctuations in econometric models

This paper is a contribution to the analysis of stochastic dynamics of linear econometric models. two topics concerning the cyclical components of the endogenous variables are considered: recent publications deal with the problem of neglecting the influence of the disturbance terms on endogenous variables in econometric models. their main point is to show that additional cycles are often generated in econometric models by the autoregressive transformation of the error variables which are not taken into account in the procedure of forecasting. in this paper these investigations are extended and the relative magnitude of the neglected error influence with reference to the endogenous variables is demonstrated. as an example a modified klein i model for the u.s. economy with a sample period from 1921 to 1967 is used. the second question of interest concerns the business cycle component of the endogenous variables. another reason for its origin is the business cycle of the exogenous variables and their transformation by the econometric model, respectively. investigations can be made as to which exogenous variables generate business cycle components of extraordinary magnitude and whether they have a compensating effect on each other. this question is of a special relevance from the point of view of economic policy because of the potential dampening effect by the instrumental variables. the mathematical instrument for this research is the theory of linear transformations of stationary processes in the frequency domain. we partition the auto spectrum of the stationary part of the endogenous variables (which contains among others the business cycle) and analyse the components with respect to their originby the exogenous variables and error terms, respectively. strictly speaking the theory of stationary processes can be applied only to the forecast with the exogenous variables alone (i.e. without taking into consideration the correlation structure of the error process). it shall be shown, however, that this forecast approaches relatively soon the forecast with the reduced form, usually applied in econometrics. as we do not deal here with the statistical aspect of the problem we assume the estimated parameters of the model and of the exogenous process to be "true".;