The Inadequacy of Testing Dynamic Theory by Comparing Theoretical Solutions and Observed Cycles

IN MODERN business-cycle research the following proceeding is being commonly used: First, a mathematical model (a determinate dynamic system) is set up, as an attempt to describe approximately the interconnections between a set of economic variables, their time derivatives, lagged values, and so on, in terms of strict functional relations. By some statistical procedure the constants in the system are estimated from the corresponding observed time series. Then the system is solved, i.e., the variables are expressed as explicit functions of time, involving the estimated parameters. The degree of conformity between these theoretical solutions and the corresponding observed time series is used as a test of the validity of the model. In particular, since most economic time series show cyclical movements, one is led to consider only mathematical models the solutions of which are cycles corresponding approximately to those appearing in the data.' This means that one restricts the class of admissible hypotheses by inspecting the apparent form of the observed time series. This condition for a good theory is of course not a sufficient one, since there are in general many different a priori setups of theory which are capable of reproducing approximately the observed cycles. But, what is more important, it may not even be a necessary condition, and its application may result in a dangerous and misleading discrimination between theories. The whole question is connected with the type of errors we have to introduce as a bridge between pure theory and actual observations. Compared with actual observations, each equation in a dynamic model splits the observed variations into two parts, one part which is explained by the equation, and another part which is not accounted for, and which is ascribed to external factors. This kind of splitting is common to all theory. We usually consider such equations as good and useful theories if, in order to get full agreement between theory and observations, it is and continues to be sufficient to allow for only relatively small and random external factors. There are two main ways in which such external factors may be