ON THE EXISTENCE OF MACRO VARIABLES AND OF MACRO RELATIONSHIPS

A common practice is to restrict the implied definition of a macro var iable to an aggregate of micro components. Using such a definition, th e aggregation problem is to determine when one can interpret macro coe fficient estimates in terms of micro economic theory and when one can recover micro coefficients from macro estimates. In this paper it is a rgued that a more useful abstract definition of a macro variable is in terms of properties of dynamical systems as a whole; such a definitio n may include aggregates of micro components as relevant macro variabl es, but they are not necessarily included and system-wide variables ar e included in this definition. The idea of macro variables and their r elationships is claimed to be more complex than a mere aggregation of micro components. An operational definition of a macro variable is giv en that defines macro relationships as well. The operational definitio n is based on examining the time variation of the transitional probabi lities of system variables. One practical conclusion is that in many c ases an analysis of a system variable, such as mean income or consumpt ion, may require examining the variances of those variables simultaneo usly. More precisely, even to a first order of approximation the time varying variances are of equal importance to the time varying means an d one must estimate the interactive effect of both together. Further, the results in this paper suggest a deep relationship between the ubiq uitous observance of ARCH processes and the nonlinearity in the Fokker -Planck equation that approximates the time variation in the probabili ty densities of macro variables.