A Genetic Approach to Econometric Modeling

An important problem in economics and other areas of science is finding the mathematical relationship between the empirically observed variables measuring a system. In many conventional modeling techniques, one necessarily begins by selecting the size and shape of the mathematical model. Because the the vast majority of available mathematical tools only handle linear models, this choice is often simply a linear model. After making this choice, one usually then tries to find the values of certain coefficients and constants required by the particular model so as to achieve the best fit between the observed data and the model. But, in many cases, the most important issue is the size and shape of the mathematical model itself. That is, one really wants first to find the functional form of the model that best fits observed empirical data, and, only then, go on to find any constants and coefficients that happen to be needed. Some techniques exist for doing this. We suggest that finding the functional form of the model can productively be viewed as being equivalent to searching a space of possible computer programs for the particular individual computer program which produces the desired output for given inputs. That is, one is searching for the computer program whose behavior best fits the observed data. Computer programs offer great flexibility in the ways that they compute their output from the given inputs. The most fit individual computer program can be found via a new “genetic programming” paradigm originally developed for solving artificial intelligence problems. This new “genetic programming” paradigm genetically breeds populations of computer programs in a Darwinian competition using genetic operations. The Darwinian competition is based on the principle of survival and reproduction of the fittest. The genetic crossover (sexual recombination) operator is designed for genetically mating computer programs so as to create potentially more fit new offspring programs. The best single individual computer program produced by this process after many generations can be viewed as the solution to the problem. In this paper, we illustrate the process of formulating and solving problems of modeling (i.e. symbolic regression, symbolic function identification) with this new “genetic programming” paradigm using hierarchical genetic algorithms. In particular, the “genetic programming” paradigm is illustrated by rediscovering the well-known multiplicative (non-linear) “exchange equation” M=PQ/V relating the money supply, price level, gross national product, and velocity of money in an economy.