A Model of Intercounty Commuting

A MODEL OF INTERCOUNTY COMMUTINGf Lawrence K. Lynch* The basic purpose of this study is to develop a theory of inter-area commuting , to build a statistical model embodying the theory, and to test the model with empirical data. A related purpose is to test two hypotheses about spatial interaction offered by others. The unit of analysis is the county. This unit was selected because it is the smallest political unit for which data are regularly published. The results may be readily adapted to larger political units such as states or regions. The theory is aggregate, relating numerical flows of commuters between counties to variables which may be defined for counties, but is based on some assumptions about individual worker behavior. Previous work in the area of commuting has been either empirical, on the aggregate level, or theoretical, on the microeconomic level. In the former instance, findings have been directional—commuting tends to increase /decrease with some variable—but not quantitative (i.e., there is no information about how much commuting increases or decreases with a unit change of some variable ), and the lack of a consistent underlying theory prevents the generalization of results of studies of some places to other places not studied. Empirical studies of areas have found a consistent relationship between aggregate commuting to a given place and population, transportation facilities , and rate of economic growth. (1 ) Differences in total commuting to particular industries have been related to the kind ofindustry (manufacturing and construction attract the most commuters ) and the stability of employment in the industry (unstable employers attract the most commuters). (2) Plant size has been directly related to total commuting only when the plant was large relative to the local population, or when the plant's initial demand for labor occurred at a time of local full employment. (3) Studies of workers have shown a positive relationship between the average home-work distance and the population of the city of work. (4) Intra-city studies have shown that the densest part of the city has the widest dispersion of workers' residences. (5) With respect to industrial factors, unstable employers or plants new to an area have had the great dispersion of workers. (6) Some findings indicate that wage levels are associated with distance commuted. (7) tThis study is based upon an unpublished doctoral dissertation, A Statistical Model of lntercounty Commuting, University of Kentucky, 1966. *Dr. Lynch is Manager, Environmental Systems Group, Spindletop Research, Inc., Lexington , Ky. The paper was accepted for publication in February 1971. 10Southeastern Geographer The theoretical analyses usually have defined an optimization process for the residential location of the worker as an economic man, based on housing and transportation costs. For example, it has been hypothesized that the maximum distance from work an employee will live is that point where further savings in housing costs are not sufficient to cover additional transportation costs. (8) Even when such a theory has been verified for a group of workers, (9 ) however, it has not been possible to aggregate the variables and derive a function for total commuting between two places. Much work has been done on "gravity" or "spatial interaction" hypotheses, but the resulting models have seldom been applied to commuting, and never to intercounty commuting. Basically, a spatial interaction model relates the number or frequency of trips or other interactions (such as telephone calls, telegrams, etc. ) between two places to an attracting factor, such as population, which is divided by a friction factor, often some exponential function of the distance between the two places. (10) The lack of a theoretical basis other than an assumed metaphysical relationship between physical and human gravitation results in models which are descriptive rather than explanatory. Further, the limitation in the number of variables considered has restricted their predictive power. At present, then, there appears to be a need to pull together the results of earlier work, and develop a theoretical framework on the macroeconomic level within which the commuting flows can be studied. A THEORY OF INTERCOUNTY COMMUTING We shall assume, after Goldner, (11 ) that every worker has, surrounding his home, a "normal preference area" (hereafter abbreviated NPA). He is indifferent as to place of work within...