Migration: Ravenstein, Thorntwaite, and Beyond

It is now over one hundred years since Ravenstein published his "Laws of Migration". How have these laws fared? His paper also includes a map of "Currents of Migration", not mentioned in the text. Thornthwaite also compared migration to currents, but did not follow through with this analogy. Others have used similar terminology. More recent migration studies may yield new laws. RAVENSTEIN'S LAWS Ernst Georg Ravenstein was a geographer of German extraction who worked at the Royal Geographical Society in London, and was that organization's first Victoria gold medallist. In 1885 he published a paper entitled "The Laws of Migration" in the Journal of the Statistical Society. This 1885 paper, the second and most interesting of three, includes his motivation as its first sentence (1885:167): "It was a remark of the late Dr. William Farr, to the effect that migration appeared to go on without any definite law, which first directed my attention to [the] subject...." What then are Ravenstein's laws of migration? I list here a short selection of ten, but a more definitive review would be desirable; Grigg (1977a,b) lists eleven slightly different laws: (1) “... even in the case of 'counties of dispersion', which have a population to spare for other counties, there takes place an inflow of migrants across that border which lies furthest away from the great centers of absorption”. (1885:191) (2) “The more distance from the fountainhead which feeds them, the less swiftly do these currents flow”. (1885:191) (3) [We have] “proved that the great body of our migrants only proceed a short distance”. (1885:198) (4) “In forming an estimate of displacements we must take into account the number of natives of each county which furnishes the migrants, as also the population of the ... districts which absorb them”. (1885:198) (5) “Migrants enumerated in a ... center of absorption will ... grow less with the distance proportionally”. (1885:199) (6) “The process of dispersion is the inverse of that of absorption, and exhibits similar features”. (1885:199) (7) “Each main current of migration produces a compensating counter current”. (1885:199) (8) “Counties having an extended boundary in proportion to their area, naturally offer greater facilities for an inflow ... than others with a restricted boundary”. (1885: 175) (9) [Migration streams] “sweep along with them many of the natives of the counties through which they pass [and] deposit, in their progress, many of the migrants, which have joined them at their origin”. (1885:191) (10) “Migratory currents flow along certain well defined geographical channels”. (1889:284) We can now ask what has happened to these laws in the intervening years? Have any been refuted? If so, which ones? If not, why not? Are they irrefutable tautologies? Do they still hold today? Have any been extended? If so, which ones? Have any new laws been added? If so, what are they? If not, why not? And finally, what could we do today with the 1881 census that Ravenstein did not? Is our theory, our methodology, or our technique better? Do we have better data? MODERN EVIDENCE It is not difficult to demonstrate that at least some of the laws still hold today. Again a more exhaustive investigation seems warranted and only small snippets are presented here. Consider the first of the cited laws: " ... in ... 'counties of dispersion' there [exists] an inflow ... across that border which lies furthest away ... " Here in the United States we currently (though it is in fact not new) have a concern with in-migration from Mexico. Ravenstein's law asserts that the Mexicans should have an inflow from Guatemala and this indeed seems to be the case. Or take the second and third of the laws previously cited. These describe the famous distance decay. Today we show this on log-log graphs; many examples can be found in Hägerstrand's paper of 1957, and indeed in most freshman college texts, or, e.g. Olsson (1965). We know that short distance moves predominate. The forth law includes the population of the sending and receiving places; contemporary evidence is given in Figure One, and is of course now known as Zipf's Law (Zipf 1946). The fifth and sixth laws again relate to distance decay and to the symmetry of in and out moves. We can sharpen these concepts of dispersion and absorption by using Hägerstrand's notion of a 'migration field', the intensity of which drops off with distance. This is shown in Figure Two using the in migration and out migration fields for Kansas. To the eye these cannot be distinguished from each other, as is expected for processes which are "inverse". The 1975 to 1980 US Census Bureau state-to-state migration table can be used to evaluate the seventh of Ravenstein laws as listed. As shown in the figures (Three and Four) the correlation between outgoing and incoming migrants remains high. CRITIQUES There are of course also critiques of Ravenstein's laws. For example, in the 'Age of Migration' (Castles & Miller 1993, pp. 19-21) it is asserted that Ravenstein's "... model is essentially individualistic and ahistorical." and "... government restrictions ... are ignored ...." Later the authors state that "... a push-pull model would predict movements from densely populated areas to more sparsely populated regions ...." Even if these criticisms were valid I would assert that they are not and that they reflect a superficial reading of Ravenstein's work; for example see the introductory comments on pages 241 and 242 of the paper of 1889 they do not refute any of his laws. The treatment in the migration literature as a whole is to ignore the laws, or to regard them as irrelevant. They are generally not refuted, but sometimes are considered incomplete (as in the work cited above), or not germane. I have not found any attacks on the substance of the laws as such. This again could provide an interesting area of study. THORNTHWAITE AND MIGRATION STUDIES Turning now to a somewhat different subject, Figure Five shows Ravenstein's (1885:183) fifth map, of the "Currents of Migration." This is by far the most interesting of his maps, yet there is no mention of it in the text of the paper, which seems very curious (would today's editor have noticed this and deleted it?) Yet the map must have been based on detailed study of census data. It shows mostly local moves, i.e., county to county movements. The map seems to have been completely ignored by scholars, historians, and cartographers. It is difficult to see how one could program a computer to produce this map using the kinds of statistics available today. Certainly it would be a challenge. The use of the word "currents" in the title of the map is also most extraordinary. What kind of currents are these? Ocean, electrical, atmospheric or what? It certainly suggests a fluid, with flowing phenomena. It is most curious that the literature on migration is replete with this kind of terminology. We speak of "migration flows" and "migration streams" and "countercurrents", and refer to intellectual or cultural "backwaters", as if there were eddy currents. One can be "outside of the mainstream". And there are "waves of immigration", etc. The language used in migration studies provides another challenging topic for epistemological examination. In this context the introduction to Warren Thornthwaite's monograph on migration is most interesting and revealing. Thornthwaite's reputation of course rests on his later work in climatology. He is not particularly known as a student of migration but the fifty-two page monograph from 1934 is still worth examination, and also contains challenging maps. His migration study was done while he was an assistant professor at the University of Oklahoma. He refers specifically to pressures and gradients, and I quote here his first paragraph (1934:1). "In America, as elsewhere, migration is a process which is dependent upon the establishment of means of communication between areas having different intensities of population pressure. These pressure gradients are brought about either through an increase in pressure in one area or through a decrease in another area. The relative intensity of population pressure may be increased within a given area either through a contraction of economic and social opportunities or through the continued growth of population, and may be reduced through an expansion of opportunity or through a diminution of population. Through the flow of population from regions of high pressure to regions of low pressure, the inequalities tend to be reduced. The importance of migration bears an inverse relation to the resistance, both physical and cultural, which it encounters. Physical isolation, inertia, prejudice, and ignorance are some of the factors, which inhibit more or less the freedom of movement of population. The flow of population is in a way analogous to the flow of an electric current, the mathematical expression of which appears to have some application to migration*. The amount of migration from one area to another is directly proportional to the pressure gradient between them and inversely proportional to the resistance." In the footnote (denoted by *, above) he even explicitly writes out "Ohm's law: i = E/R." He did not follow up on his use of this equation, and uses no mathematical models in the monograph. Recall also that none of Ravensteins's laws were stated in mathematical terms; Ravenstein used only the simplest form of arithmetic in his several papers. Observe further that Thornthwaite did not, in the 1930's, refer to 'spatial interaction' or 'gravity models', but he clearly understood an economic benefit argument, later picked up by economists. One of course also notes his reliance on physical concepts, perhaps reflecting his interest in climatology. Nowhere does he refer to Ravenstein's papers. In his masters thesis at the University of Washington in the 1920's Harold Hotelling did develop the pressure/gradient idea mathematically, but Thornthwaite was not aware of this work; it was not published until 1978. More recently the economist Robert Lucas expressed a view similar to that of Thornthwaite (Lucas, 1981:85), viz: "Migration is comparable to a flow of water or electricity an adjustment flow responding to pressure differentials at opposite ends of a pipeline. This view suggests that it is neither the absolute level of push nor pull factors which matters, but the existing difference in relative attraction elements." This differential attractivity model of migration is common in the economic literature, but much less favored by sociologists and political scientists. Guido Dorigo and I did (1983) relate something like Ohm's law to migration, putting migration proportional to a pressure, and inversely related to resistance. This is not the place to repeat this work except to state that it did allow us to translate many of Ravenstein's laws into equation form, and also to produce electrical (or hydrodynamic) current-like maps of migration (Tobler 1981, 1990). The 'population pressure' in our work is deduced by computation from the actual migration amounts and is not given in advance, in contrast to most other studies. The model also takes into account simultaneous two way movements. NEW EVIDENCE AND NEW LAWS To the question of new evidence and new laws of migration we must remember that Ravenstein used data from only a few censuses. Using data broken down by age classes and for multiple time periods, now available, we can extend some of his results. Whether we call them laws or simply empirical regularities seems to me immaterial. In Ravenstein and Thornthwaite's time only place-of-birth to place-of-current-residence tables were available whereas we now have place-ofprevious-residence to place-of-current-residence tables, and, in the USA, spanning fifty-five years. The brief comments given here do not constitute a through literature search for new laws, but are based on my casual reading over a decade or so. This is certainly another domain for the interested student. One of the most studied regularities is the age profile of migrants. This has been parameterized by Andrei Rogers et al (1978) and surely warrants the name of a migration "law". The rule about the similarity of the sizes of the in and out migrations also seems to hold for individual age groups (compare Figure 3.4, p. 36, of Stillwell, et al. 1991), which we should have been able to deduce. Many studies have replicated the migration age structure profile. Interzonal and intra-zonal movements show the same effect (see for example, Figure 7, p. 28 of Rees & Stillwell, 1982), as do males and females. It seems a timeless