Concept, Measurement, and Data in Migration Analysis

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<ul><li><p>CONCEPT, MEASUREMENT, AND DATA IN MIGRATION ANALYSISWILLIAM HAENSZEL'"</p><p>RESUMENSe discute dos metodo para computar tasas de migraci6n, uno relaciona el desplazamiento con</p><p>la poblaci6n someiida al riesgo en ellugar de origen y el otro que usa como denominador el productocruzado de la poblaci6n en los lugares de origen y de destino. Se concluye que el segundo asumeimplicitamente que los desplazamientos se originan y terminan como una variable poblacionalfortuita.</p><p>Se senalan algunas dificultades con este modele particular y el autor sugiere que deben buscarseotras perspectivas analiticas para tratar datos sobre migraci6n y en conecci6n con esto se refiere a laliteratura sobre la teoria matemdtica de las epidemias.</p><p>SUMMARYTwo metlwds of computing migration rates-one relating moves to population at risk in place of</p><p>origin and the other using as a denominator the cross-product of population in places of origin anddestination-are discussed. It is concluded that the second assumes implicitly that moves origi-nate and terminate as a random population variable.</p><p>Some difficulties with this particular model are pointed out and the author suggests that otheranalytical approaches to migration data be sought and in this connection refers to the literature on themathematical theory of epidemics.</p><p>or, more generally,,: Pi I</p><p>when several places of destination are in-volved.</p><p>of measurement for this rate can be ex-pressed as time/population"; the timedimension is introduced by specificationof the interval in which the count ofmoves was made.</p><p>A second approach follows conven-tional vital statistics practice in which therate estimates the probability of the eventin question. The migration rate in thisform is based on the familiar triad ofevent, population at risk (population atplace of origin), and period of observation.The corresponding units of measurementare time/population-s</p><p>Rate = Pr( obability) (M ii) = ~:i (2)</p><p>2 B. MacMahon, T. F. Pugh, and J. Ipsen,Epidemiologic Methods (Boston: Little, Brown &amp;Co., 1960); M. Spiegelman, Introduction toDemography (Chicago: Society of Actuaries,1955).</p><p>253</p><p>(1)</p><p>The literature on migration presents anambivalent position with respect to thecomputation and presentation of migra-tion rates. One frequently used methodrelates the number of moves (net or gross)between places of origin and destinationto the product of the respective popula-tions:'</p><p>R _MiiMiiate- PiPi '</p><p>where M represents the number of moves,the direction being indicated by the orderof subscripts, and Pi and Pi the popula-tions at origin and destination. The units</p><p>* National Cancer Institute, Bethesda, Mary-land.</p><p>1 T. R. Anderson, "Intermetropolitan Migra-tion: A Comparison of the Hypotheses of Zipf andStouffer," American Sociological Review, XX(1955), 287-91; J. Q. Stewart, "The Gravitationor Geographic Drawing Power of a College,"Bulletin of the American Association of UniversityProfessors, XXVII (1941), 70-75; H. ter Heide,"Migration Models and Their Significance forPopulation Forecasts," Milbank Memorial FundQuarterly, XLI (1963), 56-76; G. K. Zipf, "TheP1P./D Hypothesis: On the Intercity Movementof Persons," American Sociological Review, XI(1946), 677-86.</p></li><li><p>254 DEMOGRAPHY</p><p>Eldridge" has stressed the need tocalculate migration rates that relate thecount of moves to a population exposedto risk. Thomlinson4 subscribed to thislatter usage in his discussion of migrationrates, although he qualified his remarksby stating that "two base populations arenecessary when using a gravitational ap-proach or when measuring the stream ofmovement-i.e., when emphasis is on themove rather than on an area." Price" alsoaccepts the position that rate of migrationshould be expressed as a probability state-ment; the purpose of his proposed mathe-matical model would be to estimate bymultivariate techniques the contributionsof various components to the force ofmigration.</p><p>Their structure and substantive ap-plications clearly show the two rates tohave different properties, and it seemssurprising that no one has discussed therationale underlying the two divergentapproaches. The views presented herehave been shaped by work in vital sta-tistics and epidemiology, and this predis-poses me to favor equation (2) and to re-gard equation (1) with reserve. I amunder no illusion that my comments willgain acceptance from all investigators, forthe purpose is to provoke discussionwhich may cast some light on the issues.</p><p>We may begin by noting that the label"migration" had been applied to two re-lated, but different, universes of discourse-a population of "moves" and a popula-tion of "people who move." A universe of"moves" can be generated by simultane-ous classification of individuals by initialand subsequent place of residence, and the</p><p>3 H. T. Eldridge, "Primary, Secondary, andReturn Migration in the United States," Demog-raphy, II (1965), 444-55.</p><p>4 R. Thomlinson, "The Determination of aBase Population for Computing MigrationRates," Milbank Memorial Fund Quarterly, XL(1962), 356-66.</p><p>6 Price, D.O., "A Mathematical Model ofMigration Suitable for Simulation on an Elec-tronic Computer: A Progress Report," in Pro-ceedings of the International Population Confer-nee (1959), pp. 665-73.</p><p>data provide useful descriptions of popu-lation redistribution. Such results, how-ever, do not lend themselves to proba-bility statements. Probabilities can becomputed only for denumerable popula-tions at risk, whether they be people,telephone poles, or transistors. Derivativedata obtained by classification proceduresdo not necessarily lead to denumerablepopulations, and this would not appear tobe a property of the data normally avail-able on "moves."</p><p>If migration data are to be reported inrate form as probability estimates, thesole option is to report on persons makingprescribed moves. The unique relation-ship between population at risk and direc-tion of move permits consideration ofunidirectional moves only, outward fromPi. Within this framework, the proba-bility of out-migration within a fixed timeperiod from a defined population at risk atplace (Pi), expressed in equation (2), hasas its complement the probability of notmoving:</p><p>Pr(Mi , ) +Pr(Mi , ) = 1. (3)Furthermore, the probabilities of movingfrom i to j, k, l . . . are additive, sinceeach comprises a subset of admissiblemoves:</p><p>One may, of course, calculate a pooledexperience for two or more areas by sum-mation of events and population at risk inthe usual manner, taking care to defineM i j and Mji as included or excluded fromthe count of events depending on thestudy objective.</p><p>Pr(M)=Mi,+Mj , (5)Pi+Pj</p><p>Appropriate definition and estimationof the base population at risk for compu-tation of migration rates of this type havebeen discussed by Thomlinson." No com-ment is required here other than to note</p><p>8 Thomlinson, op, cit.</p></li><li><p>Concept, Measurement, and Data in Migration Analysis 255</p><p>that the distinction drawn between thenumber at risk at the beginning of an ob-servation period and the average numberat risk over a time interval has receivedmeticulous attention in the actuarial lit-erature with reference to measurements offorce of mortality.</p><p>If one is concerned with moves ratherthan with a population at risk of migra-tion, the vital statistics approach to rateconstruction offers no escape from theone-way traffic limitation just noted. Thedesire to handle data on two-way trafficand to admit the concept of net migrationundoubtedly motivated the search forother measures. The crces-product-c-Pzl",-was an obvious candidate for denomina-tor of a migration rate, given its symmetryvis-a-vis M i j and ~fji and invariant rela-tionship with direction of move. An im-portant property of PiP j has been statedby ter Heide, who introduces the notionof the universe of messages (moves)." Ifmoves are assumed to originate and termi-nate as a random population variable, thedistribution of moves originating within iand terminating within j, or vice-versa,will vary in direct proportion to PiP j </p><p>The analytical implications of Pi andPP, for measures of migration can be con-sidered in the context of how observationson migration are collected. The threemethods in general use can be cataloguedas follows:1. In an area of origin, count and trace out-</p><p>migrants.2. In an area of destination, count and classify</p><p>in-migrants by place of origin.3. For a population characterized by census</p><p>or register data, distribute individualswithrespect to residence as of two dates.1. In observations on a source popula-</p><p>tion, the distinction between moves andthe person who moves has little operation-al significance, and the two will often beidentical. The moves occur in one direc-tion, and study objectives and definitionswill determine the treatment accorded topersons who move away but subsequently</p><p>7 ter Heide, op. cit.</p><p>return. The base population and sub-groups categorized by age, sex, and otherattributes are fixed, so that the propor-tionate distribution of out-migrants withrespect to destination remains unchanged,whether the data are shown as absolutenumbers (M ih M i k, ) or as rates viadivision by Pi. As stated earlier, Mii/P idescribes the probability of an individualmoving from i to j within a stipulatedtime interval. The observations can beincorporated in new measures by intro-ducing other characteristics linked withthe move, such as distance and popula-tion size of the area of destination.</p><p>The transformed rates are useful fortests of study hypotheses (migrationvaries inversely with distance of migra-tion, number of migrants attracted to agiven destination is directly proportionalto population at terminus, and so forth).However, they no longer represent de-scriptive estimators of population parame-ters, because the latter variables are mani-festations of the event (migration) andclassification of individuals becomes pos-sible only after, and not before, the fact.</p><p>2. The investigator using place of desti-nation as the vantage point also will notfind the distinction between a "move" and"person moving" to be important in prac-tice. For any destination, the distributionof in-migrants by place of origin can bestated in absolute numbers, as a percent oftotal in-migrants, or as a ratio, Mii/Pj,without disturbing the internal relation-ships; only the form, not the substance, ofthe data is changed. While the formalarithmetic for calculating Mii/Pj andMii/Pi is the same, they have a differentlogical content. The latter, being linkedwith a population at risk, has been statedto estimate the probability that an indi-vidual from i will move to j; the formerconstitutes a relative frequency state-ment, which must be handled with cau-tion and whose range of permissible infer-ences is restricted. The difficulties can beillustrated by a parallel problem whichoften arises on review of percentage distri-butions by disease in autopsy and hos-</p></li><li><p>256 DEMOGRAPHY</p><p>pital-admission series. Does the high (low)frequency of a given disease in a seriesarise from a high (low) risk for this diseasein the underlying population, or does itreflect in part the operation of low (high)risks from other diseases?</p><p>Relative frequency ratios have descrip-tive properties in the sense that the re-sults are derived from observations onindividuals. When they are manipulatedby adjustment for distance of move, popu-lation concentrations, and so forth, weagain leave the realm of factual descrip-tion to engage in tests of consistency withpostulated models.</p><p>3. Given a population sample charac-terized by residence at two points in time,the primary frame of reference for analysiscould be either place of origin (first resi-dence) or place of destination; the re-marks in items 1 and 2 would then holdwithout change. Or, alternatively, theinformation on origin and destination con-sidered jointly can define a universe of"moves." Moves between i and j, andvice-versa, can be summed and repre-sented by a single figure (gross migration).Since moves have direction, their additionas vector quantities would cancel outmoves in opposite directions (net migra-tion). Counts of both gross and net migra-tion describe population redistribution,although neither retains all the informa-tion contained in the separate figures forM ij and M ji. Difficulties arise when theabsolute numbers are converted to rates,since the simple additive properties of theabsolute numbers no longer hold withoutrestriction. In the probability approachto rate construction, we are confronted bytwo populations at risk to two differentevents. M,j and M j, are generated, re-spectively, by Pi and P j, and there is noobvious way in which the specific informa-tion contained in Mij/Pi and Mij/Pj canbe combined into one summary figure.The step of rate computation has relatedeach individual stream of migration to itssource in a manner analogous to describ-ing the flow of a river in relation to itswatershed characteristics.</p><p>The device of relating migration to PiP jwas introduced to define a rate combininginformation on M ij and M j i This line ofattack, however, required the assumption(implied by the universe of messages de-scribed by ter Heide) that volume of mi-gration is directly proportional to thepopulations in the areas of origin and des-tination. For this a price has been paid,one not always recognized by the pro-ponents. The ratio M ii Mji/PiPj is nota descriptive estimator determined solelyby the data, since an analytical model hasbeen incorporated at the outset. Rather,it constitutes a test of the hypothesis thatmigration is a random variable propor-tionate to population. As Tolley has re-marked, "The resulting ratios should notdiffer significantly from the overall migra-tion rate in the universe under study, ifthe null hypothesis is true."!</p><p>The use of P ,Pi is essentially equivalentto the computation of expected numbersof moves for cells in a contingency tableand closely resembles the familiar x2-testfor independence of row and column ef-fects, in which expected numbers arecalculated as (A)(B)/N, where A, B, andN are the observed values for the cor-responding column, row, and total table.</p><p>This may not be immediately obvious,but the point can be elaborated as follows.Table 1 is a schematic representation of apopulation distributed by place of resi-dence at two points in time (t l and t2).While not essential for the discussion thatfollows, it may be noted that such a tablewould conceal information on interme-diate moves (return moves from j to icanceling out moves from i to j) and thuscould report on net migration only. Also,the table would normally cover only indi-viduals surviving to t2 ; allowance for mi-gration associated with terminal illnesscould be introduced by substituting resi-dence at time of death for residence at t2</p><p>a G. S. Tolley, "Migration Research in Rela-tion to Agricultural Policy," in The Farmer andMi(J1'ation in the United States (API Series No.3 [Raleigh: North Carolina State College ofAgriculture and Engineering, 1961]), pp. 14-23.</p></li><li><p>Concept, Measurement, and Datain Migration A...</p></li></ul>