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<ul><li><p>European Journat of Population 4 (1988) 145-156 145 North-Holland </p><p>THE DEMOGRAPHIC EFFECT OF MIXED MARRIAGES </p><p>Fjalar FINNAS * ~4bo Akademi, Vasa, Finland </p><p>Received September 1988, final version received November 1988 </p><p>Abstract. This paper gives a formal expression for the demographic effect of mixed marriages; i.e., the effect on the number of children, and thereafter illustrates the long-term effects of these marriages with a simple simulation model </p><p>Rdsumd. L 'effet ddmographique des mariages mixtes Cet article formalise l'effet d6mographique des mariages mixtes, c'est-~-dire leur effet sur le nombre d'enfants, et illustre ensuite l'effet h long terme de ces mariages en utilisant un mod61e simple de simulation. </p><p>1. Introduction </p><p>SociM scientists have shown great interest in the study of different kinds of mixed marriages. The frequency of mixed marriages has often been considered to be the most conclusive and objective indicator of the degree of assimilation of a minority (see, e.g., Mittelbach and Moore (1968)). Mixed marriages are of great interest f rom a demo- graphic point of view, too, but so far very little research has been done in this respect. </p><p>Unless one of the two spouses joins the group to which his or her partner belongs (this is possible for example in religious groups), a mixed marriage does not by itself have any direct effect on population size. The demographic effect of the mixed marriage appears in the generations which follow, mainly via the classification of the children of such marriages into subpopulations. In the case of language groups this classification is not necessarily predetermined. In this paper, I will first derive a formal expression for the demographic effect of mixed </p><p>* Author's" address: Social Science Research Unit, Vasaesplanaden 15B, SF-65100 Vasa, Finland. </p><p>0168-6577/88/$3.50 1988, Elsevier Science Publishers B.V. (North-Holland) </p></li><li><p>146 F. Finniis / Demographic effect of mixed marriages </p><p>marriages i.e., the effect on the number of children, and thereafter illustrate the long-term effects of these marriages with a simple simula- tion model. </p><p>2. The first-generation effect </p><p>In what follows I will ignore classification problems. Further, I will consider only populations in which all individuals can unequivocally be classified according to a given variable - such as religion, citizenship, race or language. In principle the number of groups involved could be more than two, but for the sake of simplicity and clarity I shall include only two subpopulations. Transitions between the two groups are allowed but, at any given time, the classification is presumed to be (and is kept) always unequivocal. To make the presentation easier, I shall deal with the following two language groups: Finnish and Swedish. </p><p>Assume that we study a closed cohort; that the fertility of this cohort is independent of its linguistic composition, and that the proportion of its members getting married is the same regardless of the existence or non-existence of mixed marriages. The number of males and females is assumed to be equal, and there are no differences between the sexes in any respect. The children of mixed marriages could belong to either language group, but in the case of unilingual marriages they are assumed to have the same language as their parents. If there are language shifts between the different groups, they are assumed to take place at the moment of marriage. After a language shift of one of the spouses, the new homogeneous marriage is considered to be no differ- ent from the originally unilingual ones. </p><p>To study the effect of mixed marriages under the assumptions noted above, we have to keep track of the marriages that remain mixed, the language of the children in these marriages, and the frequency of the language shifts involved together with their direction. Given the fairly well-known result that the frequency of mixed marriages in a subpopu- lation is to a great extent determined by the relative size of the subpopulation (see e.g. Blau (1977)) we think it necessary to study the effect of relative subpopulation size in differing situations. From the study of the Swedish population in Finland it is also evident that the other factors may depend on the linguistic composition of the popula- tion. I shall introduce the following notations, where x (0 < x < 1) is the proportion of Swedes in the population: </p></li><li><p>F. Finn6s / Demographic effect of mixed marriages 147 </p><p>n~ = the proportion (among all Swedes who marry) of Swedish per- sons marrying Finns, </p><p>G = the proportion of the children who are Swedish in mixed mar- riages that remain mixed, </p><p>kx = the proportion of mixed marriages in which one of the spouses shifts to the language group of the other, </p><p>w~ = the proportion of language shifts directed from the Finnish to the Swedish language group. </p><p>To study the effect of mixed marriages we have to compare the number of children in a cohort where mixed marriages occur, with one in which only unilingual marriages take place. In the latter case the number of Swedish children, Sbo(X), can be expressed as </p><p>Sb o (x) = c lc2 x, </p><p>where c 1 and c 2 are constants representing the total number of marriages taking place and the number of children per marriage, respectively. </p><p>Since the total number of marriages is Cl, the number of Swedish males as well as females getting married is ClX. Under the assumptions made, qxn~ of both sexes will marry a Finnish partner resulting in a total of 2qxn~ mixed marriages and qx(1 - nx) unilingual Swedish ones. Out of the mixed marriages, 2qxnxk ~ become unilingual as a result of language shifts, 2clxn~kxw ~ become unilingual Swedish and 2cxxn:~k~ (1 - wx) unilingual Finnish. The number of unilingual Swedish and mixed marriages are therefore qx(1 - n~) + 2Caxn~k~w x and 2qxnx (1 - k~), respectively. </p><p>If mixed marriages occur, the total number of Swedish children is therefore </p><p>Sb l (X) = ClC2X((1 -- nx) + 2nxkxw~ + 2n~(1 - kx)G) . </p><p>The effect of mixed marriages, i.e., the relative change in the number of Swedish children, is then </p><p>d(x )= Sba(x) - Sb(x) Sbo(x) =n~(kx(Zw~- l )+(1-k~) (ZG-1) ) </p><p>In any given population we have to estimate the values of the functions n:~, kx, wx and G to calculate the expression for d(x). If we </p></li><li><p>148 F. Finniis / Demographic effect of mixed marriages </p><p>Tab le 1 </p><p>The re la t ive e f fect o f mixed marr iages on the number o f Swed ish ch i ld ren under d i f fe rent </p><p>l ingu is t ic cond i t ions w i th v x = (1 + x ) /3 , w x = (1 + 3x) /5 and n ~ = (1 - x ) /2 . </p><p>x k </p><p>0.1 0.2 0.3 0.4 </p><p>0.05 - 0 .154 - 0.165 - 0.177 - 0.188 </p><p>0.10 - 0 .130 - 0 . I39 - 0.149 - 0.158 </p><p>0.25 - 0.068 - 0.073 - 0.078 - 0.083 </p><p>0.50 0.000 0.000 0.000 0.000 </p><p>0.75 0.023 0.024 0.026 0.028 </p><p>0.90 0.014 0.015 0.017 0.018 </p><p>0.95 0.008 0.009 0.009 0.010 </p><p>study not just one, but several populations under widely varying conditions, it may be necessary to estimate their entire functional forms. This was the case in the study of the Swedish population in Finland, since the Swedish proportion of the total population varies very much in the different municipalities (Finn~is (1986)). To illustrate the magnitude of the expression d(x), I will now present some calcula- tions for different linguistic situations and varying proportions of language shifts. To make the assumptions about the functions realistic, I have based them on the results from the Finnish study. I assume that the proportion intermarrying is nx - - (1 - x) /2; that a proportion w x --(1 + 3x)/5 of the language shifts is directed from Finnish to Swedish, and that the Swedish proportion of the children in the remaining mixed marriages is v x = (1 + x)/3. The frequency of lan- guage shifts is assumed to be independent of the linguistic conditions, i.e., kx = k. Note that these assumptions imply that the language groups in question are equal in the sense that the outcome is indepen- dent of which group makes up the majority. </p><p>Now let us look at the situation where the Swedes are one tenth of the whole population, and there are language shifts in 30 per cent of the originally mixed marriages, i.e., k = 0.3. Under the assumptions made, we then have n0.1 = 0 .45 , i.e., 45 per cent of the Swedes marry Finnish partners, and since v0.1 = 0.367, 36.7 per cent of the children in the remaining mixed marriages becomes Swedish. Further, w0.1 -- 0.26, which means that 26 per cent of the language shifts take place from the Finnish to the Swedish language group. Taken together, the effect of the mixed marriages is a reduction of the number of Swedish children by 14.9 per cent. With language shifts in 40 per cent of the mixed </p></li><li><p>F. Finniis / Demographic effect of mixed marriages 149 </p><p>marriages, the number of Swedish children is reduced by a total of 15.8 per cent. Out of this total reduction, 7.2 per cent is the result of the marriages that remain bilingual, while the rest, or 8.6 per cent, arise from the marriages in which language shifts among the parents occur. These figures show that if we are interested in the total effect of mixed marriages, and if transitions between the groups are possible, then it is of decisive importance to start from the contracted marriages instead of studying the remaining mixed marriages only. </p><p>Although the effect for both groups is of equal size in absolute figures, the relative effect is much smaller for the majority. The reduction of 15.8 per cent mentioned above corresponds to an increase of only 1.8 per cent for the majority. Another result of the shift in favour of the majority is that the Swedish proportion of all children is reduced to 8.4 per cent. </p><p>The expression for the total effect presented above is based on a comparison of the number of children in a cohort in which mixed marriages occur with the number in a situation where all the contracted marriages are unilingual. For that reason this effect may be called a first-generation effect. If we regard mixed marriages as part of an assimilation process, it is also interesting to study the effect in a long-term perspective. We should then be aware of the fact that the effect presented above may change from one generation to the next. Note first that even in a closed population, the relative sizes of the subpopulations will probably change, as an effect of the mixed mar- riages. Note also, at least for religious (Thomas (1951)) and language groups (Finn~is (1982)), that persons with a homogeneous background tend to choose their partners more endogamously than do persons with a heterogeneous background. This means that the function nx, intro- duced before, will change in successive generations, and that the effect of mixed marriages will accumulate. One way of studying how the function nx, as well as the total effect d(x), changes is to specify a model for the mating process, and to study consequent developments in successive generations. In the next section, I give a short presentation of such a model and the main results obtained from its use. </p><p>3. The long-term effect </p><p>The model constructed for the mating process is based on the assumption that all individuals can be classified as 'endogamous' or </p></li><li><p>150 F. Finniis / Demographic effect of mixed marriages </p><p>'exogamous' with respect to their behaviour in the mate selection process. 'Exogamous' persons are assumed to select their partners randomly, ignoring the factor of language, while a marriage between two 'endogamous' persons from different groups is taken to be impossi- ble. This means that 'endogamous' persons choose their partners only among persons from their own language group and among 'exogamous' persons from the other one. A much more easily understood descrip- tion is obtained in our case if we replace the terms 'endogamous' and 'exogamous' by 'unilingual' and 'bilingual', respectively, thus taking into account actual ability to use language. The model then implies that mate selection is done randomly as regards language; the combination ' unilingual Swedish' and 'unilingual Finnish' being considered impossi- ble. The process is assumed to be independent of age and sex, and all the persons are assumed to be equally active in the marriage market. </p><p>Family background enters the model through the classification of individuals as 'endogamous' or 'exogamous'. I assume that all persons with a heterogeneous background and a certain proportion of those with a homogeneous background are 'exogamous', while the rest of the latter group is 'endogamous'. Further, the division of persons with a homogeneous background into 'endogamous' and 'exogamous' is as- sumed to be dependent on the relative sizes of the subpopulations. </p><p>The mate selection process under discussion can also be described mathematically as an urn model with two urns. Assume that we have one urn with blue (men) balls and one with red (women) ones. In both urns the balls have a number, 1, 2, 3 or 4, corresponding to 'endoga- mous Swedish', 'exogamous Swedish', 'exogamous Finnish' and 'endo- gamous Finnish', respectively. For every pair to be formed we first pick an urn at random, and then draw a ball (a 'suitor', who may be a female) from it also at random. From the other urn we draw another ball at random. If the two balls form a forbidden combination (1-4 or 4-1), the latter ball is put back into the urn, and a new ball is drawn from it. We continue until a permitted pair is obtained. This pair of balls is put aside before we start to form a new pair. If it is impossible to find a permitted 'partner' for a given 'suitor', the ball corresponding to the latter has to be put back and we have to draw another one instead. The process terminates when new permitted pairs cannot be formed, or when a predetermined proportion of" the balls has been drawn. </p><p>The urn model is simple, though no explicit mathematical expression </p></li><li><p>F. Finniis / Demographic effect of mixed marriages 151 </p><p>for the expected outcome of the process has yet been found. In principle we can cMculate the expected outcome recursively, but this requires an enormous amount of computer resources in practice. Another and much simpler method is to simulate the process, and that is what I have done. </p><p>Although I have simulated the mate selection process in stochastic fashion, all the other calculations measuring the effect of mixed mar- riages are deterministic. I started from the outcome of the process, i.e., the number of marriages (pairs) of different combinations, and as- sumed that the number of children was independent of the linguistic composition of the marriage. Language shifts are permitted, and the language of the children in the remaining mixed marriages is de- termined by a function G. Assuming that children choose partners of their own generation, and that this happens according to the same pattern as their parents, it is possible to study how the effect of mixed marriages changes in successive generations as the result of changes in the composition of t...</p></li></ul>