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The Demographic Effect of Mixed MarriagesAuthor(s): Fjalar FinnsSource: European Journal of Population / Revue Europenne de Dmographie, Vol. 4, No. 2(Jun., 1988), pp. 145-156Published by: SpringerStable URL: http://www.jstor.org/stable/20164474 .Accessed: 25/06/2014 03:19

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European Journal of Population 4 (1988) 145-156

North-Holland

145

THE DEMOGRAPHIC EFFECT OF MIXED MARRIAGES

Fjalar FINN?S *

Abo Akademi, Vasa, Finland

Received September 1988, final version received November 1988

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

R?sum?. L effet d?mographique des manages mixtes

Cet article formalise l'effet d?mographique des mariages mixtes, c'est-?-dire leur effet

sur le nombre d'enfants, et illustre ensuite l'effet ? long terme de ces mariages en

utilisant un mod?le simple de simulation.

1. Introduction

Social 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 from a demo

graphic point of view, too, but so far very little research has been done

in this respect. 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

* Author's address: Social Science Research Unit, Vasaesplanaden 15B, SF-65100 Vasa, Finland.

0168-6577/88/53.50 ? 1988, Elsevier Science Publishers B.V. (North-Holland)

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146 F. Finn?s / Demographic effect of mixed marriages

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.

2. The first-generation effect

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. 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.

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:

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F. Pinnas / Demographic effect of mixed marriages 147

nx = the proportion (among all Swedes who marry) of Swedish per

sons marrying Finns,

ux = the proportion of the children who are Swedish in mixed mar

riages that remain mixed,

kx = the proportion of mixed marriages in which one of the spouses

shifts to the language group of the other,

wx = the proportion of language shifts directed from the Finnish to

the Swedish language group. 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, Sb0(x), can be expressed as

Sb0(x) =

clc2x,

where cx and c2 are constants representing the total number of

marriages taking place and the number of children per marriage,

respectively. Since the total number of marriages is cv the number of Swedish

males as well as females getting married is cxx. Under the assumptions made, c1xnx of both sexes will marry a Finnish partner resulting in a

total of 1clxnx mixed marriages and cxx(l -

nx) unilingual Swedish ones. Out of the mixed marriages, 2clxnxkx become unilingual as a

result of language shifts, 2cxxnxkxwx become unilingual Swedish and

2cxxnxkx (1 -

wx) unilingual Finnish. The number of unilingual Swedish and mixed marriages are therefore ctx(l

- nx) + 2clxnxkxwx

and 2cxxnx (1 -

kx\ respectively. If mixed marriages occur, the total number of Swedish children is

therefore

Sb^x) =

clClx{{\ -

nx) + 2nxkxwx + 2nx(l -

kx)vx).

The effect of mixed marriages, i.e., the relative change in the number of Swedish children, is then

dix)=Sbl%(SX)?{X) ="?kx(2?x-l) + (l-kx)(2vx-l)).

In any given population we have to estimate the values of the functions nx, kx, wx and vx to calculate the expression for d(x). If we

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148 F. Finn?s / Demographic effect of mixed marriages

Table 1 The relative effect of mixed marriages on the number of Swedish children under different

linguistic conditions with vx =

(1 + x)/3, wx =

(1 4- 3x)/5 and nx =

(1 -

x)/2.

0.1 0.2 0.3 0.4

??5 -0.154 -0.165 -0.177 -0.188

0.10 -0.130 -0.139 -0.149 -0.158

0.25 -0.068 -0.073 -0.078 -0.083

0.50 0.000 0.000 0.000 0.000

0.75 0.023 0.024 0.026 0.028

0.90 0.014 0.015 0.017 0.018

0.95 0.008 0.009 0.009 0.010

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?s (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

= (l? x)/2\ that a proportion

wx =

(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 ?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. 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., fc = 0.3. Under the assumptions

made, we then have n01 =

0.45, i.e., 45 per cent of the Swedes marry

Finnish partners, and since v01 =

0.367, 36.7 per cent of the children in

the remaining mixed marriages becomes Swedish. Further, w0l =

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

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F. Finn?s / Demographic effect of mixed marriages 149

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.

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.

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?s (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.

3. The long-term effect

The model constructed for the mating process is based on the

assumption that all individuals can be classified as 'endogamous' or

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150 F. Finncis / Demographic effect of mixed marriages

'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.

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. 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) ball...