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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