The Dynamic Household as a Logical Concept and Its Use in Demography

The Dynamic Household as a Logical Concept and Its Use in DemographyAuthor(s): Mike MurphySource: European Journal of Population / Revue Européenne de Démographie, Vol. 12, No. 4(Dec., 1996), pp. 363-381Published by: SpringerStable URL: http://www.jstor.org/stable/20164784 .

Accessed: 28/06/2014 12:10

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

Springer is collaborating with JSTOR to digitize, preserve and extend access to European Journal ofPopulation / Revue Européenne de Démographie.

http://www.jstor.org

This content downloaded from 91.220.202.141 on Sat, 28 Jun 2014 12:10:41 PMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=springer

http://www.jstor.org/stable/20164784?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


European Journal of Population 12: 363-381,1996. 363

? 1996 Kluwer Academic Publishers. Printed in the Netherlands.

The Dynamic Household as a Logical Concept and

its Use in Demography

MIKE MURPHY Population Studies, London School of Economics, Houghton Street, London WC2A 2AE, UK

Received 4 January; accepted in final form 9 July 1996

Murphy, M. 1996, The dynamic household as a logical concept and its use in demography, European Journal of Population. Revue Europ?enne de D?mographie, 12: 363-381.

Abstract. Event history models for aggregate units such as households are complicated by the fact

that such entities do not have a well-defined identity through time.The difficulties of applying conven tional transition-based models to household change are discussed. More generally, what constitutes

'time' and 'change' are also considered. It is argued that many changes occurring within households

such as leaving home are better-considered as 'fuzzy' than crisp phenomena. An alternative perspec tive based on household change considered as an evolving network is proposed. The implications for

sample designs which are designed to track explicit household dynamics (such as the Panel Study on Income Dynamics) are discussed. The ways in which particular forms of analysis come to dominate

the scientific literature, including those for analysing household change is discussed in relation to non-linear dynamic models. Finally, it is argued that there would be considerable benefits if insights available from the physical, mathematical and biological sciences were to be more widely incorpo rated within technical demography.

M. Murphy, 1996. Le M?nage en dynamique comme concept logique et son utilisation en d?mographie.

European Journal of Population. Revue Europ?enne de D?mographie, 12: 363-381.

R?sum?. Les mod?les d'analyse biographique d'unit?s agr?g?es, telles que les m?nages, sont com

plexes, car ces entit?s ne peuvent ?tre d?finies avec pr?cision au cours du temps. Nous discutons ici

les difficult?s d'appliquer les mod?les habituels bas?s sur des transitions, aux changements connus

par les m?nages. Plus g?n?ralement, nous analysons ce qui constitue ?le temps? et le ?change ment?. Nous montrons ainsi que de nombreux changements connus par les m?nages, tels que la

d?cohabitation, sont mieux saisis comme des ?v?vements ?flous? plut?t que comme des ?v?nements

ponctuels. Nous proposons d?s lors une autre perspective, bas?e sur les changements survenus dans

des r?seaux en ?volution. Nous en discutons les implications sur les m?thodes d'?chantillonnage destin?es ? tracer l'?volution explicite des m?nages (telles que l'?tude par panel sur l'?volution des revenus). Les fa?ons selon lesquelles certaines formes d'analyse en viennent ? avoir une position dominante dans la litt?rature scientifique, y compris celles qui permettent l'analyse des changements dans les m?nages, sont discut?es en liaison avec les mod?les dynamiques non-lin?aires. Finalement, nous montrons qu'il y a des avantages importants ? ce que des approches suivies dans les sci

ences physiques, math?matiques et biologiques, soient plus largement introduites dans les techniques

d'analyse d?mographique.



364 MIKE MURPHY

1. Introduction

While demographers have a (possibly deserved) reputation for keeping 'close to

the data' (Bumpass, 1991, p. 177), nevertheless the topic of household1 change raises more fundamental issues than those simply of measurement. In this paper, I

will attempt to go beyond the orthodox approach to this topic, which is based on the

individual as the unit of analysis and in which changes in the household position and status of these individuals are analysed using mainstream demographic and

statistical approaches such as life table and hazards models (Willekens, 1988). I will concentrate on some of the logical and practical issues which arise when

analysing household change by drawing on work not only in the social but also

in the physical and biological sciences, philosophy and mathematics to give some

insights into the processes of change in households, although some of the linkages are inevitably speculative.2 The following topics will therefore be discussed:

the difficulties in defining 'longitudinal' households, and insights which may be obtained into this topic by applying similar ideas to the individual

how widely-used basic concepts such as 'change' and 'time' have been analysed in other disciplines, and some of difficulties which have been encountered

many demographic processes are analysed by being considered as well-defined

transitions between states, but this is frequently a simplification and there

may be a need for fuzzy rather than sharp classifications for many aspects of

household change the sampling strategies for maintaining representative household structures

over time in surveys and issues of representativeness including self-similarity the ways in which the current emphasis on the use of survey data for the

analysis of household change has arisen may be similar to the ways in which

particular technologies have come to dominate other markets.

In later sections these will be discussed in more detail, but in order to introduce

some of the ideas, I will start by considering the one demographic entity which

is usually considered as well-defined and which forms the building block of the

household, namely the individual, in order to show that even here there are some

fundamental issues of definition which have direct analogies with those in the study of households. The individual for demographic purposes has been definfed by Franz

Willekens (quoted in Carey, 1993, p. 5) as '... a single organism that is a carrier of

demographic attributes'.3 While it is not a major topic of interest in demography, what constitutes 'a person' has attracted the attention of philosophers and physical

scientists; indeed it forms one of their most basic questions:

What is it that gives a particular individual his personal identity? Is it, to some

extent, the very atoms that compose his body? Is his identity dependent upon the particular choice of electrons, protons, and other particles that compose those atoms? There are at least two reasons why this cannot be so. In the first

place, there is a continual turnover in the material of any living person's body. This applies in particular to the cells in a person's brain, despite the fact that



THE DYNAMIC HOUSEHOLD AS A LOGICAL CONCEPT AND ITS USE IN DEMOGRAPHY 365

no new actual brain cells are produced after birth. The vast majority of atoms

in each living cell (including each brain cell) -

and, indeed, virtually the entire

material of our bodies - has been replaced many times since birth (Penrose

1989, pp. 31-32).

This quotation from Sir Roger Penrose serves to emphasise that the apparently well-defined idea of an 'individual' is more fragile than usually assumed; 'house

hold' is obviously a less clear-cut concept, but there are some analogies with the

previous discussion.4 If we were to substitute'persons' for 'atoms' and 'household'

for 'person's body/brain' in the quotation above, then we would have the situation

where we can envisage people moving in and out of a particular household which

although changing in its composition, nevertheless remains well-defined through time (in an analogous way as an individual does).5 By the same argument that a

person is not a simple aggregation of his or her constituent parts, but rather defined

by the linkages between them which lead to structures qualitatively different and

more complex than those of the individual elements (emergent properties in biolog ical terminology) the household is more than the aggregation of its members, and

overall life course experience is more than the aggregation of a series of unrelated

changes.6 Much - possibly too much - of modern demographic analysis is based

either on the individual as the unit of analysis, often using micro-level survey data, rather than on entities which relate to aspects of the wider physical and social

environment7 or on abstractions which refer to no real individual or group (how ever much period measures such as TFR or expectation of life at birth might appear to do so to the unwary; indeed the primacy of such measures has been advocated

in a sophisticated way by Ni Bhrolch?in, 1992). While tracking a particular individual through time is possible (although Penrose

(1989) gives a number of examples where this might not be the case in future), this

does not mean an end to all problems. One example is an individual's response at a particular time to a question such as 'What job would you like to do?'.

The two hemispheres of the brain are sometimes separated (severing of the corpus callosums is sometimes done as a form of treatment for particularly severe forms of

epilepsy), and in one such case where both halves of the brain were able to respond

independently (the right hemisphere cannot usually do so, but in this case it appears to have taught itself), the two halves had different likes and desires: the left wanted

to be a draughtsman, the right to be a racing driver! (Reported in Penrose, 1989,

p. 498: an extended discussion of this multiple personality syndrome is given by

Dennett, 1991.) Thus in this apparently exceptional case, the assumption of being able to collect a response to such a question for one individual through time is not

valid: to put it simply, is there one person or two inside that brain? Once more, the

analogy with household change may be made: for example, if a two-child couple

separates, each keeping one child, then does the previous household still exist and

if so, are there two new distinct households, or some other situation? These two

new households comprise the same people as the former single household, but are



366 MIKE MURPHY

they like the severed brain referred to above? And, if so, how should we analyse

change through time in households in general? To illustrate such problems, the following situations could be considered. Does

the same household (or family in some cases) remain if:

i. a family has a lodger living with it; the lodger leaves but is replaced by another

one?

ii. in a family with children, one child leaves home?

iii. in a lone parent family with one child, the child leaves home?

iv. in a two-parent family with two children, one partner leaves?

v. as case iv., but one child remains with each partner? vi. the members of the household move as a group to a new address?

. Thus without some additional conditions it is impossible to use the household

as the unit of analysis across time (Macmillan and Herriott, 1985; Murphy, 1995). Of course there is always the possibility of analysing change in households, or

other variables, at the macro-level. One could relate, for example, the proportion of

one-person households in a population across time or space to variations in overall

demographic structure, cultural attitudes or income levels, but such macro-level

approaches hold in more general situations and refer only to that level, so they will

therefore not be considered here.

Since the principal focus of this paper is in the conceptual basis of household

change through time, we need to consider whether it is necessary to analyse house

hold change in terms of discrete transitions between household states experienced

by individuals, the conventional widely-used approach to formal demographic

analysis in this area and whether alternative approaches may also provide useful

insights. Before doing so, the idea of 'change' will be considered.

'Change' considered

'Change' refers to some measurable difference at two points of time. None of

measurable, time midpoint are straightforward concepts.8 'In social science, time

remains a largely unmapped terrain' and that in general, social science has 'devel

oped little in the way of a coherent theory of time' (Toffler, 1984, p. xviii), apart from anthropology, where the substantial differences in concepts of time between

different cultures, including those of linear and cyclical time is acknowledged

(Gell, 1992). However, the main authors of the Volume in which the quotation above appears in the Introduction, state that there is a 'conflict between the atem

poral view of classical science and the time-oriented view that prevails in a large

part of the social sciences and humanities' (Prigogine and Stengers, 1984, p. xxviii). The household/family is the primary unit of reproduction and socialization, and

forms the main mechanism for transmitting not only biological (genetic) DNA,

but also 'cultural DNA' (Gell-Mann, 1994), and its interaction with time has been

of interest to anthropologists, in both historical and developing country studies

(Greenhalgh, 1995). Work by historians who have been largely responsible for the




development of life course approaches (Elder, 1978) have also been sensitive to

the interplay between historical time, individual ageing and living arrangements.

Although the household was regarded as only of minimal interest until the early

1960s, since that time it has attracted considerable attention (Netting et al., 1984). Jack Goody and Meyer Fortes (1958) emphasised the idea of the developmental group, a pattern of states through the individual moves and indeed one which has

resonances with the work of Seebohn Rowntree in York around 1900 (Murphy,

1995). These ideas of the interaction between individual, household in time and

space have been refined by studies of diverse populations, such as in historical

England (Laslett, 1972) and Serbia (Hammell, 1972; Halpern and Wagner, 1984), and a contemporary developing country, Botswana (Townsend, 1996). Halpern and

Wagner (1984) explicitly use a framework which combines the formulation of time

as linear (historical) which is used to mark changes in variables such as fertility and mortality, and cyclical which marks processes such as the replacement of one

generation by its successors. The idea that time has both linear and cyclical aspects, the latter reflected also in the recurrent patterns of day and night and the seasons,

is one which is deeply ingrained in human thought. While this study represents a

particularly insightful analysis of different frameworks of time in relationship to

family change, the empirical analysis is based on cross-sectional measures relating to household and kinship distributions at given historical points of time.

Demography provides a particularly suitable starting point for attempting to

develop and synthesise some of these issues. It has probably as basic an interest

in the passage of time as any social science (Vilquin, 1994). Although subject to qualification in recent decades, demographic transition theory, which many consider to be its intellectual core, is temporal in nature, as are its two major technical underpinnings, the balancing equation and Lexis diagram.

While some demographers may regard some of these issues as esoteric, data

quality is a key concern of the discipline, and it must be acknowledged that there

are theoretical as well as empirical limits on the accuracy to which variables

can be measured. Of more practical importance is the fact that many apparently

simple real-life systems cannot be modelled by linear (or acceptably approximated

linearised) systems where small initial changes are associated with later small

outputs. Even the pattern of drips from a leaking tap cannot be modelled using the

types of linear statistical model that are widely used for complicated demographic

applications such as household change, which are known to be subject to a myriad number of influences. There is no convincing demonstration of how, where or when

these various factors influence the system (Brown, 1995a).

2. Household dynamics: conceptual issues

Household change as a fuzzy concept

I believe that most people would agree that the question: 'At what point does

a human life begin?', is a meaningful and important one, but there would be a



368 MIKE MURPHY

substantial variety of answers given. This is not just a semantic point, since this

question has underpinned much of the controversy concerning the legalization of

induced abortion in a number of countries in recent years, indeed people going about

their lawful business have been gunned down by others who take a different view.

There are a number of ways of approaching this question: an individual may give a subjective probability, presumably increasing with time since fertilization (itself not uniquely defined) to live birth, or a frequentist view could be taken. However,

it would also be possible to deny that this is a well-posed question in that 'life'

requires a number of conditions which makes it inappropriate to use this term in the

context of the fetal environment.9 Similar difficulties in defining 'life' also occur

at the opposite end of the age range. Once more, this is an important practical issue

as recent legal and ethical controversies related to the use of life support machines

emphasise. It must be concluded that all classifications are compromises, even those

which might appear to be relatively straightforward. The conventional Western

definition of a household does not fully encompass the full range of household

living arrangements, even in its own time and place: for example, the treatment of

Caribbean-style visiting and LAT ('living-apart-together') unions where a person

may have two sets of household living arrangements is problematic. While such

classifications are bipolar, in that each person's position is defined by one or more

binary value (YES or NO to living in the private household sector; YES or NO to living in a given household), in practice living arrangements are multivalent.

The appropriate framework for such processes is 'fuzzy logic' (in engineering

terminology), although many of the ideas were developed half a century ago in

quantum mechanics by Max Black under the title 'vague logic' (Kosko, 1994, p.

19). In order to make this idea more precise, we could consider a child leaving the

parental home. The empirical evidence is that in many cases, this is a protracted and

fuzzy concept (except, for example, in the decreasing proportion of cases where

children leave to set up an independent household on marriage). However, surveys

typically solicit precise dates such as in the National Child Development Study

(NCDS) and the British Household Panel Study (BHPS):

NCDS, 1981, for children

have you ever moved away from your parent's home?

(if YES) have you ever gone back to live with your parents for six months

or more?

when did you first leave ... to live elsewhere?

BHPS, 1992, for parents

does s/he still live with you?

(if NO) what age was s/he when s/he last lived with you?




It may well be that the responses of parents and children would differ to such

questions; for example, if the child retains a room in the parental home, the parents

may consider him/her as still living there, but the child may not concur, and more

generally it is feasible for A to believe that B is a member of the same household,

but for B to have a different perception of the situation.10 If one defines two polar

states, wholly living and wholly not living there, then there is a period, perhaps for a number of years, when neither is true. However, it would be artificial and

uninformative to try to define a quantitative measure of the degree of attachment to

the parental home: to ask, for example, on a score of between 0 and 100, how far an

individual considers him/herself to be living at home, ignoring the fact of whether

such a figure should be averaged over the responses of parents, 'significant others'

etc. It may be that for practical purposes such as paying some form of residence tax

or filling in a census return, a single location may have to be selected. However,

this decision will often tend to be determined by expediency rather than actuality and definitional simplicity may conflict with empirical utility.

Given that a single useful operational index of the 'degree of living in the

parental home' cannot be derived, it would be appropriate to use a methodology which is based on exactly that premise, namely fuzzy logic.11 This is a stronger statement than one which says that because we cannot define the concept precisely

today, we will use approaches which could be appropriate if this were to be able

to do so in future: rather it says that we are extremely unlikely ever to be able to

measure it satisfactorily.12 It may be tempting, especially for those whose work is based on traditional

statistical practice, to assume that the fuzzy sets approach is an incomplete or

misguided version of conventional statistical methods or possibly a broadly sim

ilar approach arising from the marginal discipline of electrical engineering. This

is incorrect in that the embedding of fuzzy sets within the statistical paradigm has been undertaken (Mant?n et al., 1994). Applications have been concentrated in

epidemiological areas for many years, although there are some more recent

demographic uses (Tan, 1991; Caselli et al., 1993) and the approach could be

applied to household change, since it incorporates dynamic processes including event history models.13 The fuzzy set approach is not simply a reformulation of

a standard statistical model (albeit in a rather sophisticated way) although there

is some similarity with the latent class model (LCM) which assumes a number

of 'crisp' latent classes, which may be estimated by standard methods such as

maximum likelihood, and each case is allocated to a single latent class on the basis

that the estimated probability of being in that class is the largest among all classes

considered. The alternative fuzzy set approach assumes that each case has partial

membership of a number of different classes, denoting each by a Grade of Mem

bership (GoM). Empirical comparisons of these two approaches have suggested that superiority of the latter approach in terms of interpretability and robustness

(Mant?n et al., 1994).



370 MIKE MURPHY

PRACTICAL APPROACHES

While the naive assumption that more data must lead to improved insights may be only weakly true, in order to quantify household change, micro-level data will

often be required, usually obtained from retrospective or prospective (longitudinal)

designs. Longitudinal studies of individuals are clear-cut in design, there are also

explicit longitudinal studies of households which need an operational definition of

a 'longitudinal household', not withstanding the points made above about the diffi

culties in defining this concept. For example, the Panel Study of Income Dynamics

(PSID) in the U.S. has been running since 1968 (Hill, 1992). The PSID has fol lowed all members of the original sample of 4,800 households in 1968 (in which blacks were over-sampled). Each year, information is collected on the original individuals in the sample, their offspring and all their current co-residents, even if

these were not members of the original sample. This means that the sample size has

increased from about 18,000 to 37,500 individuals 20 years later. Under this design

(and ignoring non-response) the sample is found empirically to retain an accurate

representation year-by-year of the non-immigrant population (to overcome this

deficit of recent immigrants, the sample was 'topped-up' with 2,043 Latino house

holds in 1990). The sample therefore remains broadly representative of its original

population,14 but the analysis of change is based largely on the household situation

of individuals classified by household status and followed over time rather than

households per se.

HOUSEHOLD CHANGE AND NETWORKS

From a formal viewpoint, the distribution of relationships between individuals

forms a series of social networks (Marsden, 1990). This includes those linking the

members of a given household although such work focuses overwhelmingly on

extra-household networks, presumably in part because those within the household

are taken for granted and in part because of the problems of obtaining information

about internal household processes.15 The key features of social network analysis are (Wasserman and Faust, 1994, p. 3):

actors and their actions are interdependent flows of resources (emotional, material, etc) occur between actors

the network influences individual action

there are enduring patterns of relations between actors.

Within this framework the household delineates a particularly intense set of

network relations among its members, joint consumption is explicitly required (see Endnote 1), and a high degree of emotional and information sharing is implicit. Thus the concept of household is not just the aggregation of its members but in

addition, the totality of interactions between them (which rises exponentially with

the number of members). It is therefore consistent with this approach that surveys are now starting to collect information about the relationship between all pairs of

members, rather than just to the head of household (Foster et al., 1995) and such




an approach is being tested for possible inclusion in the 2001 Census of Great

Britain, although methods for analysing such data even at a given point of time

are much less well-developed than those for the traditional ways in which data on

relationships within households are collected. Thus the full analysis of household

change does not simply involve examination of a number of changes experienced

by individuals, both because in many cases change does not involve well-defined

transitions, but also because a change in household circumstances will affect all

members rather than the individual who is the focus of analysis. For example, the

number of distinct groups of people (of size greater than one) in a household of

size n is 2n-n-l, so that if one person leaves, the number of such groups is reduced

by at least 50%: correspondingly, the number of groups in the household entered

would more than double. There are benefits in considering household change in

terms of evolving networks, especially with the emphasis of this paper on neural

networks.16

Scale and the dynamics of households

For a large population, it is possible to obtain a sample of individuals which has

effectively the same distributions as the overall population on an appropriate scale.

If the overall population has total numbers N, with Ni in the ith group, then if

the uniform sampling fraction is /, the numbers of this group in the sample will

be approximately equal to flfi since, of course, individuals are only observed

in integral values.17 At this level, the property of fractal sets where the pattern is

independent of the scale at which a set is viewed ('self-similarity', Schroeder, 1991) does not hold. By using appropriate weights, it is possible to give the appearance of recovering some of the exact properties of the original population. However,

this will not be possible in some cases. If, for example, we confine discussion to

categorical variables, then if these are/? such variables, each of which has ra? values

1 < i < P, then the total number of possible combinations is given by

p

Y[rrii i=\

If there are no structural null values (males who have given birth etc) and we have

i=\ i=\

then there must be at least one empty cell in the sample (i.e. there is one combination

of characteristics which may exist in the initial population, but cannot exist in the

sample). This is not a debating point: surveys such as the NCDS and BHPS

referred to earlier both have sample sizes of just over 10,000 people and each

records of the order of 1000 variables. If a massively conservative lower limit is



372 MIKE MURPHY

made by assuming that all of these variables are binary ones, then the number

of combinations is 21000 for an individual (for a household, this number could

be multiplied by itself a number of times). This is equivalent to 10301 states:

for comparison, the age of the universe is estimated to be about 1010 years, and

the total number of elementary particles in the universe at 1080, with the total

number of stars at a mere 1040! Thus the problem of maintaining self-similarity becomes impossible even with relatively modest numbers of discrete variables and, of course, with re-interviewing the volume of data collected grows year-by-year.

So far, the difficulties of obtaining a representative cross-sectional sample of individuals with discrete characteristics only has been considered. As we progres

sively relax these limitations, the difficulty of obtaining a representative sample became even greater. These three generalizations will be considered individually in reverse order.

INTRODUCTION OF 'CONTINUOUS' VARIABLES

'Continuous' variables are of various types, height, weight etc, but the one which

underpins this discussion is, of course, time (including time differences which

give rise to the core variables of age, duration etc). While it is frequently stated

that such variables cannot be measured to an arbitrary accuracy, nevertheless

applications often implicitly assumed that this is the case and continuous time

models are widely used. Apart from the empirical value of recording data to a

high degree of accuracy, the assumption of 'coarse graining' is subject to three

main types of objections, two physical and one mathematical. The physical ones

rely on Heisenberg's uncertainty principle, which sets a lower limit in the joint measurement of certain pairings of physical variables, an associated point is the

extent to which time itself displays discrete as well as continuous aspects. Moreover, there is the possible sensitivity of systems to initial conditions leading to chaotic

behaviour. In addition, recent mathematical work has given considerable attention

to the concept of computability, in that not all numbers are computable in a finite

time (in the sense of being generated by a countably infinite set of Turing machines,

Penrose, 1989).18 It may be that it is considered that human population systems are increasingly

insensitive to the fineness of detail which is measured - for example, if one measures

a demographically important continuous variable such as height (Elo and Preston,

1992) little information may be lost by truncating measurements to a certain value

such as the nearest mm. Whether such 'coarse graining' (Gell-Mann, 1994, p. 29) matters is an empirical question, in the same way that there is a continuing debate

about whether this is so for the accuracy with which we measure the motions of

the planets around the Sun and whether they are likely to be predictable into the

long-term future for this system, which was formerly considered to be among the

most stable of all (Peterson, 1993, Chapter 11).




3. Post-script

There is a more fundamental point which is concerned with the logic of empirical social research itself. A frequent implicit assumption is that more data will permit resolution of basic hypotheses. In recent decades, data on event histories using various combinations of retrospective and prospective designs have become widely

available, but these improved data sources have not been able to explain major issues such as the factors determining the trend of fertility in developed societies

in recent decades, or the reasons for the substantial differences between countries

in the proportions of people living alone. The main result has been to emphasise the diversity of experiences to be explained and to increase the number of potential

explanations, so making it more difficult to generalise. Substantial advances in demographic knowledge have come from the analysis

of transitions between discrete states using statistical models for event history data

from sources such as those in the World Fertility Survey and DHS programmes. Such analysis requires that the states be clearly-defined and then an appropriate

model is fitted; for example, a Poisson model may be fitted to a given process under the assumptions of no measurement error and a simple random sample

design. These approaches have frequently been fitted sensitively in relation to the

acknowledged deficiencies in data and more recently, a number of methods for

incorporating wider community-level variables have been applied. If the approach based on the analysis of a series of particular individual-level transitions between

well defined states is not the dominant approach in demography, it is certainly

among the most widespread and informative.19 The method has been found use

ful, initially by a small group: the benefits are recognised and more take up the

method: soon it becomes difficult to publish findings, and obtain research funding or academic posts without utilizing such methods. Thus it is possible (and in my view probable) that this emphasis on event history analysis is itself an example of

such "lock in". A simple example of this argument has been used by Brian Arthur

(1990) to explain why one make of car rather than another comes to dominate

the market even if it has no "objective" advantage: the fact that a small perceived initial advantage, possibly randomly generated, means that a bandwagon develops in its favour. He gives particular examples such as the dominance of petrol-driven rather than steam-driven cars; VHS and Beta video-recording systems; and light and heavy water nuclear reactors, and he has also demonstrated that any mix of

outcomes can arise from such decision-making processes. The existence of such mechanisms has proved useful in the analysis of migra

tion, where essentially arbitrary small initial decisions can lead to large well-defined

persistent migration streams. For example, there are neighbouring villages in

Italy where completely different patterns of international migration have been

established, for example to North America or South America, and conversely

immigrants to Britain from different islands in the Caribbean tended to concentrate

themselves in different parts of London, presumably due to the chance location of



374 MIKE MURPHY

a small number of early migrants. Individual-level sample survey data would show

why these streams persist, because diffusion of information and links with potential

migrants are important, but they would not explain why the initial decision was

made.

The appropriateness of such a diffusion model to fertility change has been

a major finding of the European Fertility Project (Coale and Watkins, 1986); a

particularly well-documented case being that of the linguistic and demographic

cleavages in Belgium (Lesthaeghe and Wilson, 1986). Even though such factors

are acknowledged to be important, they are rarely included in analysis compared

with, for example, variables such as individuals' educational level. Moreover,

although the mechanisms of how such divergences occur has been discussed,

why such differences might come to be established has not been subject to such

precise investigation, and even to formulate such a project would be difficult.

More fundamentally, the extent to which particular patterns are determined by

unique experience of historical events makes it impossible to generalise results: for

example, if county A were to have the socio-economic and cultural characteristics

that county B had twenty years ago, not only would its demographic development not necessarily be the same, it could be diametrically different in principle. One

suspects that it is much easier to obtain funding from policy agencies for work

which implies that the results obtained can be applied elsewhere and help to inform

decisions.20 It is ironic that this analysis of 'run-away' processes is undertaken in a

research environment where such discussion is itself squeezed because the research

process is itself partaking in a run-away process in a meta-analytic sense.21

The idea of a run-away process can be applied to household models as well as to

methods of analysis. At least in its simple static form, the analogy of 'household as

firm' is a major paradigm, the fact that a Nobel Prize can be won for work in such

areas (by Gary Becker in economics) may further stimulate the development of such

approaches. On the other hand insights from the life sciences such as sociobiology

(Wilson, 1975), ethology (Lorentz, 1963), descriptive studies (Bateson, 1983) and

genetics (Rowe, 1994) have been neglected. The reason for the lack of attention to

such disciplines may be an unwillingness to draw insights from what are regarded as overly-simple systems and because that human society has such powerful non

biological influences that non-human models are inappropriate (this is not to say that the firm is a more complex entity, indeed Gell-Mann, 1994, suggested that the

economy is simpler in its organization than a single bacterium - it may be the fact

that it may not be perceived as being as simple as animals' social organizations is partly responsible for its popularity). Other disciplines such as genetics may be

unpopular for largely unrelated historical reasons such as its association with the

eugenics movement and possibly the level of technical sophistication required. The use of physical systems as analogues for models for household change is

rare, but it could be that the patterns of splitting and re-combination of entities

such as bubbles in boiling water, the ways in which magnetic moments do or do

not line up with their neighbours, or the dynamics of cement setting might well




prove at least as fruitful (Coveney and Highfield, 1995). However the use of such

models would be likely to receive even less initial acceptance than the sceptical

response to the 'babies as consumer durables' analogy (Blake, 1968), even though such insights might prove to be rewarding.

Models of human population dynamics show a high degree of robustness in

terms of their theoretical ergodic properties. Attempts to generate self-sustaining

periodic cycles have been unsuccessful (W?chter, 1991). This is not inconsistent

with the sorts of models discussed here in that the external macro-level processes involved could lead to different, but fixed, demographic parameters in different

societies. There remains the problem of specifying, operationalizing and fitting such models: as Brown (1995a, p. 49) notes: 'for non-linear social science to

progress in the area of chaos requires some degree of faith, at least in the short

term. In my view, social scientists need to be open to the possibility that human

behaviour- both long term and short term - may be as non-linear as are the dynamic

properties of the remainder of the manifest universe' (this passage suggests that he

does not include economics within the domain of social science although there is

a substantial literature in this area, see also Brown, 1995b). However, it has been

noted that there are conceptual benefits from using this perspective, even if the

operationalization is infeasible (Ward, 1995).

Underling the previous discussion is the idea of reductionism, the extent to

which one attempts to explain a particular phenomenon, in this case, household

change, in terms of the most 'basic' possible approach; individuals, the atoms

which make up the individual, the physical laws which lead to the existence of the

fundamental particles etc. Social scientists might be regarded as being at the top of

this hierarchy (and on this basis, the least prestigious); for example Atkins (1992,

p. 3) sets out an extreme example of reductionism;

a great deal of the universe does not need any explanation. Elephants, for

instance. Once molecules have learnt to compete and to create other molecules

in their own image, elephants, and things resembling elephants, will in due

course be found roaming though the countryside ... Some of the things resem

bling elephants will be men. They are equally unimportant [in their specific

make-up].

Clearly there are aspects of human society which cannot be reduced to such a

basic level. This may be illustrated by an example: analysis of family and house

hold processes at the national level across Western Europe shows that the historical

influence of Protestantism had the largest single influence when included in a model

with variables such as female education and labour force participation (Lesthaeghe,

1995). Thus the research emphasis shifts to the higher level to explain why cer

tain countries have established administrative systems and adopted cultural values

which appear to facilitate the emerging patterns of this 'Second Demographic Transition'.



376 MIKE MURPHY

Within such a framework, the analysis of individual household transitions will

contribute relatively little to understanding without incorporation of such wider

factors in an historically-sensitive way. There is also a more general set of counter

arguments to reductionism that interacting elements (in this case human beings) lead to systems that are more complex than the sum of their constituent parts and

attempts have been made to generalise about the ways in which such systems

organise themselves (Kauffman, 1993; Coveney and Highfield, 1995; for special reference to social processes, see also Mainzer, 1994). If it is accepted that analysis at the higher (complex) level is necessary for elucidating family and household

change, this will require more than relatively minor adaptions of methods designed for the analysis of individuals, but a rather more substantial shift in both data and

methods; whether this will prove to be possible and/or fruitful remains unclear, but

it is an intriguing question.

Acknowledgements

An earlier version of this paper was originally presented at the European Population

Conference, Milan 4-8 September 1995, Session VI-3 Event History Analysis. Thanks are due to the Economic and Social Research Council who partially funded

this work as part of a project, Formal Modelling of Household, Families and

Kinship, Ref L315 25 3017. The valuable comments of an anonymous referee are

gratefully acknowledged.

Notes

The statistical definition of a private household recommended by the United Nations (United Nations Statistical Commission and Economic Commission for Europe Conference of European Statisticians 1987) for use in contemporary developed counties is either:

a one-person household - a person who lives alone in a separate housing unit or who occupies,

as a lodger, a separate room (or rooms) of a housing unit but does not join with any of the other

occupants of the housing unit to form part of a multi-person household; or

a multi-person household - a group of two or more persons who combine to occupy the whole or

part of a housing unit and to provide themselves with food and possibly other essentials for living. The group may pool their income to a greater or lesser extent. The group may comprise related and/or

unrelated persons, including boarders, but excludes lodgers. 2 I will not consider the widely-used analogy of the household as a firm, for which there is a

substantial literature stretching back for nearly four decades now (but see Note 18 later). This work has been based on static or equilibrium approaches, rather than on more realistic non-equilibrium

models where useful insights might be expected to be obtained from analysis of events such as

takeovers, mergers, bankruptcies, and why particular firms or industries expand. Much of the rest of

this paper is concerned with such dynamic systems (Arthur, 1990). Non-specialists who are presented with analyses based on the analogy of 'household as firm' should note that this is usually based on

models which have been increasingly challenged within economics itself. 3

This definition is relevant both to cross-sectional and longitudinal analyses, although the ways in which one chooses to operationalize some attributes may differ in these two cases. For example, in cross-sectional approaches, age and time period are frequently used for analysis, whereas in

longitudinal approaches, age and cohort would be more common, although any one of these three




variables is defined by knowledge of the other two. In the latter framework, the unit of analysis has one fixed attribute, date of birth, and one exogenous time-varying one, namely age (Kalbfleisch and Prentice, 1980; Blossfeld and Rohwer, 1995). 4

While it is tempting to treat analogy as an inferior method of analysis to deductive reasoning, G?del 's theorem shows that even the logical consistency of mathematical systems cannot be established from

within the axioms of the system itself (see, Hofstadter, 1979, for a summary of the importance of

this finding, and for a more detailed discussion of the implications of this inherent lack of formal

consistency within axiomatic systems see Penrose, 1994). 5 The question of identifiability is not a trivial point in the context of the EC Directive on Data Protection (95/467EC) which has important implications for research and, in particular, for studies which require the retention of a personal identifier which is necessary for example to link two sources,

either at one point in time from two different sources, or for undertaking longitudinal research. This is

an issue on which social and medical researchers have generally been insufficiently involved. While

this analogy should not be pushed too far, the requirement that individuals should not be identifiable in published output is a common requirement of data collection systems. For example, to do so from

the British Census is a criminal offence, even though a sample of anonymised individual-level records

has been made public. 6 Emergent properties, an example of which is the fact that cells which are made of molecules can

do things that molecules cannot such as reproduce, has been a recurrent topic of interest in biology since at least Charles Darwin's time. While the ability of Darwinian natural selection to explain the

evolution of groups of cells to form such specialised organs as eyes has been emphasised (Dawkins,

1986), its power to account for the mechanisms of development of even the most simple self

replicating organisms remains less clear-cut; for example, Sir Fred Hoyle and N C Wickramasinghe

(1981) concluded that the probability of obtaining a simple self-replicating organism by chance was

comparable to finding that 'a tornado sweeping through a junk yard might assemble a Boeing 747 from the materials within'. The sorts of chemical mechanisms which might resolve this apparent contradiction have been discussed by Stuart Kauffman (1995). As biologists acknowledge, emergent

properties do not stop at the individual level in that it is at the population and biosphere levels that

they also appear: for example, as Purves et al. state (1995, p. 4): 'individuals are born and they die, but an individual does not have a birth rate and a death rate. A population does'. At this stage, the

link becomes apparent with sociological schools, such as the Durkheimian one, which emphasise the

importance and indeed the primary of 'society' over the individual person. 7 Recently, multi-level models which acknowledge the existence of wider influences have been used,

and applications have produced varying degrees of insight (DiPrete and Forristal, 1994; Rodriguez and Goldman, 1995). It will become clear that such approaches are not adequate for analysing

processes such as household change discussed here.

This paper is concerned with time, a subject which has proved to be highly intractable to define, even though our perception of it is straightforward (Landsberg, 1982; Newton-Smith, 1980; Vilquin, 1994). A particularly wide-ranging review of the concepts of time, including both historical and

contemporary populations from a number of continents is given by Clark (1992), who argues that it is

precisely this awareness of time which as enabled our species to develop language and human society which, for example, chimpanzees have not been able to do even though we share over 98% of genetic material in common (Jones, 1993). Measurable is related to the constraints imposed by Heisenberg^

uncertainty principle, and there are logical inconsistencies which occur when points in conventional

four-dimensional space-time are considered. Attempts to unify the two principal physical theories of

general relativity and quantum mechanics have led to theories that require the concept of a point to

be replaced by one which assumes space-time comprising 10 dimensions, and that 'strings' form the

basic geometrical units. Such effects would only tend to act at a scale of 10~33 cm (Planck's length), whereas the diameter of the typical atomic nucleus is 10~13 cm (Davies and Brown, 1988, p. 71). The

topological arguments for why three space-like, perceivable dimensions are necessary for complex

adaptive systems such as the brain are considered by Atkins (1992). 9

The idea of 'life' has become a topic of wide discussion in recent decades with the debate of whether

such a property may be attributed to the cellular automata, computers, etc. This debate remains lively and inconclusive. 10

Ron Lesthaeghe (personal communication) reports that a rule of thumb in the USA is that the



378 MIKE MURPHY

defining event is when the child moves his or her stereo from the parental home; in France it is when

the child no longer brings washing home. 11 This is a rather different use of the term 'fuzzy' than that of Courgeau and Leli?vre (1988). 12

Once more, the links with quantum physics and, in particular, Heisenberg 's uncertainty principle are marked. It should be noted that the logically straightforward but possibly statistically complicated

manipulations associated with measurement error are not considered as a problem here, the problem is to do with the nature of the underlying concept. 13

These alternative approaches may be illustrated by considering the definition of 'leaving home'

referred to earlier.

i. each person is classified either as living or as not living at home, and a model may be fitted for

the probability of an individual not having left home in relation to various socio-demographic factors (typically using methods such as logistic regression)

ii. there are two 'ideal types', one completely living at home, the other living completely away. An

individual may be simultaneously associated with both of these types, although some may be

completely characterised by one only of these ideal types. 14

However, over time only those living individuals who change the people they co-reside with can

enter the sample; those who do not join up with new people cannot do so. Thus the sample will tend

to accumulate such mobile people. 15

It should be noted that in the area of social networks, the difficulties of extending such analyses to dynamic situations have been noted (Doreian, 1988). See also Weesie and Flap (1990). 16 The model is derived from the ways in which the neurons of the brains are linked by synapses, but this model has been suggested as forming a formal model of self-organising order (Kauffman, 1993;

Dawkins, 1986). 17

Leaving aside the split-brain problem mentioned earlier. 18

It is tempting to dismiss such aspects as too abstract and 'theoretical', in that they refer to effects

which arise at a very small scale - typically atomic: however, as pointed out by Penrose, our macro

level existence as a consequence of these effects, both in terms of the existence of atoms (in that

otherwise the electrons would simply radiate their energy in a fraction of a second and collapse into the nucleus) and the more subtle effects which lead to atoms forming molecules and the way in turn that these in turn combine to produce the visible material which comprises both us and our

environment. The concept of computability is used in practice, for example, to provide encryption and

to suggest the intractability of apparently straightforward problems such as the 'travelling salesman'

one. It should also be noted that such theories provide for experimental verification: for example to

an accuracy of about 1 part in 108 for the value of the magnetic moment of an electron (equivalent to

measuring the distance from New York to Los Angeles to the accuracy of the diameter of a human

hair), itself based on an abstract notion of the emission and almost immediate absorption of a pho ton (Feynmann, 1985, pp. 7 & 115). It is therefore ironic that 'theoretical' discussion of household

change frequently revolves around ideas imported from disciplines such as micro-economics where

the experimental basis - the 'gold standard' of the scientific approach

- is actually in conflict with

the theoretical postulates even in its core areas (Davis and Holt, 1992, p. 510). 19

Although other approaches have produced insights which the micro-level one is not necessarily

well-adapted, such as the importance of cultural and linguistic factors in the European fertility decline

(Coale and Watkins, 1986). 20

Since researchers and research funders are need to 'breed' further research, the relationship can

be likened to that of sexual reproduction where the process of evolutionary selection can also lead to

apparent anomalies such as the emergence of positively disadvantageous characteristics for survival

of a given individual, such as the peacock's tail (Fisher, 1930; Dawkins, 1986, p. 199). 21

'Meta analysis' here is used in the same sense as 'meta physics' and in this context refers to the

analysis of methods of analysis, and not to the technique of combining a series of related studies.




References

Arthur, B., 1990. 'Positive feedbacks in the economy', Scientific American (February, 1990) 262:

80-85.

Atkins, P. W., 1992. Creation Revisited. W.U. Freeman, New York.

Bateson, P. (ed.), 1983. Mate choice. Cambridge University Press, Cambridge.

Blake, J., 1968. 'Are babies consumer durables?', Population Studies 22(1): 5-27.

Blossfeld, H.-P. and Rohwer, G., 1995. Techniques of Event History Analysis: New Approaches to

Causal Analysis. Lawrence Erlbaum, Mahwah NJ.

Brown, C, 1995a. Chaos and Catastrophe Theories -

Sage Series Quantitative Applications in the

Social Sciences No. 107. Sage, Thousand Oaks CA.

Brown, C, 1995b. Serpents in the Sand: Essays on the Nonlinear Nature of Politics and Human

Destiny. University of Michigan Press, Ann Arbor.

Bumpass, L., 1991. Emerging issues in demographic research in the United States, in M. Murphy and J. Hobcraft (eds), Population Research in Britain: Supplement to Population Studies 45.

Population Investigation Committee, London, 177-188.

Caselli, G., Cerbara, L. and Leti, G., 1993. 'The geography of adult mortality: results from the fuzzy

clumping method', Genus 49(1-2): 1-24.

Carey, J. R., 1993. Applied Demography for Biologists. Oxford University Press, Oxford.

Clark, G., 1992. Space, Time and Man: a Pre historian s View. Cambridge University Press, Cam

bridge.

Coale, A. J. and Watkins, S. C. (eds), 1986. The Decline of Fertility in Europe. Princeton University

Press, Princeton NJ.

Courgeau, D. and Leli?vre, E., 1988. 'Estimation of transition rates in dynamic household models', in

N. Keilman, A. Kuijsten and A. Vossen (eds), Modelling Household Formation and Dissolution.

Clarendon Press, Oxford, 160-176.

Coveney, P. and Highfield, R., 1995. Frontiers of Complexity: the Search for Order in a Chaotic

World. Faber and Faber, London.

Davies, P. C. W. and Brown, J., 1988. Superstrings: a Theory of Everything? Cambridge University Press, Cambridge.

Davis, D. D. and Holt, C. A., 1992. Experimental economics. Princeton University Press, Princeton

NJ.

Dawkins, R., 1986. The Blind Watchmaker. Longman, London.

Dennett, D. C, 1991. Consciousness Explained. Little, Brown and Co, Boston.

DiPrete, T. A. and Forristal, J. D., 1994. 'Multilevel models: methods and substance', Annual Review

of Sociology 20: 331-357.

Doreian, P., 1988. 'Mapping networks through time'. Paper presented at MASO Conference on

Network Analysis, Utrecht, The Netherlands.

Elder, G. H. Jr., 1978. 'Family history and the life course', in T. K. Hareven (ed), Transitions: the

family and the life course in historical perspective. Academic Press, New York, 17-64.

Elo, I. T. and Preston, S. H., 1992. 'Effects of early-life conditions on adult mortality: a review',

Population Index 58:186-212.

Feynmann, R. P., 1985. QED: the Strange Theory of Light and Matter. Princeton University Press, Princeton NJ.

Fisher, R., 1930. The Genetical Theory of Natural Selection. Clarendon Press, Oxford.

Fortes, M., 1958. 'Introduction', in J. Goody (ed), The Developmental Cycle in Domestic Groups.

Cambridge University Press, Cambridge, 1-14.

Foster, K., Jackson, B., Thomas, M., Hunter, P. and Bennnett, N., 1995. General Household Survey 1993. H.M.S.O., London.

Gell, A., 1992. The anthropology of time: cultural constructions of temporal maps. Berg, Oxford/Prov idence.

Gell-Mann, M., 1994. The Quark and-the Jaguar. Little, Brown and Co., London.

Goody, J. (ed), 1958. The Developmental Cycle in Domestic Groups. Cambridge University Press, Cambridge.

Greenhalgh, S. (ed), 1995. Situating fertility: anthropology and demographic inquiry. Cambridge

University Press, Cambridge.



380 MIKE MURPHY

Halpern, J. M. and Wagner, R. A., 1984. 'Time and social structure: a Yugoslav case study', Journal

of Family History 9(3): 229-244. Hammell, E. A., 1972. 'The Zadruga as process', in P. Laslett and R. Wall (eds), Household and

Family in Past Time. Cambridge University Press, Cambridge, 335-374.

Hill, M. S., 1992. The Panel Study of Income Dynamics: A User's Guide. Sage, Newbury Park.

Hofstadter, D. R., 1979. G?del, Escher, Bach: an Eternal Golden Braid. Harvester, Sussex.

Hoyle, F. and Wickramasinghe, N. C. 1981. Evolution from Space. Dent, London.

Jones, S., 1993. The Language of the Genes. Harper Collins, London.

Kalbfleisch, J. D. and Prentice, R. L., 1980. The Statistical Analysis of Failure Time Data. John Wiley, New York.

Kauffman, S., 1993. The Origins of Order. Oxford University Press, Oxford.

Kauffman, S., 1995. At Home in the Universe: the Search for Laws of Self-organization and Com

plexity. Viking, London.

Kosko, B., 1994. Fuzzy Thinking: The New Science of Fuzzy Logic. Harper Collins, London.

Landsberg, P. T. (ed), 1982. The Enigma of Time. Adam Hilger, Bristol. Laslett, P., 1972. 'Introduction', in P. Laslett and R. Wall (eds), Household and Family in Past Time.

Cambridge University Press, Cambridge, 1-89.

Lesthaeghe, R. and Wilson, C, 1986. 'Modes of production, secularization and the pace of fertility decline in Western Europe 1870-1930', in A. J. Coale and S. C. Watkins (eds), The Decline of Fertility in Europe. Princeton University Press, Princeton NJ, 261-292.

Lesthaeghe, R., 1995. 'The Second Demographic Transition in Western Countries: an Interpretation', in K. O. Mason and A.-M. Jensen (eds), Gender and Family Change in Developed Societies.

Clarendon Press, Oxford, 17-62.

Lorentz, K., 1963. On aggression. Harcourt, Brace and World Inc., New York.

Macmillan, D. B. and Herriott, R. A., 1985. 'Towards a longitudinal definition of households',

Journal of Economic and Social Measurement 13: 349-360.

Mainzer, K., 1994. Thinking in complexity: the complex dynamics of matter, mind and mankind.

Springer-Verlag, Berlin.

Mant?n, K. G., Woodbury, M. A. and Tolley, H. D., 1994. Statistical Applications Using Fuzzy Sets.

John Wiley, New York. Marsden, P. V, 1990. 'Network data and measurement', Annual Review of Sociology 16: 435-463.

Murphy, M., 1995. 'The collection and comparability of demographic and social data in Europe: the family life cycle', in J. Duch?ne and G. Wunsch (eds), Collect et comparabilit? des donn?es

d?mographiques et sociales en Europe, Chair Quetelet 1991. Academia/L'Harmattan, Louvain

la-Neuve, 149-182.

Netting, R. McC, Wilk, R. R. and Arnould, E. J., 1984. Households: Comparative and Historical

Studies of the Domestic Group. University of California Press, Berkeley.

Newton-Smith, W. H., 1980. The Structure of Time. Routledge and Kegan Paul, London.

Ni Bhrolch?in, M., 1992. 'Period paramount? A critique of the cohort approach to fertility', Popu lation and Development Review 18: 599-629.

Penrose, R., 1989. The Emperor's New Mind. Oxford University Press, Oxford.

Penrose. R., 1994. Shadows of the Mind: the Search for the Missing Science of Consciousness. Oxford

University Press, Oxford.

Peterson, I., 1993. Newton's Clock: Chaos in the Solar System. W.H. Freeman, New York.

Prigogine, I. and Stengers, I., 1984. Order out of Chaos: Man's New Dialogue with Nature. Bantam,

USA.

Purves, W K., Orains, G. H. and Heller, H. C, 1995. Life: the Science of Biology. W.H. Freeman,

New York.

Rodriguez, G. and Goldman, N., 1995. 'An assessment of estimation procedures for multilevel models

with binary responses', Journal of the Royal Statistical Society. Series A 15: 73-89.

Rowe, D. C, 1994. The limits of family influence, genes, experience and behavior. Guilford, New

York.

Schroeder, M., 1991. Fractals, Chaos, Power Laws. W.H. Freeman, New York.

Tan, L., 1991. 'Analysis of fuzzy classification of women's status in China', Chinese Journal of

Population Science 3(1): 69-73.




Toffler, A., 1984. 'Foreword: Science and change', in I. Prigogine and I. Stengers (eds), Order out of Chaos: Man's New Dialogue with Nature. Bantam, USA, xi-xxvi.

Townsend, N., 1996. 'Men, migration, and households in Botswana'. Unpublished manuscript PTSC, Brown University, Providence RI, USA.

United Nations Statistical Commission and Economic Commission for Europe Conference of Euro

pean Statisticians, 1987. Recommendations for the 1990 Censuses of Population and Housing in

the ECE Region. Regional Variants of the world recommendations for the 1990 round of popu lation and housing censuses. Statistical Standards and Studies No 40. United Nations Economic

Commission for Europe, New York.

Vilquin, E. (ed), 1994. Le temps et la d?mographie: Chaire Queletet 1993. Academia/L'Harmattan,

Louvain-la-Neuve.

W?chter, K. W., 1991. 'Elusive cycles: are there dynamically possible Lee-Easterlin models for U.S.

births?', Population Studies 45(1): 109-135. Ward, M., 1995. 'Butterflies and Bifurcations: Can Chaos Theory Contribute to our Understanding

of Family Systems?', Journal of Marriage and the Family 57: 629-638.

Wasserman, S. and Faust, K., 1994. Social network analysis: Methods and applications. Cambridge

University Press, New York.

Weesie, J. and Flap, H. (eds), 1990. Social networks through time. University of Utrecht/ISOR, Utrecht.

Willekens, F., 1988. 'A life course perspective on household dynamics', in N. Keilman, A. Kuijsten and A. Vossen (eds), Modelling Household Formation and Dissolution. Clarendon Press, Oxford,

87-107.

Wilson, E. O., 1975. Sociobiology: the new synthesis. Harvard University Press, Harvard.



Documents

The Dynamic Household as a Logical Concept and Its Use in Demography