From the Model of Reality to the Reality of the Model


  • Author: Chris Smaje
  • Date: 31 Mar 2013
  • Copyright: Image appears courtesy of iStock Photo.

What do we mean when we say that we’ve constructed a model? In the social sciences, to ‘construct a model’ usually means to come up with some kind of simplifying hypothesis about relationships between real world things which can then be tested with data.

A sociologist, for example, might hypothesise that income level is affected by issues such as education, employment history, employer type, childcare responsibilities and unionisation. Perhaps s/he might further hypothesise that these independent variables can account for the fact that on average men earn more than women. A study by Olsen and Walby (1) looked at exactly this question, using data from the British Household Panel Survey. They found that women working full-time earned 18% less per hour than men working full-time. Most of the gap could be accounted for by gender differences in the sort of independent variables mentioned above, but there was a residual 9% difference unexplained by the model. This is pretty good going. Models, as I mentioned, are simplifications of real world relationships, and the residual variation is often higher. Olsen and Walby suggested that direct discrimination against women in the workplace, which is difficult to measure, may be another relevant factor – the 9% residual difference setting an upper limit on its contribution to the gender pay gap.

It would be possible to probe more deeply into the mathematical logic of such modelling exercises to interrogate the way that concepts of social causality such as gender discrimination are extracted from the distribution of sample variances, a journey into the heart of statistical darkness that few working sociologists dare tread. But instead I’m going to pursue a parallel line of enquiry by turning attention away from the particulars of statistical modelling itself and looking, as it were, ‘upstream’ at the models behind the models, and ‘downstream’ at the models created jointly by the statistical models and the models behind them. And if that sentence seems baffling, you should try reading the work of Pierre Bourdieu. We’ll come to Bourdieu shortly, but hopefully all will soon be clear.

thumbnail image: From the Model of Reality to the Reality of the Model

I mentioned earlier that models involve hypotheses about relationships between ‘real world things’. But if we look more closely ‘upstream’ from our statistical models at these real world things – things like gender and education that were used in the example above – these too can start to look like models rather than actual things. This, at any rate, is what emerges from a good deal of cultural anthropology, which delights in showing that such taken-for-granted everyday categories are less secure than we often suppose. For example, in her classic book The Gender Of The Gift (2), Marilyn Strathern uses examples from New Guinea to show how ideas about gender need not be thought of as mere cultural elaborations of ‘real world’ biological sex difference, but as aspects of personhood wholly separate from any notion of ‘real’ biological sex. In putting these two different ways of thinking about gender side by side – our western conception of it as a cultural overlay to real biological difference, and the New Guineans’ conception of it as a partible property of persons – the anthropology suggests that even basic concepts of the social world such as gender that we mobilise both in everyday life and in scholarly, statistical research are models too – specific and simplifying hypotheses about relationships between things.

For the purposes of a study like Olsen and Walby’s, this doesn’t matter much. Their distinction between ‘men’ and ‘women’ involves a model of gender difference that is so universal and basic to our understanding of social life in Britain that it requires no justification, and the results of their statistical modelling point to the practical consequences of the distinction. But it’s as well to remember that as individuals and societies we possess our own particular models of social relationships which we deploy, often unconsciously, in our conversations and our research.'s as well to remember that as individuals and societies we possess our own particular models of social relationships which we deploy, often unconsciously, in our conversations and our research.

This becomes important when we look ‘downstream’ from our statistical models to the inferences that we draw from them. In the Olsen and Walby study, policy recommendations include looking at issues such as childcare provision, training for women returning to work after childcare and flexible work schemes – issues which can be framed in terms of market efficiency. In their words,

'An important HM Treasury policy objective is to raise the productivity of the UK economy and its rate of economic growth....The research has found that labour markets are not perfectly competitive, and that they contain significant rigidities (such as occupational segregation) and forms of discrimination' (3).

So the specific empirical findings of a gender pay gap are put into a wider normative or policy context of increasing economic growth and productivity. There’s nothing especially controversial here – Olsen and Walby’s conclusions seem eminently sensible to me – but it’s worth unpicking the structure of the argument. A social model (gender) is taken as a starting point for a statistical model (the correlates of gender pay differentials), and the results are interpreted in the context of another social model (economic productivity/growth). The first and third steps are important and recurrent features in social statistics, because statistical analysis cannot justify any particular policy interpretation in itself. Everything depends on the wider context of the social models within which it’s framed, in this case that people are gendered and that gender pay disparities threaten goals of social equity and economic efficiency.

I don’t think that’s news to most social statisticians. Sophisticated multivariate statistical methods, particularly ones with a temporal element such as panel studies, can be effective at suggesting causal relationships, but social statisticians are usually well aware of the dangers of turning an ‘is’ into an ‘ought’ and don’t claim any prerogatives as policy-makers. Nevertheless, a danger lurks. The late French anthropologist Pierre Bourdieu expressed it thus:

'To slip from regularity, ie. from what recurs with a certain statistically measurable frequency and from the formula which describes it, to a consciously laid down and consciously respected ruling...or to unconscious regulating by a mysterious cerebral or social mechanism, are the two commonest ways of sliding from the model of the reality to the reality of the model (original emphasis)' (4).

Probably the most important of these ‘mysterious cerebral or social mechanisms’ in modern thought comes in the field of economics, via Adam Smith’s famous dictum about social benefit accruing from the pursuit of self-interest by the individual, who is “led by an invisible hand to promote an end which was no part of his intention” (5). Smith’s notion of the ‘invisible hand’ has proved remarkably durable despite more than two centuries of persistent critique. It ultimately underlies the Treasury objective to increase economic productivity and growth referred to by Olsen and Walby, and it underlies global economic policy more generally in its antipathy to social expenditure, exchange controls and trade protectionism. Critics have suggested that here we have a social model for which the empirical evidence is at best questionable but which has acquired a powerfully persuasive force in contemporary politics, to the extent that policies such as free trade agreements are enacted in order to make the world better conform to its model of how things ought to work, rather than making a model that better conforms to how the world actually does work.

There’s nothing necessarily wrong with espousing a particular view of how the world ought to work. The problem is when that view is clothed in some kind of analysis that implicitly overplays its grounding – as in the old cliché about ‘lies, damned lies and statistics’, or when one slides from the model of reality to the reality of the model in Bourdieu’s terms.

There’s nothing necessarily wrong with espousing a particular view of how the world ought to work. The problem is when that view is clothed in some kind of analysis that implicitly overplays its grounding – as in the old cliché about ‘lies, damned lies and statistics’, or when one slides from the model of reality to the reality of the model in Bourdieu’s terms. Sometimes reality punishes us when we mistake it for our models. The banking crisis that exploded in 2008 when it turned out that the money we thought we had didn’t really exist is a classic example, but there are countless other ones across the field of human endeavour that can have some surprising twists. One that I’m personally working on presently concerns plant breeding efforts to produce perennial grain crops that don’t exist in nature even though our models suggest that they could – a case of people attempting to bring the world into line with our model of it, which I suspect will invite the natural punishment of crop failure when it turns out that our models just weren’t very good.

But rather than dwelling on any particular examples I want to conclude by attempting some cautionary generalisations for the innocent social statistician, based on a classic paper by another late anthropologist, Clifford Geertz. Geertz argued that the word ‘model’ has two senses – models ‘of’ and models ‘for’. His example of the former is when we apprehend reality through symbolic parallels, such as constructing a flow chart to model the functioning of a dam. His example of the latter is when we manipulate reality in accordance with prior symbolic structures, as when we build a dam by following a flow chart. Geertz suggests that models for are commonly found in nature, such as the genetic recipes coded in DNA molecules, whereas models of are typically a feature of culture. In his words,

'Unlike genes, and other nonsymbolic information sources, which are only models for, not models of, culture patterns have an intrinsic double aspect: they give meaning, that is, objective conceptual form, to social and psychological reality both by shaping themselves to it and by shaping it to themselves' (6).

This captures something of the issues I’ve tried to highlight above in the way that we do social statistics. Typically we start with some models, often a mix of ‘models of’ and ‘models for’ (eg. gendered persons, social equity, life history), that guide our choice of variables. Then we construct a statistical ‘model of’ the relationships between these variables. We usually wish to mobilise the statistical analysis into some kind of claim about what should be done, about how social reality should be shaped, but whatever the results we can usually only do this by invoking other ‘models for’ (eg. economic growth), themselves based – sometimes rather insecurely – on their own empirical histories and their own mixtures of models.

Geertz’s discussion of models came in an essay on religion, which he defined as,

'A system of symbols which acts to establish powerful, pervasive, and long-lasting moods and motivations in men by formulating conceptions of a general order of existence and clothing these conceptions with such an aura of factuality that the moods and motivations seem uniquely realistic' (7).

It’s not a bad definition of religion. The only problem I have with it is that it doesn’t seem tightly drawn enough around what we usually understand by ‘religion’ – it could apply to a lot of science too, certainly to a lot of social science. By that I don’t at all mean to suggest that there’s no value in statistical analysis or that we inhabit a wholly relativistic universe in which science is simply a religion and there is no nonsymbolic reality. But I do think that social scientists and social statisticians might usefully ponder the parallel when they formulate their conceptions of the general order of existence, and take care that their analyses don’t simply clothe these prior conceptions with an aura of factuality. They might, in other words, take care not to slide from their models of reality to the reality of their models.

1. Olsen, W. and Walby, S. (2004) Modelling Gender Pay Gaps, Manchester: Equal Opportunities Commission.
2. Strathern, M. (1992) The Gender of the Gift, Berkeley: University of California Press.
3. op cit p.31-2.
4. Bourdieu, P. (1990) The Logic of Practice, Cambridge: Polity, p.39.
5. Smith, A. (1776 [1993]) Wealth of Nations, Oxford: Oxford University Press, p.292.
6. Geertz, C. (1973) The Interpretation of Cultures, New York: Basic Books, p.93.
7. ibid. p.90.

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