Empirical Generalisationsin Social Science

Federica RussoInstitut Supérieur de PhilosophieUniversité catholique de Louvain

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OverviewThe question:are there laws in social science?

Relevance of the questionHistoricallyIn the current debate

The consensus and the challenge

Empirical generalisationsin structural models

On invariance:Pandora’s box is open

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Relevance of the questionQuetelet (1869):society is regimented by lawsas much as Nature

Statistics is a science of the general,it establishes laws by analysing

regularities

The Average Man, i.e. the meanaround which social elements oscillate,is the basis of a social physics

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Quetelet’s reading showsThe goal of finding laws of society has fairly long

history

“Laws” in a strong sense, not just Humean regularities

HoweverQuetelet is liable to objections, e.g.:

Laws can’t be established by investigating regularities,but, if at all, by investigating variations

Statistics is not the study of the meanbut the study of the variance

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Relevance of the questionThe debate is still open

The social sciences cannot establish lawsbecause they are not as matureas the natural sciences

They are mature but there aren’tany laws to discover

There are laws, but we cannot know them

If there are laws, it is unclear whatkind of entities and mechanisms are involved

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Consider for instance:1) Roberts 2004

Laws are universal regularities

The special sciencesdo not have such laws

The absence of laws points toan essential difference betweenthe natural and social sciences

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Consider for instance:2) Kinkaid 2004

Some laws of physics do not establishuniversal generalisationsbut causal mechanisms

Such laws describe general tendencies,sometimes fragile

Many laws in social science are of this type

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Consider for instance:3) Woodward and Hitchcock 2003

Laws are empirical generalisations having

the characteristic of being invariant

Invariance gives themexplanatory and predictive power

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An implicit consensusIf there are laws, they don’t have the same

characteristics of the laws of physics

Whence the questionWhat are they?

AnswerEmpirical generalisations

A weaker concept

A different concept

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The challenge

To give an account ofempirical generalisations that is

Reasonable Meaningful Useful

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The strategyWhat is an empirical generalisation

in social science?

Goals of social science

Cognitive

Action-oriented

Role of causal knowledge

Structural modelling:

Establishing empirical generalisations

Their characteristics will depend on the conditiions of structural models

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Goals

CognitiveUnderstand/explainingsocial phenomena

Action-orientedInform/direct social policies

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Role of causal knowledgeCognitive aspect

Beyond description,to provide foundations for action

Action-oriented aspectIt presupposes intervening oncausal relationships/mechanisms

How to acquire suchcausal knowledge?

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Structural modelling,the quantitative approach

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ElementsAssumptions

StatisticalExtra-statisticalCausal

MethodologyHypothetico-deductivism

Key notionsBackground knowledgeExogeneityInvariance

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In more detail:H-D methodology

1) formulate the hypothesis2) build the model3) confirm/disconfirm the hypothesis

Note:Not exactly Popperian H-DTerminological problems

H-D methodology makesstructural models flexible

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In more detail:background knowledge

General knowledge of thesocio-political context

Similar evidence of the same causalmechanism in other populations

Knowledge of thephysical-biological-physiological

mechanism

Use of similar/different methods and/or of data

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In more detail:exogeneity

An exogenous variable:“its” mechanism does not influencethe mechanism of interest

In a structural model,an exogenous variable isa causal variable

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4

13

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12

2

X1Economic

development

X2Social

development

X3Sanitary

infrastructures

X4Use of sanitary infrastructures

X5Age structure

YMortality

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In more detail:invariance

The traditional definition:Causality requires “invariance underintervention”, i.e. a relation has to beinvariant under a large class ofinterventions or environmental changes

The testinvariance require setting updifferent initial conditions

A counterfactual characterisation

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In more detail:invarianceWoodward & Hitchcock 2003:

A relationship R between variables X and Y is invariant if it would continue to be true (or approximately true) in at least some hypothetical situations or possible worlds in which the value of X is changed as the result of an intervention. That is, there must be some non-actual value x of X such that the following counterfactual is true: ‘if X were equal to x, then the values of X and Y would stand (approximately) in the relation R.’

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In more detail:invariance

Distinguish:Invariance concerning the variablesStructural stability concerning the model

Invariance is a property of observations,not of the model

The test:parameters have the same value or at leastthe same sign across sub-samples of the data

base

We get out of counterfactuals

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In more detail:structural stability

A model is structurally stable ifThe causal variables are exogenous

Relations among variables are invariant

Background knowledge backs upexogeneity, invariance and the structure

DistinguishInternal vs external stability

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Structural – what does it mean?

Looking for structures, mechanisms

A special case of thegeneral statistical model

An umbrella for different typesof causal models

Qualitative analysis is also structural

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That’s all to sayStructural models establishempirical generalisations

A causal claim that state an invariantrelation in structural model

Empirical generalisations causalSummary of statistics descriptive

Empirical generalisations allowexplanation – prediction – interventionbecause they are the result of a structural model

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What’s new, then?

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Woodward’s invarianceGoal

Defend a theory of explanationand of explanatory generalisations

The claimEmpirical generalisations areexplanatory because invariant

The scopeExplanation in the special sciences,social and natural

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The divergenceWoodward’s central idea

Empirical generalisations show patterns of counterfactual dependence

Their explanatory power is due to their being able to answer WITHBD-questions

Counterfactuality is central toInvarianceExplanationCausal modelling

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Deeper and deeper divergences

Invariance-based approaches andin general counterfactual approaches

claim that they will establishcausal relations by evaluating

effects of interventions

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Pandora’s box is open

Woodward’s invariance presupposesan experimentalist approach

But what do we do in social sciencewith observational data?

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The counter-objection1) Interventions do not have an

anthropomorphic characterisationOK, fine

2) If we cannot intervene, we consider a hypothetical experiment

Pandora’s box is wide open

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In extremis rescue?Woodward 2003:

Instead, the role of [interventions] is to serve as a regulative idea: they tell us what must be true of the relationship between X and Y if X causes Y and in this way tell us what we should aim at establishing, perhaps on the basis of an imperfect or nonideal experiment, if we want to show that a causal claim is true.

But that’s exactly the problem!

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To sum upAre there laws in social science?

The question is relevant

We’d better look into theconcept of empirical generalisation

I’ve done that through ananalysis of structural modelling

The divergence with the “received views”opened a Pandora’s box

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Some remarksPartisans of counterfactual approachesoppose partisans of decision theory

Opposition is due to the weak foundationsof the counterfactual approach

Either we get rid of counterfactuals orwe provide them with better foundations

But mostly, counterfactuals do not sayhow to draw causal conclusionsfrom observational data

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To concludeAre there laws in social science?

Perhaps, but right now we havebut empirical generalisations,

that is causal statements that claim an invariant relation in a structural model