On the causal interpretation of statistical models in social research

Alessio Moneta & Federica Russo

The dawn of historyof causal modelling

Staunch causalistsQuetelet, Durkheim, Wright …, Blalock, Duncan, …

Moderate skepticsPearl, Heckman, Hoover, …

… and the evergreen question:When and how can we drawcausal conclusions from statistics?

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This presentation

Alessio• Statistical vs Causal

Information• Associational vs Causal

Models

Federica• Interpreting statistical

models causally:– Truthmakers vs Validity– Epistemic way out

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Important distinction (1)

Associational models Causal models

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Example

Associational model:

Engel curves:measure of the dependence of expenditure (Y) on income (X)

Regression functions:Y = f (X) + e

Cannot be used to sustain counterfactual

Causal model:

Demand system:system of equations in which consumer behaviour is modeled as based on theory of utility maximization.

Estimated and tested ex post.

Used to sustain counterfactuals

Important distinction (2)

Statistical InformationA summary of data

Inferential statistics(sample to population)

Adequate and parsimonious description of the phenomenon

Statistical dependence

Causal InformationOpening the ‘black box’

From association to causationStatistical informationto provide the formalisedempirical evidence

Background ‘constraints’

Tests

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Statistical dependence

Statistical independence: X ind. Y iff f(X,Y) = f(X) f(Y)

Conditional ind.: X ind. Y given Z iff f(X,Y|Z) = f(X|Z) f(Y|Z)

Measures of dependence: correlation

Pearson’s correlation coefficient:Corr(X,Y) = Cov (X,Y) / [Var(X) Var (Y)]1/2

From association to causation

Background constraints:

theoretical knowledge (e.g. about exogeneity)

institutional mechanisms (e.g. central banks)

temporal priority

rules of inference (Markov and Faithfulness)

All nice but …

A vicious circle introduced?Not quite …

How much background knowledge?Just the right amount …

Cfr. “inductivist” and “deductivist” approaches in econometrics

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What’s interpretinginterpreting a statistical model causally?

The philosophers’ huntfor truthmakerstruthmakers

… … that isthat is, what makes a causal claim true

Difference-makersProbabilistic, counterfactual, manipulation

Mechanisms

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Anything wrong with the hunt?

Conceptual analysis in philosophy of causalityWhat explicates the concept of ‘causality’What makes causal claims trueWhat is causality, metaphysically

Conceptual analystsfailed to distinguish between evidence and conceptlost on the way epistemic practices

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What’s interpretinginterpreting a statistical model causally?

An epistemic activity …

In the footprints of epistemic theorists

Evidence and conceptEvidential pluralism:

difference-making and mechanistic considerations

Conceptual monism:causation is an inferential map

Causality:an epistemic category to interpret the world

rather thana physical relation in our ontology

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InterpretingInterpreting in causal terms …

… is deciding whether a model is valid or not

Making successful inferences

Not merely dependent onthe physical existence of mechanisms

Mechanisms have explanatory import

Mechanistic and difference-makingevidential components are tangled

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The causal interpretation is model-dependent

Causal conclusions depend onthe statistical information and machineryfrom which they are inferred

Not a bad thing after allCausation is not a ‘all or nothing’ affairNor a ‘once and for all’ affair

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