# On the causal interpretation of statistical models in social research

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```					  On the causal interpretation of
statistical models in social research

Alessio Moneta & Federica Russo
The dawn of history
of causal modelling

Staunch causalists
Quetelet, Durkheim, Wright …, Blalock, Duncan, …
Moderate skeptics
Pearl, Heckman, Hoover, …

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

2
This presentation
Alessio                     Federica
• Statistical vs Causal     • Interpreting statistical
Information                models causally:
• Associational vs Causal      – Truthmakers vs Validity
Models                      – Epistemic way out

3
Important distinction (1)

Associational models   Causal models
Associational Models      Causal Models
Causal context;
Theoretical
Background                               knowledge;
Choice of variables
Knowledge                                Institutional
knowledge;
…

Statistical;
Assumptions          Statistical        Extra-statistical;
Causal

Model-based           Hypothetico-
Methodology
statistical induction     deduction
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Example
Associational model:               Causal model:

Engel curves:                      Demand system:
measure of the dependence of      system of equations in which
expenditure (Y) on income (X)     consumer behaviour is modeled
as based on theory of utility
Regression functions:                maximization.
Y = f (X) + e
Estimated and tested ex post.
Cannot be used to sustain
counterfactual                  Used to sustain counterfactuals
Important distinction (2)

Statistical Information        Causal Information
A summary of data             Opening the ‘black box’

Inferential statistics        From association to causation
(sample to population)           Statistical information
to provide the formalised
description of the
phenomenon                     Background ‘constraints’

Statistical dependence           Tests

7
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:

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

10
What’s interpreting
a statistical model causally?
The philosophers’ hunt
for truthmakers

… that is, what makes a causal claim true

Difference-makers
Probabilistic, counterfactual, manipulation

Mechanisms

12
Anything wrong with the hunt?
Conceptual analysis in philosophy of causality
What explicates the concept of ‘causality’
What makes causal claims true
What is causality, metaphysically

Conceptual analysts
failed to distinguish between evidence and concept
lost on the way epistemic practices

13
What’s interpreting
a statistical model causally?
An epistemic activity …
In the footprints of epistemic theorists
Evidence and concept
Evidential pluralism:
difference-making and mechanistic considerations
Conceptual monism:
causation is an inferential map

Causality:
an epistemic category to interpret the world
rather than
a physical relation in our ontology

15
Interpreting in causal terms …
… is deciding whether a model is valid or not
Making successful inferences
Not merely dependent on
the physical existence of mechanisms
Mechanisms have explanatory import
Mechanistic and difference-making
evidential components are tangled

16
The causal interpretation
is model-dependent

Causal conclusions depend on
the statistical information and machinery
from which they are inferred

Not a bad thing after all
Causation is not a ‘all or nothing’ affair
Nor a ‘once and for all’ affair

17
Methodology of causality

Models that establish            Models that establish
associations                    causal relations

Information having               Information having
mere statistical import              causal import

Philosophy of causality

Hunting for                Interpreting a model
truthmakers                    in causal terms

18

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