counterf. beamer present 080707

Rubin’s potential outcome modelLewis’counterfactuals

Structural modelling: a general frameworkDiscussion and Conclusion

Potential Outcomes, Counterfactuals and Structural

Modelling

Causal Approaches in the Social Sciences

Federica Russoa, Guillaume Wunschb and Michel Mouchartc

aPhilosophy, bDemography and cStatisticsUniversity of Louvain (UCLouvain - Belgium)

Federica Russoa, Guillaume Wunschb and Michel Mouchartc Conterfactuals 1



Causal Analysis in Social Sciences

In agreement with Pearl(2000), two approaches to causality:

the potential outcome/counterfactual framework aschampioned most notably by Donald Rubinthe causal/structural modelling framework à la Wright,Haavelmo, Blalock, and others (including Pearl himself)

Counterfactuals, Not a new idea:to check what would happen were the putative cause absent ratherthan present.

A (possible!) historical path:David Hume (1748)

⇒ David Lewis (1973, 2004)⇒ Donald Rubin (1974, ...)

⇒ ...Federica Russoa, Guillaume Wunschb and Michel Mouchartc Conterfactuals 2



This paper

Rubin’s model: very influential but also severely criticised.

In this paper, we tackle two questions:

(i) Are all the criticisms addressed to the potential outcomemodel sound? If so,

(ii) Are counterfactual questions to be dismissed altogether?




Outline

1 Rubin’s potential outcome modelRubin’s definition of a causal effectEpistemological flaws

2 Lewis’counterfactuals

3 Structural modelling: a general frameworkThe meaning of “structural”

4 Discussion and Conclusion




Rubin’s definition of a causal effectEpistemological flaws

Outline









Measure of causal effect

Example: treatment of a headache

E : taking 2 aspirins

C : drinking a glass of water (control)

Yj(·): outcome of the treatment for individual j

Measure of the causal effect for individual j : Yj(E ) − Yj(C )

Average causal effect for a population of N individuals:

1

N

∑

1≤j≤N

Yj(E ) − Yj(C )

“Potential outcome" means: impossible to observe on a sameindividual Yj(E ) and Yj(C )





“Potential outcome" issue

Rubin shows that

randomization

1/2[Y1(E ) − Y2(C )] + 1/2[Y2(E ) − Y1(C )]

or

(perfect) matching

Y1(E ) − Y2(C ) = Y2(E ) − Y1(C )

allows us to by-pass the potential outcome issue when evaluatingan average causal effect.





Problems

Two challenges, however:

Individual heterogeneity: how to deal with the fact thatdifferent individuals may experience different effects from asame cause?

Assignment issue: in many observational studies, there areselection biases in the assignment of treatments





Problems raised by Rubin’s approach

Potential outcomes: a "Platonic heaven"?i.e. one of the two potential outcomes will never be observed

Attributes: Rubin’s approach cannot take them into accounti.e. is "manipulation" an intrinsic ingredient of the concept ofcausality?

Causes of Effects: not only effects of causesIs experimentation an essential element of the concept ofcausality?

The individual or the population?i.e. statistics as a methodology of learning by observing aheterogeneous population of reference?

Counterfactuals or Causal Modelling?That’s the question...




Outline








Counterfactuals

Counterfactuals:

Subjunctive conditional statements the antecedent of whichstates a contrary-to-fact situation

Example

Statement “Had Mr Jones taken an aspirin half an hour ago,

his headache would have gone now”Presuppositions:

Mr Jones did not take the aspirin

Mr Jones still has headache




Morals to be drawn from Lewis and Rubin

Lewis’counterfactuals are single-case,i.e. they concern a specific causal relation taking place at acertain time and space

e.g. Mr Jones (not) taking the aspirin and (not) havingheadache

Lewis’counterfactuals are not generic

e.g. whether aspirin is an effective treatment

e.g. an individual randomly sampled from the population

would recover from headache, were she to take aspirin

Counterfactual questions in Rubin’s model

share the same idea of Lewis

namely: had the cause not been, the effect would not have

been either

are not single-case but generic














been either





To sum up

Are all criticisms addressed to the potential outcome model sound?

YESIn particular, the potential outcome model is problematic forestablishing generic causal claims.

An alternative: structural modelling




The meaning of “structural”

Outline









Introduction

Structural Models: models uncovering the structure of the datagenerating process and providing a causal explanation.

This involves

developing a conceptual model out of background knowledge

and then translating it into an operational model taking intoaccount the available indicators





Introduction

Ingredients:

background knowledge(making sense of present data on the basis of pastobservations)

marginal-conditional decomposition(“explaining” by decomposing a complex mechanism into“simpler” pieces)

stability - invariance(disentangling structural from incidental)





Recursive Decomposition and Causality

Such a recursive decomposition provides a causal explanation aslong as:

1 each component of (1) represents a distinct mechanism

2 in each component, the explanatory (conditioning) variablesrepresent causal factors.i.e. background knowledge often involves conditionalindependence properties implying to drop some of theconditioning variables




Outline








The State of the Art: up to now

Causal Analysis concerns:

measuring effects of causes

providing causal explanations.

Rubin’s potential outcome/counterfactual approach: attention tothe importance of correctly assigning the units

to the treatment in experimental situations

to the control groups in non-experimental situations,

in order to avoid biases resulting from self-selection into the groups.




BUT: Flaws

BUT, methodological and epistemological flaws, e.g. :

As the manipulability of the cause is required, thecounterfactual approach cannot take attributes such as genderor ethnicity into account.

the approach is furthermore not adapted to the study of thecauses of an effect, but only to the effects of the causes




This paper: an alternative to Rubin’s model

A general structural modelling framework based on :

a thorough inventory of background knowledge required for

selecting the reference population

constructing the conceptual model composed of the relevant

variables and the putative causal relations among them, to be

transformed into an operational model .

a marginal-conditional - or recursive- decomposition of themultivariate distribution, represented in most cases by adirected acyclic graph, provided that the decomposition isstructurally valid (i.e. stability and invariance)

a non-parametric approach, more precisely: coordinate-free, orσ-algebraic, i.e. the fundamental- or: intrinsic- structure of themodel does not depend on an arbitrary choice of coordinates.




Concluding Remarks

1 At variance from Pearl’s or Heckmann’s causal modellingapproaches, our causal framework does not imply a particularclass of statistical models

2 Compared to Rubin’s potential outcome/counterfactualframework, the structural modelling framework does notrequire interventions or manipulation of causes, and can dealboth with the effects of causes and with the causes of an effect

3 Qualitative methods also fall under this approach


counterf. beamer present 080707

Technology

causal modelling

guillaume wunschb

general frameworkdiscussion

jnpotential outcome

yj c federica russoa

conclusionmeasure of

yj e yj c average causal

potential outcomemodel