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MT Causality Counterfactuals Randomized Experiments
Causality:Explanation versus Prediction
Department of GovernmentLondon School of Economics and Political Science
MT Causality Counterfactuals Randomized Experiments
1 Brief Review of MT Material
2 Causality
3 Fundamental Problem of Causal Inference
4 Randomized Experiments
MT Causality Counterfactuals Randomized Experiments
1 Brief Review of MT Material
2 Causality
3 Fundamental Problem of Causal Inference
4 Randomized Experiments
MT Causality Counterfactuals Randomized Experiments
What did we learnabout during MT?
MT Causality Counterfactuals Randomized Experiments
New territory. . .
By the end of today you should be able to:Identify what makes for a causalrelationshipDistinguish causation fromcorrelation/associationBegin to analyse research problemsusing counterfactual thinking
MT Causality Counterfactuals Randomized Experiments
The broad story arc for LTCausal inference!
Generating causal theories andexpectationsMaking comparisonsStatistical methods useful for causalinference(Quasi-)Experimentation
Developing your research proposalsOne-on-ones w/ ThomasLiterature review (Reading Week)
MT Causality Counterfactuals Randomized Experiments
The broad story arc for LTCausal inference!
Generating causal theories andexpectationsMaking comparisonsStatistical methods useful for causalinference(Quasi-)Experimentation
Developing your research proposalsOne-on-ones w/ ThomasLiterature review (Reading Week)
MT Causality Counterfactuals Randomized Experiments
1 Brief Review of MT Material
2 Causality
3 Fundamental Problem of Causal Inference
4 Randomized Experiments
MT Causality Counterfactuals Randomized Experiments
Pre-Post Change HeuristicOur intuition about causation relies tooheavily on simple comparisons ofpre-post change in outcomes before andafter something happens
No change: no causationIncrease in outcome: positive effectDecrease in outcome: negative effect
Several reasons why this is inadequate!
MT Causality Counterfactuals Randomized Experiments
Flaws in causal inferencefrom pre-post comparisons
1 Maturation or trends2 Regression to the mean3 Selection4 Simultaneous historical changes5 Instrumentation changes6 Monitoring changes behaviour
MT Causality Counterfactuals Randomized Experiments
Directed Acyclic Graphs
Causal graphs (DAGs) provide a visualrepresentation of (possible) causal relationships
Causality flows between variables, which arerepresented as “nodes”
Variables are causally linked by arrowsCausality only flows forward in time
Nodes opening a “backdoor path” fromX → Y are confounds
“Selection bias” or “Confounding”
MT Causality Counterfactuals Randomized Experiments
Directed Acyclic Graphs
Causal graphs (DAGs) provide a visualrepresentation of (possible) causal relationships
Causality flows between variables, which arerepresented as “nodes”
Variables are causally linked by arrowsCausality only flows forward in time
Nodes opening a “backdoor path” fromX → Y are confounds
“Selection bias” or “Confounding”
MT Causality Counterfactuals Randomized Experiments
Directed Acyclic Graphs
Causal graphs (DAGs) provide a visualrepresentation of (possible) causal relationships
Causality flows between variables, which arerepresented as “nodes”
Variables are causally linked by arrowsCausality only flows forward in time
Nodes opening a “backdoor path” fromX → Y are confounds
“Selection bias” or “Confounding”
MT Causality Counterfactuals Randomized Experiments
Smoking Cancer
MT Causality Counterfactuals Randomized Experiments
Smoking Cancer
Age
Environment
GeneticPredisposition
ParentalSmoking
MT Causality Counterfactuals Randomized Experiments
Smoking Cancer
Age
Environment
GeneticPredisposition
ParentalSmoking
MT Causality Counterfactuals Randomized Experiments
Smoking Cancer
Age
Environment
GeneticPredisposition
ParentalSmoking
MT Causality Counterfactuals Randomized Experiments
Smoking Cancer
Age
Environment
GeneticPredisposition
ParentalSmoking
CoinFlip
MT Causality Counterfactuals Randomized Experiments
The 3 or 4 or 5 principles
1 Correlation
2 Nonconfounding
3 Direction (“temporal precedence”)
4 Mechanism
5 (Appropriate level of analysis)
MT Causality Counterfactuals Randomized Experiments
The 3 or 4 or 5 principles
1 Correlation
2 Nonconfounding
3 Direction (“temporal precedence”)
4 Mechanism
5 (Appropriate level of analysis)
MT Causality Counterfactuals Randomized Experiments
Smoking Cancer
Age
Environment
GeneticPredisposition
ParentalSmoking
MT Causality Counterfactuals Randomized Experiments
The 3 or 4 or 5 principles
1 Correlation
2 Nonconfounding
3 Direction (“temporal precedence”)
4 Mechanism
5 (Appropriate level of analysis)
MT Causality Counterfactuals Randomized Experiments
The 3 or 4 or 5 principles
1 Correlation
2 Nonconfounding
3 Direction (“temporal precedence”)
4 Mechanism
5 (Appropriate level of analysis)
MT Causality Counterfactuals Randomized Experiments
Smoking Cancer
Age
Environment
GeneticPredisposition
ParentalSmoking
MT Causality Counterfactuals Randomized Experiments
Smoking Cancer
Age
Environment
GeneticPredisposition
ParentalSmoking
MT Causality Counterfactuals Randomized Experiments
Smoking Cancer
Age
Environment
GeneticPredisposition
ParentalSmoking
MT Causality Counterfactuals Randomized Experiments
The 3 or 4 or 5 principles
1 Correlation
2 Nonconfounding
3 Direction (“temporal precedence”)
4 Mechanism
5 (Appropriate level of analysis)
MT Causality Counterfactuals Randomized Experiments
The 3 or 4 or 5 principles
1 Correlation
2 Nonconfounding
3 Direction (“temporal precedence”)
4 Mechanism
5 (Appropriate level of analysis)
MT Causality Counterfactuals Randomized Experiments
Smoking Cancer
Age
Environment
GeneticPredisposition
ParentalSmoking
MT Causality Counterfactuals Randomized Experiments
The 3 or 4 or 5 principles
1 Correlation
2 Nonconfounding
3 Direction (“temporal precedence”)
4 Mechanism
5 (Appropriate level of analysis)
MT Causality Counterfactuals Randomized Experiments
The 3 or 4 or 5 principles
1 Correlation
2 Nonconfounding
3 Direction (“temporal precedence”)
4 Mechanism
5 (Appropriate level of analysis)
MT Causality Counterfactuals Randomized Experiments
The 3 or 4 or 5 principles
1 Correlation
2 Nonconfounding
3 Direction (“temporal precedence”)
4 Mechanism
5 (Appropriate level of analysis)
MT Causality Counterfactuals Randomized Experiments
Source: The Telegraph. 27 June 2016. http://www.telegraph.co.uk/news/2016/06/24/eu-referendum-how-the-results-compare-to-the-uks-educated-old-an/
MT Causality Counterfactuals Randomized Experiments
Questions?
MT Causality Counterfactuals Randomized Experiments
1 Brief Review of MT Material
2 Causality
3 Fundamental Problem of Causal Inference
4 Randomized Experiments
MT Causality Counterfactuals Randomized Experiments
Causal InferenceCausal inference (typically) involves
gathering data in a systematic fashion inorder to assess the size and form of
correlation between nodes X and Y in such away that there are no backdoor paths
between X and Y by controlling for (i.e.,conditioning on, holding constant) any
confounding variables, Z.
MT Causality Counterfactuals Randomized Experiments
In essence, this means finding orcreating counterfactuals.
MT Causality Counterfactuals Randomized Experiments
Counterfactual Thinking
Causal inference involves inferring whatwould have happened in acounterfactual reality where thepotential cause took on a different value
Counterfactual : relating to what hasnot happened or is not the case
MT Causality Counterfactuals Randomized Experiments
“A Christmas Carol”
1843 novel by Charles Dickens
Ebenezer Scrooge is shown his own future bythe “Ghost of Christmas Yet to Come”
Has the choice to either:1 stay on current path (one counterfactual), or2 change his ways (take a different counterfactual)
MT Causality Counterfactuals Randomized Experiments
Dickensian Causal Inference
Causal effect: The difference betweentwo “potential outcomes”
The outcome that occurs if X = x1The outcome that occurs if X = x2
The causal effect of Scrooge’s lifestyle isseen in the difference(s) between twopotential futures
MT Causality Counterfactuals Randomized Experiments
Other Counterfactualsin TV & Film
Groundhog DayRun Lola RunMinority ReportSource CodeX-Men: Days of Future Past
MT Causality Counterfactuals Randomized Experiments
Fundamental problem ofcausal inference!
We can only observe any given unitin one reality! So any counterfactual
for a given unit is unobservable!!!
MT Causality Counterfactuals Randomized Experiments
Fundamental problem ofcausal inference!
We can only observe any given unitin one reality! So any counterfactual
for a given unit is unobservable!!!
OH NO!
MT Causality Counterfactuals Randomized Experiments
Two solutions!1 “Scientific” Solution1
(Assume) units are all identicalEach can provide a perfect counterfactualCommon in, e.g., agriculture, biology
2 “Statistical” SolutionUnits are not identicalRandom exposure to a potential causeEffects measured on average across unitsKnown as the “Experimental ideal”
1From Holland
MT Causality Counterfactuals Randomized Experiments
Two solutions!1 “Scientific” Solution1
(Assume) units are all identicalEach can provide a perfect counterfactualCommon in, e.g., agriculture, biology
2 “Statistical” SolutionUnits are not identicalRandom exposure to a potential causeEffects measured on average across unitsKnown as the “Experimental ideal”
1From Holland
MT Causality Counterfactuals Randomized Experiments
Mill’s methods2
AgreementDifferenceAgreement and DifferenceResidueConcomitant variations
2Discussed in Holland
MT Causality Counterfactuals Randomized Experiments
Mill’s Method of Difference
“If an instance in which the phenomenonunder investigation occurs, and an instancein which it does not occur, have everycircumstance save one in common, that oneoccurring only in the former; thecircumstance in which alone the twoinstances differ, is the effect, or cause, or annecessary part of the cause, of thephenomenon.”
MT Causality Counterfactuals Randomized Experiments
“Rerum cognoscere causas”Causal inference is meant to help“explain” the social world
Other notions of explainConcept generation and labellingDescriptive typologies
Explanation may or may not involvemechanistic claims (see LT Week 5)
Causation is deterministic at the unitlevel!Counterfactual approaches to causalinference are “forward” in nature
MT Causality Counterfactuals Randomized Experiments
“Rerum cognoscere causas”Causal inference is meant to help“explain” the social world
Other notions of explainConcept generation and labellingDescriptive typologies
Explanation may or may not involvemechanistic claims (see LT Week 5)
Causation is deterministic at the unitlevel!Counterfactual approaches to causalinference are “forward” in nature
MT Causality Counterfactuals Randomized Experiments
“Rerum cognoscere causas”Causal inference is meant to help“explain” the social world
Other notions of explainConcept generation and labellingDescriptive typologies
Explanation may or may not involvemechanistic claims (see LT Week 5)
Causation is deterministic at the unitlevel!Counterfactual approaches to causalinference are “forward” in nature
MT Causality Counterfactuals Randomized Experiments
“Rerum cognoscere causas”Causal inference is meant to help“explain” the social world
Other notions of explainConcept generation and labellingDescriptive typologies
Explanation may or may not involvemechanistic claims (see LT Week 5)
Causation is deterministic at the unitlevel!
Counterfactual approaches to causalinference are “forward” in nature
MT Causality Counterfactuals Randomized Experiments
“Rerum cognoscere causas”Causal inference is meant to help“explain” the social world
Other notions of explainConcept generation and labellingDescriptive typologies
Explanation may or may not involvemechanistic claims (see LT Week 5)
Causation is deterministic at the unitlevel!Counterfactual approaches to causalinference are “forward” in nature
MT Causality Counterfactuals Randomized Experiments
Prediction is not causation.Causation is not prediction.
MT Causality Counterfactuals Randomized Experiments
Prediction is not causation.Causation is not prediction.
Why are these distinct?
MT Causality Counterfactuals Randomized Experiments
1 Brief Review of MT Material
2 Causality
3 Fundamental Problem of Causal Inference
4 Randomized Experiments
MT Causality Counterfactuals Randomized Experiments
The Experimental IdealA randomized experiment, or randomized controltrial is:
The observation of units after, andpossibly before, a randomly assignedintervention in a controlled setting, whichtests one or more precise causalexpectations
This is Holland’s “statistical solution” to thefundamental problem of causal inference
MT Causality Counterfactuals Randomized Experiments
Random AssignmentA physical process of randomization
Breaks the “selection process”Units only take value of X = x becauseof assignment
This means:Treatment groups, on average, provide insight into counterfactual “potential”outcomesRandomization means potentialoutcomes are balanced between groups,so no confounding
MT Causality Counterfactuals Randomized Experiments
Random AssignmentA physical process of randomization
Breaks the “selection process”Units only take value of X = x becauseof assignment
This means:Treatment groups, on average, provide insight into counterfactual “potential”outcomesRandomization means potentialoutcomes are balanced between groups,so no confounding
MT Causality Counterfactuals Randomized Experiments
Smoking Cancer
Age
Environment
GeneticPredisposition
ParentalSmoking
CoinFlip
MT Causality Counterfactuals Randomized Experiments
Experimental Inference ICausal inference is a comparison of twopotential outcomes
A potential outcome is the value of theoutcome (Y ) for a given unit (i) after receivinga particular version of the treatment (X )
Each unit has multiple potential outcomes(y0i , y1i), but we only observe one of them
A causal effect is the difference between these(e.g., yx=1 − yx=0), all else constant
MT Causality Counterfactuals Randomized Experiments
Experimental Inference ICausal inference is a comparison of twopotential outcomes
A potential outcome is the value of theoutcome (Y ) for a given unit (i) after receivinga particular version of the treatment (X )
Each unit has multiple potential outcomes(y0i , y1i), but we only observe one of them
A causal effect is the difference between these(e.g., yx=1 − yx=0), all else constant
MT Causality Counterfactuals Randomized Experiments
Experimental Inference ICausal inference is a comparison of twopotential outcomes
A potential outcome is the value of theoutcome (Y ) for a given unit (i) after receivinga particular version of the treatment (X )
Each unit has multiple potential outcomes(y0i , y1i), but we only observe one of them
A causal effect is the difference between these(e.g., yx=1 − yx=0), all else constant
MT Causality Counterfactuals Randomized Experiments
Experimental Inference ICausal inference is a comparison of twopotential outcomes
A potential outcome is the value of theoutcome (Y ) for a given unit (i) after receivinga particular version of the treatment (X )
Each unit has multiple potential outcomes(y0i , y1i), but we only observe one of them
A causal effect is the difference between these(e.g., yx=1 − yx=0), all else constant
MT Causality Counterfactuals Randomized Experiments
Experimental Inference IIWe cannot see individual-level causal effects
We want to know: TEi = y1i − y0i
We can see average causal effects
Ex.: Average difference in cancerbetween those who do and do not smokeATEnaive = E [y1i |xi = 1]− E [y0i |xi = 0]
Is this what we want to know?
Yes, if X randomizedYes, if all confounds controlled
MT Causality Counterfactuals Randomized Experiments
Experimental Inference IIWe cannot see individual-level causal effects
We want to know: TEi = y1i − y0i
We can see average causal effectsEx.: Average difference in cancerbetween those who do and do not smokeATEnaive = E [y1i |xi = 1]− E [y0i |xi = 0]
Is this what we want to know?
Yes, if X randomizedYes, if all confounds controlled
MT Causality Counterfactuals Randomized Experiments
Experimental Inference IIWe cannot see individual-level causal effects
We want to know: TEi = y1i − y0i
We can see average causal effectsEx.: Average difference in cancerbetween those who do and do not smokeATEnaive = E [y1i |xi = 1]− E [y0i |xi = 0]
Is this what we want to know?
Yes, if X randomizedYes, if all confounds controlled
MT Causality Counterfactuals Randomized Experiments
Experimental Inference IIWe cannot see individual-level causal effects
We want to know: TEi = y1i − y0i
We can see average causal effectsEx.: Average difference in cancerbetween those who do and do not smokeATEnaive = E [y1i |xi = 1]− E [y0i |xi = 0]
Is this what we want to know?Yes, if X randomized
Yes, if all confounds controlled
MT Causality Counterfactuals Randomized Experiments
Experimental Inference IIWe cannot see individual-level causal effects
We want to know: TEi = y1i − y0i
We can see average causal effectsEx.: Average difference in cancerbetween those who do and do not smokeATEnaive = E [y1i |xi = 1]− E [y0i |xi = 0]
Is this what we want to know?Yes, if X randomizedYes, if all confounds controlled
MT Causality Counterfactuals Randomized Experiments
MT Causality Counterfactuals Randomized Experiments
Preview of next week
What is a “scientific literature”?
How do we accumulate scientificevidence?
Mill’s Methods
Agreement
If two or more instances of the phenomenonunder investigation have only onecircumstance in common, the circumstancein which alone all the instances agree, is thecause (or effect) of the given phenomenon.
DifferenceIf an instance in which the phenomenonunder investigation occurs, and an instancein which it does not occur, have everycircumstance save one in common, that oneoccurring only in the former; thecircumstance in which alone the twoinstances differ, is the effect, or cause, or annecessary part of the cause, of thephenomenon.
Agreement and DifferenceIf two or more instances in which thephenomenon occurs have only onecircumstance in common, while two or moreinstances in which it does not occur havenothing in common save the absence of thatcircumstance; the circumstance in whichalone the two sets of instances differ, is theeffect, or cause, or a necessary part of thecause, of the phenomenon.
Residue
Subduct from any phenomenon such part asis known by previous inductions to be theeffect of certain antecedents, and the residueof the phenomenon is the effect of theremaining antecedents.
Concomitant variations
Whatever phenomenon varies in any mannerwhenever another phenomenon varies in someparticular manner, is either a cause or aneffect of that phenomenon, or is connectedwith it through some fact of causation.
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