Summary Dynamics and causality in the social and behavioural sciences
Lecture 1 – 13/11/2023
We will focus mostly on causation tasks in the form of ‘what if?’.
In the social/behavioral/health sciences, the randomized controlled trial (RCT) is considered a gold
standard for causal research questions.
Reasoning:
• Random assignment ensures groups are the same to begin with
• If we find a difference between the groups after one group is treated and the other is not, this
must be caused by the treatment
But... --> it’s not always possible to randomly assign people to different conditions.
- Ethics can be a reason
- Sometimes it's just not practical
As a result, the groups are likely to be different to start with.
In this scenario, what can we now conclude if:
• there is a difference between the groups on the outcome variable?
• there is no difference between the groups on the outcome variable?
Paul Holland and Don Rubin came up with the motto ‘no causation without manipulation’. In other
words, for there to be a causal relationship between an independent variable and a dependent
variable, there must be a possible way to manipulate or change the independent variable. This does
not necessarily imply that the manipulation must actually take place, but it is important that
hypothetically an intervention is possible. For example, if we want to investigate the causal
relationship between smoking and lung cancer, it is necessary to consider how to manipulate the
smoking, such as, for example, through a randomized experiment in which some people are asked to
stop smoking and others are not.
,In many non-experimental studies they avoid explicit causal language, just avoiding the ‘c-word’ like
‘teenage drug use puts one at risk for school dropout’ instead of ‘teenage drug use causes school
dropout’.
The work of David Card, Joshua Angrist and Guido Imbens has helped to deepen our understanding
of complex economic issues by using real situations as natural experiments. Unlike in medicine or
other sciences, economists cannot conduct rigidly controlled clinical trials. Instead, natural
experiments use real-life situations to study impacts on the world, an approach that has spread to
other social sciences.”
Marginals, conditionals, and regression (basic concepts needed to understand the causal inference
literature):
Marginal distribution: For example, if you have a dataset with information on both income and
educational attainment of individuals, then the marginal distribution of income is the probability
distribution of income regardless of educational attainment, and vice versa. The idea is to focus on
only one variable without considering the possible influence of other variables.
Joint distribution:
Conditional distribution P ( Y |X= x ) :
These conditional distributions all have different means. We can now make predictions conditional
on educational attainment: E ( Y |X =x ) .
We can then consider contrasts (e.g., E ( Y |X =5 )−E ( Y | X=4 ) ), to see the difference in expected
income for two different levels of educational attainment.
A confounder is a common cause of the two variables we are interested in.
,Conditioning: why?
If we have a measurement of intelligence, we can condition on this: We thus consider the relation
between years of education and income, conditional on intelligence.
> Conditioning means: We look at the relation between years of education and income, within
a group of people with the same level of intelligence.
> Goal of conditioning: Remove the effect of the third variable (here: Intelligence), mimicking
an RCT.
Some ways to condition on intelligence are:
- select a particular group (only people who score in a particular region on intelligence)
- create groups based on intelligence (i.e., strata)
- match individuals on intelligence (e.g., make pairs of individuals with same intelligence, but
different educational levels)
- use multiple regression analysis with intelligence as covariate
Multiple linear regression
When using multiple linear regression, we include:
• years of education (the “treatment” variable of interest) as a predictor • intelligence (the
confounder) as a predictor (covariate)
• income (the outcome of interest) as the outcome
It means we assume:
• linear relations between predictors and outcome
• no interaction between intelligence and years of education
Other researchers may ask: What is the effect of intelligence on income?
In this case, years of education is a mediator: It is on a causal path from
intelligence to income.
Causal inference: Some basics
We will focus on different frameworks of causality:
• Potential outcomes framework by Rubin (Imbens)
• Structural causal model by Pearl
Causal statements should be based on specific actions or treatments and should aim to establish the
causal effect of one action versus another. For example, if we want to understand whether aspirin
actually reduces headaches, we should compare the treatment (taking aspirin) with no treatment
(not taking aspirin).
Suppose Daan has a headache. A well-defined causal question requires us to define:
• treatment (aka exposure): Aspirin (X = 1) and No Aspirin (X = 0)
• outcome: Headache under both actions one hour later (Y x=1 and Y x=0 )
, Suppose Daan has these two potential outcomes:
Potential outcome Y x=1 =0 (i.e., no headache 1h after aspirin)
Potential outcome Y x=0 =1 (i.e., headache 1h after no aspirin)
Causal effect: Y 1−Y 0=0−1 = reduction (i.e., improvement) due to Aspirin
Either we give Daan the aspirin, or we don’t:
• the potential outcome we observe is the fact
• the potential outcome we do NOT observe is the counterfact
Two key features to notice Note: measuring the same person at different occasions (under
here are: different treatments), is NOT necessarily the solution; that requires
• the causal effect is defined additional assumptions (cf. Holland, 1986):
at the level of the unit • temporal stability: effect of treatment does not depend on time
• we can only observe one • causal transience: there is no carry-over effect from earlier
potential outcomes per unit treatment
-->This is known as: “The
fundamental problem of
causal inference” (p.947, Individual vs. average causal effect
Holland, 1986).
Causality is defined as the difference in potential outcomes of an
individual:
Individual causal effect: ICEi =Y 1i −Y 0i
Note the ICE may be different for different individuals. As we cannot observe both potential
outcomes, we typically focus on the average causal effect instead: Average causal effect:
ACE=E [ Y i −Y i ] =E [ Y i ]−E [ Y i ]
1 0 1 0
(The ICE and ACE are also sometimes referred to as the individual treatment effect (ITE) and the
average treatment effect (ATE).)
The difference between "seeing" and "doing": looking at the average results in different treatments
(seeing) does not tell us the same thing as actively manipulating the treatment and observing its
effect (doing). In other words, the fact that the probability of passing the exam is different between
those who have or have not undergone training does not automatically mean that training is the
cause of the difference. Chances are, those who go through the training are more likely to struggle
with the subject.
---> It is necessary to actively intervene to better understand causal relationships.
Assumptions for identification of a causal effect (potential outcomes framework)
