Lecture notes AMT
Lecture 1
Causal relationships
X affects Y : X => Y
Reverse causality: Y affects x : X <= Y
o Reverse causality means that X and Y are associated, but not in the way you would
expect. Instead of X causing a change in Y, it is really the other way around: Y is
causing changes in X
Simultaneity: X affects Y and Y affects X : X <=> Y
o Simultaneity is where the explanatory variable is jointly determined with the
dependent variable. In other words, X causes Y but Y also causes X.
Omitted variable: O affects both X and Y: X <= O => Y
o Omitted variable bias: An omitted variable bias occurs when a variable X affects both
the treatment A and the outcome variable B but is not (adequately) taken into
account.
Selection bias: Selection bias occurs when the subjects who select or who are selected into
treatment differ from the subjects who don‘t.
Correlation: relationship between x and y
Causality: x causes y
What is policy evaluation?
Systematic assessment of the change in an outcome variable that can be ascribed to a
specific policy measure/intervention.
Key element of any evaluation: construction of an adequate counterfactual situation
What would have happened in the absence of the intervention?
Key aim: isolating (identifying) the causal effect of an intervention
o How? Comparing the actual situation to the counterfactual situation
Steps
1. Defining the unit of observation
2. Defining the outcome variable
3. Selecting the evaluation parameter
4. Selecting an evaluation strategy (identification strategy)
5. Determining the costs of the invervention
, The Rubin causal model
• D i : Treatment Variable
{
D i= 1 ,if treated(treatment group)
0 , otherwise ( control group )
• Example: Student i receives a study grant
• Potential outcomes
• Y 0 i : potential outcome without treatment (D i=0) .
• Y 1 i : potential outcome with treatment (D i=1).
• Exists for both groups independent of the treatment status
• Observed outcomes
• Y i=Di Y 1 i+ ( 1−Di ) Y 0 i
• We either observe Y 1 i or Y 0 i!
• We do not observe the counterfactual outcome\
• Individual causal effect
• Causal effect of the treatment for unit i:
Δ i=Y 1 i−Y 0 i
• Average causal effect
• Average of the individual causal effects across the units n
n n n
1
Av gn [ Δ i ] = ∑ [ Y −Y 0 i ]= 1n ∑ Y 1 i− 1n ∑ Y 0 i
n i=1 1 i i=1 i=1
• We only observe an individual either treated or untreated, but never both
• Fundamental Problem of Causal Inference: It is impossible to observe Y i ( 1 ) and Y i ( 0 ) for
the same unit i at the same time. Therefore it is impossible to measure the individual causal
effect of D on Y.
• We do not know the counterfactual situation, i.e. what would have happened had individual i
not received the treatment
• Evaluation is a problem of missing data
• Difference in conditional means = average causal effect + selection bias
Lecture 1
Causal relationships
X affects Y : X => Y
Reverse causality: Y affects x : X <= Y
o Reverse causality means that X and Y are associated, but not in the way you would
expect. Instead of X causing a change in Y, it is really the other way around: Y is
causing changes in X
Simultaneity: X affects Y and Y affects X : X <=> Y
o Simultaneity is where the explanatory variable is jointly determined with the
dependent variable. In other words, X causes Y but Y also causes X.
Omitted variable: O affects both X and Y: X <= O => Y
o Omitted variable bias: An omitted variable bias occurs when a variable X affects both
the treatment A and the outcome variable B but is not (adequately) taken into
account.
Selection bias: Selection bias occurs when the subjects who select or who are selected into
treatment differ from the subjects who don‘t.
Correlation: relationship between x and y
Causality: x causes y
What is policy evaluation?
Systematic assessment of the change in an outcome variable that can be ascribed to a
specific policy measure/intervention.
Key element of any evaluation: construction of an adequate counterfactual situation
What would have happened in the absence of the intervention?
Key aim: isolating (identifying) the causal effect of an intervention
o How? Comparing the actual situation to the counterfactual situation
Steps
1. Defining the unit of observation
2. Defining the outcome variable
3. Selecting the evaluation parameter
4. Selecting an evaluation strategy (identification strategy)
5. Determining the costs of the invervention
, The Rubin causal model
• D i : Treatment Variable
{
D i= 1 ,if treated(treatment group)
0 , otherwise ( control group )
• Example: Student i receives a study grant
• Potential outcomes
• Y 0 i : potential outcome without treatment (D i=0) .
• Y 1 i : potential outcome with treatment (D i=1).
• Exists for both groups independent of the treatment status
• Observed outcomes
• Y i=Di Y 1 i+ ( 1−Di ) Y 0 i
• We either observe Y 1 i or Y 0 i!
• We do not observe the counterfactual outcome\
• Individual causal effect
• Causal effect of the treatment for unit i:
Δ i=Y 1 i−Y 0 i
• Average causal effect
• Average of the individual causal effects across the units n
n n n
1
Av gn [ Δ i ] = ∑ [ Y −Y 0 i ]= 1n ∑ Y 1 i− 1n ∑ Y 0 i
n i=1 1 i i=1 i=1
• We only observe an individual either treated or untreated, but never both
• Fundamental Problem of Causal Inference: It is impossible to observe Y i ( 1 ) and Y i ( 0 ) for
the same unit i at the same time. Therefore it is impossible to measure the individual causal
effect of D on Y.
• We do not know the counterfactual situation, i.e. what would have happened had individual i
not received the treatment
• Evaluation is a problem of missing data
• Difference in conditional means = average causal effect + selection bias
