Summary / Synthesis Flashcards
ATE, ATU, ATT, LATE, TET?
What happens with homogenous treatment effects?
ATE = Average Treatment Effect on the Treated = E [Y(1) - Y(0) | T = 1]
ATU = Average Treatment Effect on the Untreated = E [Y(1) - Y(0) | T = 0]
ATT = Average Treatment Effect = E [Y(1) - Y(0)]
LATE = Local Average Treatment Effect = E [Y(1) - Y(0) | complier] (for those affected by the instrument)
TET = Treatment Effect at the Threshold = E [Y(1) - Y(0) | X = c] (for those with running variable X at the threshold c
With homogeneous treatment effects (i.e. treatment effect is the same for everyone in the population) ATE = ATU = ATE = LATE = TET, but generally not true
Why is the Hausman test of exogeneity not always a valid test?
It compares OLS with IV estimates and test whether they differ (if they differ significantly, you reject exogeneity)
But not rejecting exogeneity is not equal to proving exogeneity, test relies on having valid IV and IV estimates LATE whereas OLS estimates ATT (can often not be compared)
How do all IE methods obtain the counterfactual?
Usually the interest is in the ATT: E [Y(1) - Y(0) | T = 1]
How do we obtain E [Y(0) | T = 1]?
Randomisation: E [Y(0) | T = 1] = E [Y(0) | T = 0] (with-and-without comparison)
Regression, Matching (controlling for observables): E [Y(0) | T = 1, X] = E [Y(0) | T = 0, X]
Twins: E [Y(0) | T = 1, twin] =E [Y(0) | T = 1, twin brother/sister]
Fixed Effects / Difference-in-Difference: E [Y(0) | T = 1, t = 1] = E [Y(0) | T = 1, t = 0] + E [Y(0) | T = 0, t = 1] - E [Y(0) | T = 0, t = 0] (DiD accounts for selection bias but assumes it stays constant over time (PTA))
Instrumental Variables: E [Y(0) | Z = 1] = E [Y(0) | Z = 0]
Regression Discontinuity Design: E [Y(0) | T = 1, X = c] = E [Y(0) | T = 0, X = c - e]
When Diff-in-Diff, when Individual Fixed effects?
DiD if you have aggregate data (treatment status is determined by a policy at a higher level of aggregation)
IFE if you have individual level data (you don’t know why treatment status changes, and why at a particular time)
Main distinction between (natural) experiments and other methods
There is some variation in treatment, do we know where the variation is coming from?
We know where the variation is coming from (= we know why someone is in the treatment group and another one is in the control group):
Randomization
Natural experiments: Difference-in-difference, synthetic controls, instrumental variables, regression discontinuity
We don’t know where the variation is coming from: regression, matching, sibling and twin fixed effects, individual fixed effects
Trade-off between internal and external validity that arises when using (natural) experiments
(Natural) experiments are the most convincing in terms of establishing causality
However, they apply to a specific group of people
So the most convincing methods usually have the lowest external validity
No problem if you want to evaluate a certain policy
Hard to generalize findings
Which methods are the most convincing / have the highest internal validity?
Randomization: perfect counterfactual, outcome of control is what would have happened to the treated in case they had not been treated
Second-best are natural experiments (DiD, IV, RDD)
Method of Altonji et al. and Oster to investigate sensitivity of multiple regression results in case of selection on unobservable variables
One can learn from the selection on observables about the selection on unobservables
The observable variables X happen to be a (random) subset of the full set of variables that affect the outcome
Typically, selection on unobservables is smaller or equal to selection on observables
They developed a method that estimates the effect of interest under a ‘worst-case’ scenario in which the selection on unobservables is equally large as the selection on observables
Useful tool to explore robustness of your multiple regression estimates
Describe and use placebo tests in your own research
Estimate pseudo-causal effects that are known to equal zero based on a-priori knowledge
General idea is to make the analysis more convincing
You (may) find something for the actual treatment
You find nothing where you should find nothing for the placebo treatment
The second set of results makes your first result more convincing (if not, the original result was maybe not credible at all)
Try using placebo outcomes that are determined before the actual treatment takes place
