Causal Catalog

Causal Catalog#

Study Designs#

Randomized Experiments#

Assumptions needed
  • Consistency
  • No interference

Assumptions ensured
  • Exchangeability

Causal quantities identified
  • Average treatment effect (ATE)

Pros/cons#

Advantages

Disadvantages
  • Not having to worry about confounders
  • Ability to make causal inferences!
  • No bias due to confounding
  • Exchangeability is guaranteed
  • Easier to generalize results
  • Expensive 💰and time consuming ⏰
  • Giving people a placebo :(
  • Hard to maintain randomness completely
  • Ethical constraints
  • May be difficult to get a large number of participants
  • Compliance/human aspect of reacting to treatment
  • Not feasible in a lot of scenarios

Observational Studies#

Assumptions needed
  • Consistency
  • No interference
  • Conditional exchangeability / unconfoundedness
  • Positivity

Assumptions ensured
  • None 😞

Causal quantities identified
  • Average treatment effect (ATE)

Instrumental Variables#

Assumptions needed
  • Consistency
  • No interference
  • Relevance
  • Exclusion restriction
  • Instrument unconfoundedness
  • Linear outcome or monotonicity

Assumptions ensured by design
  • None, but does not need conditional exchangeability / unconfoundedness

Causal quantities identified
  • Average treatment effect (ATE)
  • Local average treatment effect (LATE)

Regression Discontinuity#

Sharp RDD#

Description
  • Treatment is completely deterministic based on the running variable
  • Treatment is "forced" once the running variable crosses the cutoff $c$

Assumptions needed
  • Consistency
  • No interference
  • Continuity

Assumptions ensured by design
  • None, but does not need conditional exchangeability / unconfoundedness

Causal quantities identified
  • Average treatment effect (ATE) at the cutoff

Fuzzy RDD#

Description
  • Treatment is not deterministically forced, but it is discontinuous

Assumptions needed
  • Consistency
  • No interference
  • Continuity
  • Monotonicity (no defiers)

Assumptions ensured by design
  • None, but does not need conditional exchangeability / unconfoundedness

Causal quantities identified
  • Local average treatment effect (LATE) at the cutoff

Pros/cons#

Advantages

Disadvantages
  • Strong causal validity
  • Easy to implement and visually verify
  • Running variable can be confounded and still have valid inference
  • Can leverage naturally occurring cutoffs in data
  • Requires a very specific situation in order to be able to use this study design (not all studies have treatment cutoffs or running variables)
  • Can be difficult to identify what kind of person a complier is
  • Aren't as useful for other causal quantities like the ATT or ATU
  • Hard to determine a good cutoff for many situations
  • Conclusions will depend on what you choose for the bandwidth, which seems difficult to try to balance

Difference-in-differences#

Description
  • Compares the change in outcomes over time between a treatment group and a control group

Assumptions needed
  • Consistency
  • No interference: also known as no spillover
  • Parallel trends

Assumptions ensured by design
  • None, but does not need conditional exchangeability / unconfoundedness

Causal quantities identified
  • Average treatment effect on the treated: (ATT)
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