ConceptsAssumptions behind each step

Assumptions behind each step

Every causal answer rests on claims the data cannot check. See how one graph assumption moves an estimate, then look up what each step of ergodic assumes.

Run the program#

The bundled birthweight data (Almond, Chay and Lee, 2005; Cattaneo, 2010) records 4,642 births, the mother's smoking and 17 background variables. The program asks the same question under three different graphs.

from ergodic import dag, estimate_effect, identify_effect
from ergodic.datasets import load_birthweight

# 1. Load the births and name the question: smoking's effect on birthweight.
births = load_birthweight()
smoking, weight = births.treatment, births.outcome


def graph(confounders, latent=()):
    edges = [f"{c} -> {smoking}" for c in confounders]
    edges += [f"{c} -> {weight}" for c in confounders]
    return dag([*edges, f"{smoking} -> {weight}"], latent=latent)


# 2. Assume every confounder is measured, and estimate.
full = estimate_effect(
    graph(births.confounders), births.data, smoking, weight,
    treated=births.treated, random_state=0,
)
print("17 confounders:", full)

# 3. Assume there are none: the same data, another answer.
none = estimate_effect(
    graph([]), births.data, smoking, weight, treated=births.treated, random_state=0
)
print("no confounders:", none)

# 4. Assume a hidden common cause: no adjustment can remove it.
hidden = graph([*births.confounders, "U"], latent=["U"])
print(identify_effect(hidden, smoking, weight))

17 confounders: EffectEstimate(aipw, analytic: ate=-222.3, se=25.8, 95% CI [-273, -172], n=4642)
no confounders: EffectEstimate(aipw, analytic: ate=-275.3, se=21.2, 95% CI [-317, -234], n=4642)
Identification(not identifiable, ['mbsmoke'] -> ['bweight'])

• Step 2. With all 17 confounders in the graph, smoking lowers birthweight by about 222 g.
• Step 3. With none, the estimate is the raw difference, about 275 g. Nothing in the data says which graph is right; the 53 g gap is your assumption at work.
• Step 4. With an unmeasured cause U of both smoking and birthweight, and no mediator or instrument to route around it, the effect is not identifiable. ergodic says so instead of returning a number.

Know what each step assumes#

The checks are graph checks. A graph you write down, or one discovery returns, is still an assumption about the world.

Read the stated assumptions#

Some results carry their assumptions in words, so they travel with the number:

• identify_mediation returns a record whose assumptions name the sequential ignorability and cross-world claims the decomposition needs.
• Quasi-experimental estimates carry a Design record. Difference-in-differences states parallel trends and no anticipation. Synthetic control states that the donors span the treated unit's untreated path, that nothing spills over to the donors, and that the pre-period fit is good. An interrupted time series states that the pre-period trend would have continued and that no other shock hit at the break.
• An instrumental-variable identification says it holds "under a linear (parametric) model".

Next steps#