Identification and Assumptions

Defining an estimand does not guarantee that data identify it. Identification is the logical step of expressing a causal quantity uniquely in terms of the observed-data distribution under stated assumptions. Estimation then learns that observed-data quantity from a finite sample.

Prerequisites

Complete Estimands: ATE, ATT, and CATE and Causal Graphs and DAGs.

Learning goals

• Separate identification from estimation and sampling precision.
• Build an identification argument from substantive assumptions.
• Recognize when the available data do not identify the target effect.

An identification argument

Target the Study Sprint ATE. Suppose $L$ is a sufficient set of pre-assignment common causes, treatment and outcome are measured consistently, there is no relevant interference, conditional exchangeability holds, and both assignments occur at every target value of $L$. Then

$$E[Y(1)-Y(0)] =\sum_l\{E[Y\mid A=1,L=l]-E[Y\mid A=0,L=l]\}P(L=l).$$

The right side contains observed-data quantities. Standardization, outcome regression, matching, or weighting may estimate it, but these methods share the same substantive identification burden. Agreement among them can reveal some modeling problems; it cannot prove no unmeasured confounding.

A practical assumption ledger

Assumption	Why it is needed here	Evidence to examine	What evidence cannot prove
Consistency	Links recorded assignment to $Y(a)$	Program protocol and implementation records	That all hidden versions are irrelevant
Conditional exchangeability	Makes groups substitute for missing outcomes	Assignment process, DAG, baseline knowledge	No unmeasured common causes
Positivity	Supplies comparisons within target strata	Assignment frequencies and propensity distributions	Support outside observed combinations
Interference definition	Makes the unit-level contrast meaningful	Class structure and resource constraints	Absence of all spillovers
Measurement and selection	Links constructs to columns and analyzed sample	Validation, missingness, data provenance	Perfect validity from reliability alone

Assumptions and limits

An assumption is not a ceremonial caveat. It connects a causal target to a design, measurement process, and formula. If an assumption is implausible, narrow the population, redefine the treatment, use another design, measure additional causes, model spillovers, or report that the effect is not identified.

Identification is not statistical significance

A huge sample can make an associational estimate precise around the wrong quantity. A randomized but tiny study may identify an effect while estimating it imprecisely. Bias from a failed causal assumption and sampling uncertainty are different problems; confidence intervals generally quantify only the latter under the fitted analysis.

Sensitivity analyses ask how conclusions change under explicit departures from assumptions. They do not transform an unknowable assumption into a testable fact, and they should be aligned with the estimand and plausible failure mode.

Common mistakes

• Presenting covariate adjustment as the identification argument.
• Claiming “causal” because the sample is large or the p-value is small.
• Using balance after adjustment as proof of balance on unmeasured causes.
• Hiding positivity violations behind model extrapolation.
• Listing assumptions without explaining how each links the data to the estimand.

Practice

Take the adjustment formula above and annotate every equality with the assumption it uses. Then imagine motivation was unmeasured: state honestly what remains descriptive or associational and what new design or data could help.

Next steps

Randomized vs. Observational Evidence compares two assignment mechanisms without treating either as automatic proof.

Primary sources

Checked 2026-10-15: Hernán and Robins, Causal Inference: What If, Greenland, Pearl, and Robins, “Causal Diagrams for Epidemiologic Research”, and ICH E9(R1).