Causal Identification & Endogeneity

← Back to Domain-Specific Families

Abstractions about causal inference using natural experiments, instruments, difference-in-differences, observable selection, specification tests, and omitted-variable control.

9 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Causal Inference — Infer the effect of changing X on Y from data by fixing a causal estimand and defending an identification design or assumption that separates that effect from noncausal association, then quantify its uncertainty and scope.
• Difference-in-Differences — Estimate a causal effect from observational data by subtracting the control group's before-after change from the treatment group's, netting out time-invariant unit confounders and common time trends — valid only if parallel trends holds.
• Endogeneity — The condition in which a regressor is correlated with a model's error term — through confounding, simultaneity, or measurement error — so OLS coefficients are biased and inconsistent for the causal effect, collapsing the coefficient's causal reading while leaving its predictive one intact.
• Instrumental variable — Recover the causal effect of a confounded treatment by finding a quantity Z that moves the treatment, reaches the outcome only through it, and is independent of the confounders — then reading the effect off the ratio of Z's reduced-form to first-stage effects, importing randomization the analyst never performed.
• Lord's Paradox — Show that two arithmetically correct analyses of the same pre-post data — raw change scores versus baseline adjustment — can reach opposite verdicts about an effect, because adjustment is a causal-modeling choice and the two answer different questions depending on whether baseline is itself caused by group membership.
• Natural Experiment — A design that borrows the RCT's identification logic from a real-world process — a policy, boundary, or lottery — judged plausibly as-good-as-random, where the as-if-random assumption must be substantively defended rather than guaranteed by protocol.
• Omitted Variable Bias — Correct for the distortion in a regression coefficient when a left-out variable both causes the outcome and correlates with an included regressor, so the estimate absorbs the omitted effect as the signable product of two relationships.
• Sargan–Hansen Test — An overidentification test for instrumental-variable or GMM models that asks whether surplus instruments are jointly orthogonal to fitted residual moments, conditional on at least one maintained valid identifying set.
• Selection on Observables — Assume that, conditional on a named set of measured covariates, treatment assignment is independent of potential outcomes — so within each covariate stratum treated and untreated units are exchangeable and adjustment recovers the causal effect.