Appendix — Revision and Evidence Map

Formula and Design Map

A compact map from causal target and counterfactual source to estimator, assumption, diagnostic and scope

Formula and Design Map

Core estimands

Name	Definition	Population
ATE	$E[Y(1)-Y(0)]$	declared target population
ATT	$E[Y(1)-Y(0)\mid D=1]$	treated units
ITT	$E[Y\mid Z=1]-E[Y\mid Z=0]$ under random $Z$	assignment-eligible units
LATE	$E[Y(1)-Y(0)\mid D(1)>D(0)]$	instrument compliers
CATE	$E[Y(1)-Y(0)\mid X=x]$	covariate-defined stratum
policy value	$E[Y(\pi(X))-c(X)\pi(X)]$	decision target under rule $\pi$

Always define the treatment version, outcome horizon and unit with the symbol.

Design map

Design	Minimal contrast	Counterfactual source	Central assumption	Primary diagnostic	Usual scope
randomised offer	$\bar Y_{Z=1}-\bar Y_{Z=0}$	random assignment	implemented assignment; attrition controlled	balance process, flow and outcome coverage	experimental population
adjusted regression	coefficient or standardised prediction contrast	conditionally comparable units	exchangeability, overlap, correct target model	DAG/control and support audit	adjustment target
IV	$RF/FS$	instrument-induced treatment	independence, exclusion, relevance, monotonicity	first stage, weak-IV and exclusion sensitivity	compliers
fixed effects	within-unit contrast	unit over time	time-varying confounding handled	timing, pre-trends, serial dependence	units with within variation
2×2 DID	$(Y_{T1}-Y_{T0})-(Y_{C1}-Y_{C0})$	comparison trend	parallel untreated trends, no anticipation	trends/placebos/sensitivity	treated group and period
staggered DID	aggregate $ATT(g,t)$	never/not-yet treated	cohort-specific trends	cohort support and simultaneous bands	supported cohorts/horizons
sharp RDD	$\lim_{c+}E[Y\mid X]-\lim_{c-}E[Y\mid X]$	cutoff neighbours	continuity, no bundled discontinuity	density, covariates, bandwidth	cutoff units
weighting	weighted outcome contrast	observed-covariate overlap	exchangeability and positivity	balance, weights, $n_{eff}$	weighted target
synthetic control	$Y_{1t}-\sum_jw_jY_{jt}$	weighted donor trajectory	donor stability and no spillovers	pre-fit, placebos, leave-one-out	treated aggregate unit
DML	orthogonal residual score	design + flexible nuisance estimation	underlying identification and nuisance rates	overlap, split/learner stability	declared low-dimensional target

Interpretation map

Reported object	Translate into
OLS coefficient	linear projection slope conditional on included regressors
logit coefficient	conditional log-odds change
$e^\beta$ in count model	conditional mean/rate ratio
event-study point	supported cohort-weighted effect at event time
causal-forest CATE	conditional effect estimate with local support/uncertainty
robustness value	violation strength under a stated sensitivity model

Uncertainty map

Variation source	Starting reference
individual random assignment	assignment/randomisation or individual sampling
cluster-level policy assignment	cluster-level variation; report cluster count
repeated panel outcomes	within-unit dependence and assignment level
RDD near cutoff	local-polynomial robust bias-corrected inference
synthetic-control case study	placebo/permutation and design-specific uncertainty
learned policy	honest out-of-sample value and policy-selection uncertainty

Standard errors are part of the design argument, not a formatting choice.

Next: Worked Pitfalls

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Appendix — Revision and Evidence Map

Compact formulas, design diagnostics, worked pitfalls and a dated literature and software map

Ten Worked Microeconometric Pitfalls

Diagnose common errors with short numerical and design examples