Glossary

54 key terms in causal inference and empirical research methods, defined precisely and accessibly.

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Showing 54 of 54 terms

A

Always-Takers: In the instrumental variables framework: units who always take treatment regardless of the instrument value. The instrument has no effect on their treatment status, so they do not contribute to the LATE estimate.
Attrition: Loss of sample units after initial assignment. Attrition can bias treatment effect estimates if it differs by treatment status — for example, if treated units are more likely to drop out. Lee bounds and other partial-identification methods can address attrition bias.
Average Treatment Effect (ATE): The average causal effect of a treatment across the entire population. Formally: E[Y(1) - Y(0)].
Average Treatment Effect on the Treated (ATT): The average causal effect of a treatment on those who actually received it. Formally: E[Y(1) - Y(0) | D=1].

B

Backdoor Path: A non-causal path between treatment and outcome in a DAG that flows through a common cause (i.e., passes through a variable with an arrow into the treatment). Backdoor paths transmit spurious associations and must be blocked — by conditioning on appropriate variables — to identify causal effects.

C

Clustered Standard Errors: Standard error correction that accounts for correlation of errors within groups (e.g., students within schools, workers within firms). Usually required when treatment is assigned at the group level.
Collider: A variable that is a common effect of two other variables on a path in a DAG (both arrows point into it). Conditioning on a collider opens a spurious association between its causes, a phenomenon known as collider bias or Berkson's paradox.
Common Support: The requirement that for every combination of covariate values, there is a positive probability of being in both the treatment and control groups. Formally: 0 < P(D=1 | X) < 1. Without common support, treatment effects cannot be estimated for units with covariate values found only in one group.
Complier: In the IV framework: a unit whose treatment status is changed by the instrument. LATE estimates the effect only for compliers.
Conditional Expectation Function (CEF): The function E[Y | X = x] that gives the expected value of the outcome Y for each value of the covariates X. OLS provides the best linear approximation to the CEF, and under certain assumptions the CEF itself has a causal interpretation.
Conditional Independence Assumption (CIA): The assumption that treatment assignment is independent of potential outcomes, conditional on observed covariates. Also called unconfoundedness or selection on observables. Formally: (Y(0), Y(1)) ⊥ D | X.
Conditioning: The act of holding a variable fixed — by controlling for it in a regression, stratifying, or matching — to block non-causal paths in a DAG. Conditioning on the right variables removes confounding, but conditioning on the wrong variables (e.g., colliders or mediators) can introduce or amplify bias.
Confounder: A variable that causally affects both the treatment and the outcome, creating a spurious association between them. Confounders must be controlled for — through conditioning, design, or identification strategy — to recover causal effects.

D

d-Separation/dee-separation/: A graphical criterion in DAGs for determining whether two variables are conditionally independent given a set of conditioning variables. Two variables are d-separated if every path between them is blocked — either by a non-collider that is conditioned on, or by a collider that is not conditioned on (and has no conditioned-on descendants).
Defiers: In the instrumental variables framework: units who do the opposite of what the instrument prescribes — they take treatment when the instrument discourages it, and vice versa. The monotonicity assumption rules out defiers, ensuring that LATE is well-defined.
Design Effect (DEFF): The ratio of the variance of an estimator under a complex sampling or experimental design to the variance under simple random sampling. A design effect greater than 1 indicates that clustering or stratification has increased the effective variance, requiring a larger sample size to achieve the same precision.
Design-Based Inference: An approach to causal inference that derives identification from features of the research design — such as randomization, a natural experiment, or a known assignment mechanism — rather than from functional form assumptions on the outcome model. Examples include RCTs, DiD, RDD, and IV.
Directed Acyclic Graph (DAG): A visual diagram showing causal relationships between variables. Arrows indicate the direction of causation. 'Acyclic' means no variable can cause itself through a chain of effects.

E

Endogeneity/en-DOJ-en-ee-tee/: When the treatment or key regressor is correlated with the error term — meaning OLS estimates are biased. The central problem of observational research.
Estimand: The quantity you are trying to estimate — defined in terms of potential outcomes, not in terms of any particular statistical method.
Estimator: The statistical procedure you apply to data to estimate the estimand. Different estimators can target the same estimand.
Exclusion Restriction: The assumption that the instrument affects the outcome only through the treatment — not through any other channel. The key (and untestable) assumption of instrumental variables.
Exogeneity/ek-SOJ-en-ee-tee/: When a variable is determined outside the system of interest — uncorrelated with the error term. Exogenous variation is the foundation of credible causal inference: it mimics random assignment.
External Validity: Whether findings from one study generalize to other populations, settings, or time periods.

F

Family-Wise Error Rate (FWER): The probability of making at least one Type I error (false rejection) across a family of hypothesis tests. Corrections such as Bonferroni, Holm, and Romano-Wolf control the FWER to guard against spurious discoveries when testing multiple hypotheses.
First Stage: In IV/2SLS, the regression of the endogenous treatment variable on the instrument(s). A strong first stage (F > 10) is necessary for reliable inference.

H

Heteroscedasticity/het-er-oh-skeh-das-TIS-ih-tee/: When the variance of the error term is not constant across observations. Requires robust standard errors.
Homoscedasticity/ho-mo-skeh-das-TIS-ih-tee/: The assumption that the variance of the error term is constant across all values of the independent variables. When this assumption is violated (heteroscedasticity), OLS standard errors are biased and robust or clustered standard errors should be used.

I

Identification: A research design is 'identified' when its assumptions are sufficient to recover the causal parameter of interest from observed data.
Intent-to-Treat (ITT): The average effect of being assigned to treatment, regardless of whether units actually comply with the assignment. The ITT is estimated by the reduced-form regression of the outcome on the instrument. It equals the LATE scaled by the compliance rate (first-stage coefficient).
Internal Validity: Whether a study correctly estimates the causal effect for the population and setting it actually studies.
Intraclass Correlation Coefficient (ICC): The proportion of total variance in an outcome that is attributable to between-cluster (rather than within-cluster) variation. A high ICC means observations within clusters are similar, which reduces the effective sample size and must be accounted for in power calculations and standard errors.

L

Local Average Treatment Effect (LATE): The average causal effect for the subpopulation of compliers — those whose treatment status is changed by the instrument.

M

Minimum Detectable Effect (MDE): The smallest treatment effect that a study is powered to detect at a given significance level and statistical power. MDE is a key output of power analysis and depends on sample size, variance, and the desired Type I and Type II error rates.
Model-Based Inference: An approach to causal inference that relies on correctly specifying a statistical model — including its functional form and distributional assumptions — to identify causal effects. Contrasted with design-based inference, where identification comes from the research design itself.
Monotonicity: In the instrumental variables framework, the assumption that the instrument affects treatment status in only one direction for all units — there are no 'defiers' who do the opposite of what the instrument encourages. This assumption is necessary for LATE to be well-defined.

N

Natural Experiment: A situation in which some external event or institutional feature creates variation in treatment assignment that is plausibly exogenous — mimicking random assignment without deliberate experimental intervention. Examples include policy changes, lotteries, and geographic boundaries.
Never-Takers: In the instrumental variables framework: units who never take treatment regardless of the instrument value. Like always-takers, the instrument has no effect on their treatment status and they do not contribute to the LATE estimate.
Neyman Orthogonality: A condition ensuring that estimation of nuisance parameters does not affect the first-order bias of the target causal parameter. Neyman orthogonality is the key property that enables double/debiased machine learning (DML) to use flexible ML estimators for nuisance functions while maintaining root-n consistency for the parameter of interest.

O

Omitted Variable Bias (OVB): Bias in a coefficient estimate caused by excluding a relevant variable that is correlated with both the treatment and the outcome. The direction and magnitude of OVB depend on the correlation of the omitted variable with the treatment and its partial effect on the outcome.

P

Panel Data: Data in which the same cross-sectional units (individuals, firms, countries) are observed across multiple time periods. Panel data enable methods like fixed effects and difference-in-differences that exploit within-unit variation over time to control for time-invariant unobserved confounders.
Parallel Trends Assumption: The assumption that, in the absence of treatment, the treated and control groups would have followed the same trend over time. The key assumption of difference-in-differences.
Partial Identification: An approach that acknowledges when data and assumptions are insufficient to point-identify a causal parameter and instead derives informative bounds on the parameter. Examples include Manski bounds, Lee bounds for attrition, and sensitivity analyses that report a range of estimates under varying assumptions.
Potential Outcomes: The outcomes a unit would experience under each possible treatment status. Y(1) is the outcome if treated; Y(0) is the outcome if not treated. We can only observe one.
Propensity Score: The probability of receiving treatment conditional on observed covariates, e(X) = P(D=1 | X). The propensity score is a balancing score: conditioning on it makes treatment assignment independent of observed confounders, enabling matching, stratification, or inverse probability weighting.

R

Randomization Inference: A mode of statistical inference that derives the distribution of a test statistic by considering all possible random assignments of treatment, rather than relying on large-sample asymptotics. Particularly useful when the number of clusters or treated units is small and conventional standard errors are unreliable.
Researcher Degrees of Freedom: The many decisions a researcher makes during data analysis — variable definitions, sample restrictions, model specifications, outcome measures — that are not dictated by theory and can be used (consciously or not) to obtain desired results. Pre-registration and specification curve analysis are remedies.
Running Variable: The continuous variable in a regression discontinuity design that determines treatment assignment based on whether it falls above or below a known cutoff. Also called the forcing variable or assignment variable. Units cannot precisely manipulate the running variable around the cutoff for RDD to be valid.

S

Selection Bias: Systematic differences between treated and control groups that exist before treatment — making simple comparisons misleading.
Sequential Ignorability: The key assumption of causal mediation analysis: (1) treatment is randomly assigned, and (2) the mediator is as-if randomly assigned conditional on treatment and observed confounders. The second part is very strong.
Sharp Null Hypothesis: The hypothesis that the treatment effect is exactly zero for every individual unit, not just on average. Under the sharp null, each unit's potential outcomes are identical regardless of treatment, which enables exact randomization inference by imputing all missing potential outcomes.
Spillovers: When the treatment of one unit affects the outcomes of other units, violating SUTVA. Also called interference or contamination. Spillovers are common in settings with social interactions, geographic proximity, or market-level treatments.
Stable Unit Treatment Value Assumption (SUTVA): The assumption that one unit's treatment does not affect another unit's outcome, and that there is only one version of each treatment level. SUTVA rules out interference (spillovers) between units and hidden variations of the treatment.

T

Treatment Effect Heterogeneity: Variation in causal effects across subgroups or individuals. When treatment effects are heterogeneous, the ATE may mask important differences. Conditional average treatment effects (CATE) can be estimated using methods like causal forests, sorted effects, and subgroup analysis.