Causal Inference and the Identification Problem

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causality identification natural-experiment selection-bias

Core Idea

Causal inference asks what would have happened to unit i had treatment status been different — the fundamental problem being that we only ever observe one potential outcome per unit. In economics, randomized controlled trials are rarely feasible, so identification relies on 'natural experiments': institutional rules, policy changes, or geographic discontinuities that create quasi-random variation in treatment. The identification strategy is the researcher's argument for why variation in the regressor of interest is as-good-as-random conditional on observables. All credible empirical economics papers lead with their identification strategy.

How It's Best Learned

Read landmark natural experiment papers (Card-Krueger minimum wage, Angrist Vietnam draft lottery) to understand how economists construct identification arguments from non-experimental settings.

Common Misconceptions

Explainer

The fundamental problem of causal inference is a problem of missing data. When you ask whether a job training program raised someone's wages, you are really asking: what would that person's wages have been *without* the program? You can never observe both outcomes for the same person at the same time — they either took the program or they didn't. This is the potential outcomes framework: each unit has two potential outcomes (treated and untreated), but you only ever see one. The causal effect is the difference between these two outcomes, and it is fundamentally unobservable at the individual level.

The naive approach is to compare wages of program participants to wages of non-participants. But participants may differ from non-participants in countless ways before the program — they may be more motivated, better connected, or from wealthier backgrounds. This is selection bias: the people who select into treatment are not a random draw from the population. When you studied omitted variable bias, you learned that OLS estimates are biased when a variable that affects both treatment assignment and the outcome is left out of the model. Causal inference is largely the problem of dealing with this bias when the omitted variable cannot be measured or controlled for.

The gold standard solution is a randomized controlled trial: randomly assign treatment, so that treated and control groups are identical on average in all characteristics, observed and unobserved. But randomization is rarely feasible in economics — you cannot randomly assign someone to grow up in poverty, attend a particular school, or serve in a war. Economists therefore search for *natural experiments*: real-world situations that create quasi-random variation in treatment. The Vietnam draft lottery assigned men to military service based on birth dates drawn randomly — this gave economists as-good-as-random variation in military service to study its effects on earnings. Geographic borders, policy cutoffs, and sudden rule changes all create similar opportunities.

The identification strategy is the researcher's argument for why the variation they are exploiting is as-good-as-random. It is not enough to have a clever instrument or discontinuity — you must argue persuasively that the variation is uncorrelated with potential outcomes conditional on observables. Every credible empirical economics paper leads with this argument, and the quality of the identification strategy is the primary criterion on which the paper is judged.

A key subtlety: 'as-good-as-random' does not mean literally random. It means that, after conditioning on the variables you can observe, the remaining variation in treatment is unrelated to unobserved factors that affect the outcome. This is a substantive assumption about the world, not a statistical one — it cannot be tested directly, only argued on institutional or theoretical grounds. Learning to evaluate these arguments is the central skill of applied econometrics.

Practice Questions 3 questions

Prerequisite Chain

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsCombining Like TermsOne-Step EquationsTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIndefinite IntegralsBasic Integration RulesRiemann SumsDefinite Integral DefinitionProbability Density Functions and Continuous DistributionsCumulative Distribution FunctionsContinuous Random VariablesNormal DistributionCentral Limit TheoremConfidence Intervals for MeansZ-Tests and T-Tests for MeansOne-Sample Z-Test for MeansOne-Sample and Two-Sample T-TestsOne-Way ANOVAF-Test and Joint SignificanceR-Squared and Model FitOmitted Variable BiasCausal Inference and the Identification Problem

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