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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

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Indefinite Integrals → Basic Integration Rules → Riemann Sums → Definite Integral Definition → Probability Density Functions and Continuous Distributions → Cumulative Distribution Functions → Continuous Random Variables → Probability Density Functions → Expected Value → Weak Law of Large Numbers → Probability Axioms and Rules → Conditional Probability → Independence of Events → Sampling Distributions → Standard Error of Estimators → Hypothesis Testing: Framework and Logic → P-values and Statistical Significance → Effect Size and Practical Significance → Hypothesis Testing: Framework and Logic → Z-Tests and T-Tests for Means → One-Sample Z-Test for Means → One-Sample and Two-Sample T-Tests → Inference in Linear Regression → Prediction Intervals in Regression → Linear Regression Basics → Residuals and Goodness of Fit (R²) → Simple (Bivariate) OLS Regression → Classical OLS Assumptions (Gauss-Markov) → Multiple Regression → Interpreting Regression Coefficients → Hypothesis Testing in Regression → F-Test and Joint Significance → R-Squared and Model Fit → Omitted Variable Bias → Causal Inference and the Identification Problem

Longest path: 116 steps · 584 total prerequisite topics

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