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Home›Econometrics›Difference-in-Differences (Diff-in-Diff)
Regression model

Difference-in-Differences (Diff-in-Diff)

Difference-in-Differences Estimator · Also known as: diff-in-diff, DiD, Farkların Farkı (Diff-in-Diff)

Difference-in-Differences is a causal-inference method that estimates the effect of an intervention by comparing how a treatment group and a control group change over time. Made famous by Card and Krueger's 1994 minimum-wage study and developed in Angrist and Pischke's Mostly Harmless Econometrics, it isolates the treatment effect as the difference between the two groups' before-after changes.

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Granger CausalityInstrumental Variables i…OLS RegressionPanel Fixed EffectsPropensity Score MatchingAdaptive Natural Experim…Bayesian Causal Impact A…Bayesian Counterfactual…Bayesian Difference-in-D…Bayesian Event Study Des…

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When to use it

Use DiD when you have an intervention or policy that affects one group but not another, and you observe outcomes for both groups in at least two periods (before and after). The data should be panel or repeated cross-sections with a continuous or binary outcome, and a reasonable sample of at least about 40 observations. The central requirement is the parallel-trends assumption: in the absence of treatment, the two groups would have moved in parallel. It is not appropriate with only a single period, or when the groups were already on diverging paths.

Strengths & limitations

Strengths
  • Identifies a causal effect from observational data without randomisation, by differencing out fixed group differences and common time shocks.
  • Simple to estimate and interpret: the treatment effect is a single interaction coefficient.
  • Robust to any time-invariant confounders that differ between the groups, since they cancel in the differencing.
Limitations
  • The whole approach rests on the parallel-trends assumption; if the groups were already diverging, the estimate is biased and the causal interpretation fails.
  • Requires at least two time periods — a single cross-section cannot support the difference of differences.
  • Small treatment or control groups (n < 40) make standard errors unreliable.

Frequently asked

What is the parallel-trends assumption?

It states that, absent the intervention, the treatment and control groups would have followed the same trend over time. DiD relies on this so that the control group's change validly stands in for what the treatment group would have experienced without treatment. You support it by checking that pre-treatment trends were parallel.

Which coefficient is the treatment effect?

The interaction term between the treatment indicator and the post-period indicator. Its coefficient β₃ is the difference-in-differences estimate of the average treatment effect on the treated (ATT).

How many periods and observations do I need?

At least two periods (before and after) are essential, since the method differences over time. A single period cannot identify the effect. A reasonable sample of around 40 or more observations is advised so the standard errors are trustworthy.

What if parallel trends do not hold?

Then the DiD estimate is biased and the causal reading is invalid. A propensity-score matching design that balances the groups on observed characteristics is a common alternative.

Sources

  1. Angrist, J. D., & Pischke, J.-S. (2009). Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press. ISBN: 978-0691120355
  2. Card, D., & Krueger, A. B. (1994). Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania. American Economic Review, 84(4), 772-793. link ↗

How to cite this page

ScholarGate. (2026, June 1). Difference-in-Differences Estimator. ScholarGate. https://scholargate.app/en/econometrics/difference-in-differences

Related methods

Granger CausalityInstrumental Variables in Health ResearchOLS RegressionPanel Fixed EffectsPropensity Score Matching

Which method?

Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.

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Referenced by

Adaptive Natural ExperimentBayesian Causal Impact AnalysisBayesian Counterfactual Impact EvaluationBayesian Difference-in-DifferencesBayesian Event Study DesignBayesian Fuzzy Regression DiscontinuityBayesian Instrumental VariablesBayesian Panel Event StudyBayesian Synthetic Control MethodBlocked Natural ExperimentCausal Discovery AlgorithmsCausal Impact AnalysisCoarsened Exact MatchingCounterfactual Impact EvaluationCounterfactual Impact Evaluation in Education ResearchCrossover Natural ExperimentDifference-in-Differences in Education ResearchDifference-in-DiscontinuitiesDoubly Robust Estimation in Education ResearchDynamic Counterfactual Impact EvaluationDynamic Difference-in-DifferencesDynamic Event Study DesignDynamic Instrumental VariablesDynamic Interrupted Time SeriesDynamic Panel Event StudyDynamic Synthetic Control MethodEvent Study Design in Education ResearchFactorial Natural ExperimentFirst-Difference EstimatorFixed Effects Panel ModelFuzzy Regression DiscontinuityFuzzy Regression Discontinuity in Education ResearchHeterogeneous Treatment Effect Coarsened Exact MatchingHeterogeneous Treatment Effect Difference-in-DifferencesHeterogeneous Treatment Effect Event Study DesignHeterogeneous Treatment Effect Interrupted Time SeriesHeterogeneous treatment effect Panel event studyHeterogeneous treatment effect Placebo testHeterogeneous Treatment Effect Propensity Score MatchingHeterogeneous Treatment Effect Sensitivity Analysis for CausalityHeterogeneous Treatment Effect Synthetic Control MethodImpact Evaluation DesignInstrumental Variables in Education ResearchInterrupted Time SeriesInterrupted Time Series in Education ResearchInverse Probability Weighting in Education ResearchMachine learning-augmented causal impact analysisMachine Learning-Augmented Counterfactual Impact EvaluationMachine learning-augmented difference-in-differencesMachine learning-augmented doubly robust estimationMachine learning-augmented event study designMachine Learning-Augmented Fuzzy Regression DiscontinuityMachine Learning-Augmented Interrupted Time SeriesMachine Learning-Augmented Panel Event StudyMachine Learning-Augmented Placebo TestMachine learning-augmented propensity score weightingMachine Learning-Augmented Sensitivity Analysis for CausalityMachine Learning-Augmented Synthetic Control MethodMarginal Structural ModelMarginal structural model in education researchMatching EstimatorMulti-period Causal Impact AnalysisMulti-period Coarsened Exact MatchingMulti-period Counterfactual Impact EvaluationMulti-period Difference-in-differencesMulti-period Doubly Robust EstimationMulti-period Event Study DesignMulti-period Interrupted Time SeriesMulti-period Matching EstimatorMulti-period Regression Discontinuity DesignMulti-period Synthetic Control MethodNatural ExperimentPanel Data Causal Impact AnalysisPanel Data Coarsened Exact MatchingPanel Data Difference-in-DifferencesPanel Data Fuzzy Regression DiscontinuityPanel Data Instrumental VariablesPanel Data Interrupted Time SeriesPanel Data Matching EstimatorPanel Data Placebo TestPanel Data Propensity Score MatchingPanel Data Regression Discontinuity DesignPanel Data Synthetic Control MethodPanel Event StudyPanel Event Study in Education ResearchPanel Fixed EffectsPanel-based Causal-Comparative ResearchPanel-based Observational Quantitative ResearchPilot Natural ExperimentPlacebo Test in Education ResearchPolicy Evaluation Causal Impact AnalysisPolicy Evaluation Coarsened Exact MatchingPolicy Evaluation Counterfactual Impact EvaluationPolicy Evaluation Difference-in-DifferencesPolicy Evaluation Entropy BalancingPolicy Evaluation Event Study DesignPolicy Evaluation Fuzzy Regression DiscontinuityPolicy Evaluation Instrumental VariablesPolicy Evaluation Interrupted Time SeriesPolicy Evaluation Marginal Structural ModelPolicy Evaluation Matching EstimatorPolicy Evaluation Panel Event StudyPolicy Evaluation Placebo TestPolicy Evaluation Propensity Score MatchingPolicy Evaluation Propensity Score WeightingPolicy Evaluation Regression Discontinuity DesignPolicy Evaluation Synthetic Control MethodPretest-Posttest Experimental DesignPropensity Score Matching in Education ResearchPropensity Score WeightingPropensity Score Weighting in Education ResearchRandom Effects ModelRegression Discontinuity DesignRegression discontinuity design in education researchRegression Discontinuity in ElectionsRegression Kink DesignRobust Counterfactual Impact EvaluationRobust Difference-in-DifferencesRobust Fuzzy Regression DiscontinuityRobust Instrumental VariablesRobust Interrupted Time SeriesRobust Marginal Structural ModelRobust Matching EstimatorRobust Panel Event StudyRobust Regression Discontinuity DesignRobust Synthetic Control MethodSensitivity Analysis for CausalitySensitivity analysis for causality in education researchShift-Share IVSpatial Causal Impact AnalysisSpatial Coarsened Exact MatchingSpatial Counterfactual Impact EvaluationSpatial Difference-in-DifferencesSpatial Doubly Robust EstimationSpatial Event Study DesignSpatial Inverse Probability WeightingSpatial Panel Event StudySpatial Regression Discontinuity DesignSpatial Sensitivity Analysis for CausalitySpatial Synthetic Control MethodStepped Wedge Cluster Randomized TrialStructural Break Panel Data AnalysisSynthetic Control MethodSynthetic Control Method in Education Research

Similar methods

Panel Data Difference-in-DifferencesPolicy Evaluation Difference-in-DifferencesStaggered Difference-in-DifferencesDynamic Difference-in-DifferencesDifference-in-Differences in Education ResearchEvent Study DesignSynthetic Difference-in-DifferencesMulti-period Matching Estimator

Related reference concepts

Quasi-Experimental and Natural Experiment DesignNatural ExperimentCounterfactual ReasoningCausal InferenceAbsolute Risk DifferenceEffect Modification and Interaction

Spotted an issue on this page? Report or suggest a fix →

ScholarGate — Difference-in-Differences (Difference-in-Differences Estimator). Retrieved 2026-07-20 from https://scholargate.app/en/econometrics/difference-in-differences · Dataset: https://doi.org/10.5281/zenodo.20539026
Quick facts
Originator
Card & Krueger (canonical 1994 application); Angrist & Pischke (textbook treatment)
Year
1994
Type
Causal inference / panel regression
Estimator
Interaction coefficient of treatment × time (ATT)
Outcome
continuous or binary
KeyAssumption
Parallel trends
Related methods
Granger CausalityInstrumental Variables in Health ResearchOLS RegressionPanel Fixed EffectsPropensity Score Matching
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