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130 lines
3.8 KiB
Markdown
130 lines
3.8 KiB
Markdown
# Difference-in-Differences (DiD)
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Causal inference estimator for measuring treatment effects using before/after comparison with a control group.
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## Installation
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```bash
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npm install @tpmjs/tools-diff-in-diff
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```
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## Usage
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```typescript
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import { diffInDiffTool } from '@tpmjs/tools-diff-in-diff';
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// Example: Evaluate impact of a policy intervention
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// Treatment group: Cities that implemented the policy
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// Control group: Cities that did not implement the policy
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const result = await diffInDiffTool.execute({
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treatmentBefore: [100, 105, 98, 102], // Before policy
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treatmentAfter: [120, 125, 118, 122], // After policy
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controlBefore: [95, 100, 92, 98], // Before (no policy)
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controlAfter: [98, 103, 95, 101], // After (no policy)
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confidenceLevel: 0.95,
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});
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console.log(result);
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// {
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// effect: 17.5, // Treatment caused 17.5 unit increase
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// standardError: 2.1,
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// tStatistic: 8.33,
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// pValue: 0.0001,
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// significant: true,
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// confidenceInterval: {
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// lower: 13.2,
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// upper: 21.8,
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// level: 0.95
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// },
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// interpretation: "The treatment effect is 17.5 (increased by 17.5 units)...",
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// groupMeans: {
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// treatmentBefore: 101.25,
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// treatmentAfter: 121.25,
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// controlBefore: 96.25,
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// controlAfter: 99.25
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// },
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// differences: {
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// treatmentDiff: 20.0, // Treatment group change
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// controlDiff: 3.0 // Control group change
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// }
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// }
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```
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## API
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### Input
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- **treatmentBefore** (required): Treatment group values before intervention
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- **treatmentAfter** (required): Treatment group values after intervention
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- **controlBefore** (required): Control group values before intervention
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- **controlAfter** (required): Control group values after intervention
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- **confidenceLevel** (optional): Confidence level (default: 0.95)
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### Output
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- **effect**: Estimated causal treatment effect (DiD estimator)
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- **standardError**: Standard error of the estimate
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- **tStatistic**: Test statistic for significance testing
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- **pValue**: Two-tailed p-value
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- **significant**: Whether effect is statistically significant
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- **confidenceInterval**: Confidence interval for the effect
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- **interpretation**: Plain English interpretation
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- **groupMeans**: Mean values for all four groups
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- **differences**: Within-group changes over time
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## Algorithm
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The DiD estimator removes time-invariant confounders by differencing:
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**Formula**: `DiD = (T_after - T_before) - (C_after - C_before)`
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Where:
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- T = Treatment group
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- C = Control group
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This double-differencing removes:
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1. Time trends (via control group)
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2. Group differences (via before/after comparison)
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**Key Assumption**: Parallel trends - Without treatment, both groups would have changed similarly.
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## Use Cases
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- **Policy evaluation**: Measure impact of new regulations
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- **Marketing**: Test effectiveness of campaigns
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- **Medicine**: Clinical trials with before/after measurements
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- **Economics**: Evaluate economic interventions
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- **Education**: Assess program effectiveness
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## Example: Minimum Wage Study
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```typescript
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// States that raised minimum wage (treatment)
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// vs states that didn't (control)
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const result = await diffInDiffTool.execute({
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treatmentBefore: [5.2, 5.5, 5.1, 5.4], // Employment before
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treatmentAfter: [5.1, 5.3, 5.0, 5.2], // Employment after
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controlBefore: [5.3, 5.4, 5.2, 5.5],
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controlAfter: [5.4, 5.5, 5.3, 5.6],
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});
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// Effect tells us the causal impact on employment
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```
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## Interpretation
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A **positive effect** means treatment increased the outcome.
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A **negative effect** means treatment decreased the outcome.
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**Statistical significance** (p < 0.05) suggests the effect is real, not due to chance.
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## Limitations
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- Requires parallel trends assumption
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- Can't control for time-varying confounders
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- Sensitive to outliers
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- Needs sufficient sample size
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## License
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MIT
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