Causal Inference

This repository demonstrates quasi-experimental methods — Difference-in-Differences (DiD) and Event-Study analysis — using simulated panel data. These examples showcase skills in causal inference, observational data analysis, and reproducible research.

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1. Problem Setup

We simulate a panel of 1,000 individuals observed from 2010 to 2020. A subset of individuals receives a “treatment” (e.g., a policy intervention or vaccination) starting in 2015. The goal is to estimate the causal effect of treatment on cognition_score.

Data variables:

• id: individual identifier
• year: year of observation
• age: individual age
• treated: 1 if the individual is in the treatment group, 0 otherwise
• post: 1 if year ≥ 2015, 0 otherwise
• cognition_score: simulated outcome
• event_time: relative time to treatment (year - 2015)

Number of observations: 1,000 individuals × 11 years = 11,000 observations

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2. Difference-in-Differences (DiD)

The standard DiD model with individual and year fixed effects is:

Y_it = α_i + λ_t + β * (T_i × Post_t) + ε_it

where:

• Y_it = cognition score for individual i at year t
• α_i = individual fixed effect
• λ_t = year fixed effect
• T_i = 1 if treated, 0 otherwise
• Post_t = 1 if year ≥ 2015, 0 otherwise
• β = treatment effect (causal estimate)
• ε_it = error term

Results:

Variable	Estimate	Std. Error	Significance
treated × post	1.995	0.077	***

• Observations: 11,000
• R²: 0.534
• Within R²: 0.063

Interpretation:

• The DiD model estimates that the treatment increases the cognition score by approximately 2 points post-intervention, controlling for individual and year fixed effects.
• The effect is highly statistically significant (p < 0.01).
• Pre-treatment trends (years < 2015) are flat, consistent with the parallel trends assumption required for causal identification.
• Parallel trends are visualized in output/plots/parallel_trends.png.

This analysis demonstrates a causal effect of the intervention under standard DiD assumptions.

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3. Event-Study Analysis

To explore dynamic treatment effects, we estimate an event-study specification:

Y_it = α_i + λ_t + Σ_{k ≠ -1} β_k * 1[EventTime_it = k] * T_i + ε_it

• EventTime_it = t - t0 (years relative to treatment)
• β_k measures the effect k years from treatment
• Reference period: k = -1

Results (select):

Event Time	Estimate	Std. Error	Significance
-5	0.147	0.179	n.s.
0	2.052	0.179	***
1	2.114	0.179	***
2	2.205	0.179	***

Interpretation:

• No pre-treatment trends (years < 0 have estimates close to 0), supporting the parallel trends assumption.
• The treatment effect appears at year 0 and persists in subsequent years, consistent with a causal effect.
• Dynamic treatment effects are visualized in output/plots/event_study.png.

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4. Reproducibility

The repository contains three R scripts:

1. scripts/generate_data.R – Simulates panel data for the example
2. scripts/analysis_DiD.R – Runs Difference-in-Differences analysis and saves output
3. scripts/event_study.R – Runs Event-Study analysis and saves output

Output folders:

• data/ – Simulated dataset (simulated_data.csv)
• output/plots/ – Figures for parallel trends and event-study
• output/tables/ – Regression tables (did_results.txt)

Run scripts in sequence:

Rscript scripts/generate_data.R
Rscript scripts/analysis_DiD.R
Rscript scripts/event_study.R