Causal Inference Guide

A skill for applying quasi-experimental causal inference methods in observational research. Covers difference-in-differences, instrumental variables, regression discontinuity designs, and synthetic control methods with implementation code and diagnostic checks.

Difference-in-Differences (DiD)

Classic Two-Period DiD

import numpy as np
import pandas as pd
import statsmodels.formula.api as smf

def did_estimation(df: pd.DataFrame, outcome: str, treatment: str,
                    post: str, covariates: list[str] = None) -> dict:
    """
    Estimate a difference-in-differences model.

    Args:
        df: Panel DataFrame
        outcome: Name of outcome variable column
        treatment: Name of treatment group indicator (0/1)
        post: Name of post-treatment period indicator (0/1)
        covariates: Optional list of control variable names
    """
    # Create interaction term
    df = df.copy()
    df['did'] = df[treatment] * df[post]

    # Build formula
    formula = f"{outcome} ~ {treatment} + {post} + did"
    if covariates:
        formula += ' + ' + ' + '.join(covariates)

    model = smf.ols(formula, data=df).fit(cov_type='cluster',
                                           cov_kwds={'groups': df.get('unit_id', df.index)})

    return {
        'did_estimate': model.params['did'],
        'se': model.bse['did'],
        'p_value': model.pvalues['did'],
        'ci_95': (model.conf_int().loc['did', 0], model.conf_int().loc['did', 1]),
        'r_squared': model.rsquared,
        'n_obs': model.nobs,
        'interpretation': (
            f"The treatment effect is {model.params['did']:.3f} "
            f"(SE = {model.bse['did']:.3f}, p = {model.pvalues['did']:.4f}). "
            f"{'Statistically significant' if model.pvalues['did'] < 0.05 else 'Not significant'} "
            f"at the 5% level."
        )
    }

Parallel Trends Test

The key identifying assumption. Test it with pre-treatment data:

def test_parallel_trends(df: pd.DataFrame, outcome: str,
                          treatment: str, time: str,
                          treatment_period: int) -> dict:
    """
    Test the parallel trends assumption using event study specification.
    """
    df = df.copy()
    pre_periods = sorted(df[df[time] < treatment_period][time].unique())

    # Create period dummies interacted with treatment
    for t in pre_periods:
        df[f'pre_{t}'] = ((df[time] == t) & (df[treatment] == 1)).astype(int)

    period_vars = [f'pre_{t}' for t in pre_periods[:-1]]  # omit last pre-period (reference)
    formula = f"{outcome} ~ {' + '.join(period_vars)} + C({time}) + C(unit_id)"

    model = smf.ols(formula, data=df).fit()

    # Joint F-test: all pre-treatment interactions = 0
    f_test = model.f_test(' = '.join([f'{v} = 0' for v in period_vars]))

    return {
        'pre_period_coefficients': {v: model.params[v] for v in period_vars},
        'f_statistic': f_test.fvalue[0][0],
        'f_pvalue': f_test.pvalue,
        'parallel_trends_hold': f_test.pvalue > 0.05,
        'interpretation': (
            'Parallel trends assumption supported (cannot reject joint null)'
            if f_test.pvalue > 0.05
            else 'WARNING: Parallel trends assumption may be violated'
        )
    }