Panel Data Simulation Lab

Actions

Generate a new random sample with current parameters, or download the simulated data for external analysis.

Scenario Presets

Click a preset to load parameter values demonstrating specific phenomena.

Data Generation Parameters

Adjust parameters to control the simulated panel data. Click headers to expand/collapse sections.

Sample Structure

Individuals (N):

More individuals → more precise estimates

Time Periods (T):

More periods → better within-person variation for FE

True Causal Effect

True β (causal effect):

The "ground truth" we're trying to estimate. Compare β̂ to this.

Selection into Treatment

Base P(D=1):

Overall treatment prevalence when there's no selection.

Selection Strength (ρ):

Key! ρ > 0 → selection bias in OLS; FE corrects this.

Switching Rate:

Higher → more within-person variation → more FE power.

Variance Components

Between-person SD (σ_u):

Unobserved individual factors. FE removes these; RE assumes uncorrelated with D.

Within-person SD (σ_ε):

Random shocks varying across time (transitory variation).

Measurement Error (σ_me):

Classical measurement error in Y. Adds noise, no bias.

Heterogeneity & Groups

Random slope SD (σ_β):

σ_β > 0 means each person has their own effect around the mean.

Groups (G):

Split sample into G groups for subgroup analysis.

Group β spread (Δβ):

Systematic heterogeneity: groups have different average effects.

Time Dynamics

Enable time trend Trend Slope (γ):

Common time trend. Can bias estimates if correlated with D timing.

Visualization & Estimation

Visualization Options

Scatter wave:

View any wave as a cross-section.

Spaghetti lines:

More lines show more heterogeneity but can clutter.

Color points/lines by group

Estimation Options

Standard errors:

Clustered SEs appropriate for panel data.

Include linear time term (t) Include quadratic time term (t²) Include group fixed effects Group split model:

📊 Data Overview 📈 Estimator Comparison 🔍 Model Diagnostics 📚 Methodology Guide

Cross-Section: Selected Wave

Observations OLS fit

Panel Trajectories Over Time

Individual paths Mean Median IQR

Mean Outcome by Wave & Treatment

D=0 mean D=1 mean

True Effect Heterogeneity (β_i)

Mean β Individuals

What You're Seeing

Left: Cross-sectional snapshot using the selected wave. This is what you'd have without panel data. The slope shows the raw association between treatment and outcome.

Right: Individual trajectories over time. Faint lines show 20 random individuals; bold lines show aggregate statistics. Look for: (1) individual heterogeneity in levels, (2) within-person variation, (3) time trends.

Data Generating Process (DGP)

The simulated data follows this model:

y_it = α + β·D_it + u_i + ε_it + γ·t + measurement error where: • y_it = outcome for individual i at time t • D_it = binary treatment indicator (0 or 1) • β = true causal effect (what we want to estimate) • u_i = individual fixed effect (time-invariant, unobserved) • ε_it = idiosyncratic error (varies by person and time) • γ·t = time trend (if enabled) Selection mechanism: P(D_it = 1) = logistic(α + ρ·u_i/σ_u) When ρ > 0, individuals with higher u_i are more likely to receive treatment, creating omitted variable bias in simple OLS.

The Four Estimators Compared

Estimator	What It Does	Key Assumption	When It Works
Cross-Section OLS	Regress Y on D using wave 1 only	E[u_i\|D_i] = 0	No selection on unobservables
Pooled OLS	Stack all waves, ignore panel structure	E[u_i\|D_it] = 0	No selection; SEs may be wrong
Fixed Effects	Within-transformation: demean by individual	E[ε_it\|D_it, u_i] = 0	Selection on time-invariant factors OK
Random Effects	GLS with quasi-demeaning (θ)	E[u_i\|D_it] = 0 (RE exogeneity)	No correlation between u_i and D

Key insight: FE eliminates all time-invariant confounding (observed and unobserved) by using only within-person variation. The cost: we can't estimate effects of time-invariant variables, and we need within-person variation in treatment.

Understanding the Hausman Test

The Hausman test compares FE and RE estimates:

H = (β_FE - β_RE)² / (Var(β_FE) - Var(β_RE)) Under H₀: RE is consistent (no correlation between u_i and D_it) Under H₁: RE is inconsistent, FE is preferred

Interpretation:

Large H (small p-value): Reject H₀ → use FE
Small H (large p-value): Can't reject → RE may be more efficient
FE is always consistent; RE is more efficient when valid

Sources of Bias

Problem	Effect on OLS	Solution
Selection on unobservables (ρ > 0)	Upward or downward bias	FE, IV, or design-based ID
Time trends	Spurious correlation if D trends	Include time fixed effects
Measurement error in Y	Larger SEs, no bias in β	Better measures, larger N
Measurement error in D	Attenuation bias toward 0	IV, validation studies
Reverse causality	Bias direction depends on sign	Lagged D, IV, timing

Practical Recommendations

Always start with descriptives: Plot the data, understand variation patterns
Compare estimators: Large differences suggest selection bias
Run Hausman test: Formally test FE vs RE
Check diagnostics: Residual plots reveal model misspecification
Use cluster-robust SEs: Standard OLS SEs ignore within-person correlation
Consider time effects: Add wave dummies if outcomes trend over time
Report multiple specifications: Sensitivity analysis builds credibility

🎯 Learning Objective

Actions

Data Generation Parameters

Visualization & Estimation

Cross-Section: Selected Wave

Panel Trajectories Over Time

Mean Outcome by Wave & Treatment

True Effect Heterogeneity (β_i)

What You're Seeing

Estimated β with 95% Confidence Intervals

Variance Decomposition

Hausman Test: FE vs RE

Detailed Regression Results

SE Sensitivity (Same β̂, Different SEs)

Split Regressions by Group

Residuals vs Fitted

Residual Distribution

Normal Q-Q Plot

Diagnostic Interpretation

Current Simulation Summary

🎯 Learning Objective

Actions

Data Generation Parameters

Visualization & Estimation

Cross-Section: Selected Wave

Panel Trajectories Over Time

Mean Outcome by Wave & Treatment

True Effect Heterogeneity (βi)

What You're Seeing

Estimated β with 95% Confidence Intervals

Variance Decomposition

Hausman Test: FE vs RE

Detailed Regression Results

SE Sensitivity (Same β̂, Different SEs)

Split Regressions by Group

Residuals vs Fitted

Residual Distribution

Normal Q-Q Plot

Diagnostic Interpretation

Current Simulation Summary

True Effect Heterogeneity (β_i)