Panel Data & Causal Inference
Statios supports canonical panel data estimators (FE, RE, Hausman test, 2SLS-IV), advanced dynamic panel methods (Arellano-Bond, System GMM), and modern causal inference designs (DiD, RDD, synthetic control, staggered DiD, IPW, mediation analysis).
51 procedures · 2 with documented limitations. Every result is computed by the open Python engine and is exportable to APA tables and reports.
| Procedure | What it does | Status | Key reference |
|---|---|---|---|
| Fixed Effects Panel Regression | Within-transformation OLS eliminating time-invariant unobserved heterogeneity. Optional two-way (entity + time) fixed effects. | ✅ Full | Seabold & Perktold (2010) |
| Random Effects Panel Regression | GLS panel estimator assuming random effects uncorrelated with regressors. | ✅ Full | Seabold & Perktold (2010) |
| Hausman Specification Test | Tests FE vs RE using Moore-Penrose generalized inverse when covariance difference non-positive semidefinite (finite-sample robust). | ✅ Full | Hausman (1978) |
| Two-Stage Least Squares (2SLS) IV | Instrumental variables regression with heteroskedasticity-robust first-stage F-test and weak-instrument diagnostics. | ✅ Full | Seabold & Perktold (2010) |
| Arellano-Bond Difference GMM | Dynamic panel estimator using lagged levels as instruments for differenced equations; includes Sargan and AR(1)/AR(2) tests. | ✅ Full | Arellano & Bond (1991) |
| Blundell-Bond System GMM | Two-step efficient GMM stacking level and difference equations; Hansen J test and AR tests. | ✅ Full | Blundell & Bond (1998); Arellano & Bover (1995) |
| Hausman-Taylor Estimator | Estimates time-varying exogenous, time-invariant exogenous, and endogenous coefficients using within and between equations. | ✅ Full | Hausman & Taylor (1981); Hausman (1978) |
| Between Estimator | OLS on entity-level means; removes within-group variation. | ✅ Full | Baltagi (2021) |
| First-Difference Estimator | Eliminates time-invariant heterogeneity via differencing; OLS on changes. | ✅ Full | Baltagi (2021) |
| Panel-Corrected Standard Errors (Beck-Katz PCSE) | Kernel-based covariance estimator robust to contemporaneous and lagged cross-sectional dependence. | ✅ Full | Beck & Katz (1995) |
| Driscoll-Kraay Standard Errors | Robust to both cross-sectional and temporal dependence via time clustering. | ✅ Full | Driscoll & Kraay (1998) |
| Panel Cointegration Tests | Pedroni, Kao, or Fisher method tests for long-run equilibrium relationships in panel data. | ✅ Full | Pedroni (1999); Pedroni (2004) |
| Panel Granger Causality (Fisher Combined) | Granger test per entity combined via Fisher's method across units. | ✅ Full | Granger (1969); Maddala & Wu (1999) |
| Cross-Sectional Dependence Test | Pesaran CD, Frees, or Friedman test for contemporaneous cross-unit correlation. | ✅ Full | Pesaran (2004); Frees (1995) |
| Panel ARDL (Mean Group / Dynamic Fixed Effects) | Panel autoregressive distributed lag models: Mean Group (averages unrestricted per-entity long-run estimates) and Dynamic Fixed Effects (pooled with entity intercepts). Reports short-run, long-run, and ECM terms. | ✅ Full | Pesaran & Smith (1995); Pesaran et al. (1999) |
| Mundlak (Correlated Random Effects) | RE model augmented with entity means; joint test on means equivalent to Hausman test; robust to cluster heteroskedasticity. | ✅ Full | Mundlak (1978) |
| Panel RE Test (Breusch-Pagan LM) | Breusch-Pagan Lagrange-multiplier test for entity random effects in a panel: from pooled-OLS residuals it forms the two-sided BP-LM (chi-squared, 1 df) and the more powerful one-sided Honda statistic (normal) from grouped within-entity residual sums, handles balanced and unbalanced panels, and verdicts whether pooled OLS is adequate or a random/fixed-effects estimator is required. | ✅ Full | Breusch & Pagan (1980); Honda (1985) |
| Panel Serial-Correlation Test (Wooldridge) | Wooldridge (2002) F-test for first-order serial correlation in the idiosyncratic errors of a linear panel model -- first-differences the equation, regresses the differenced residuals on their own lag and tests whether the slope equals the no-serial-correlation value of -0.5 (cluster-robust, as Stata xtserial), and also reports the Baltagi-Wu LBI. | ✅ Full | Wooldridge (2002); Drukker (2003); Baltagi & Wu (1999) |
| Anderson-Hsiao Dynamic Panel | Anderson-Hsiao IV estimator for dynamic panels: first-differences out the fixed effect, then instruments the differenced lagged dependent with its t-2 level via 2SLS, recovering a consistent persistence coefficient where pooled OLS and within are biased. | ✅ Full | Anderson & Hsiao (1981, JASA; 1982, J. Econometrics) |
| FOD-GMM Dynamic Panel (Helmert) | Arellano-Bover (1995) forward-orthogonal-deviations (Helmert) GMM for dynamic panels: removes fixed effects via the FOD transform (which keeps the idiosyncratic errors serially uncorrelated, so the one-step weight is simply (Z'Z)^-1), instruments the transformed lagged dependent with the expanding set of lagged levels, and reports coefficient estimates (coef/se/z/p) with entity-clustered robust SEs and a Hansen J over-identification test - markedly less biased than the within estimator for short T. | ✅ Full | Arellano & Bover (1995, J. Econometrics 68:29-51) |
| Bias-Corrected FE (dynamic panel) | Within (LSDV) fixed-effects estimation of a dynamic panel with a lagged dependent variable, then the analytical Nickell (1981) / Kiviet (1995) correction of the finite-T within (Nickell) bias subtracted from the autoregressive coefficient, returning the uncorrected and bias-corrected persistence plus the bias estimate. | ✅ Full | Nickell (1981); Kiviet (1995) |
| Parks-Kmenta FGLS (long panel) | Feasible GLS for long balanced panels (T > N) that simultaneously corrects for panel heteroskedasticity, contemporaneous cross-sectional correlation, and panel-specific AR(1) serial correlation, returning efficient slope estimates, per-entity AR(1) coefficients, and Parks-Kmenta standard errors (with the standard over-optimism caveat). | ✅ Full | Parks (1967); Kmenta (1986) |
| Common Correlated Effects (CCE) | Pesaran (2006) CCE estimator for heterogeneous panels with cross-sectional dependence: augments each unit's regression with cross-sectional averages of the dependent and regressors to proxy and absorb the unobserved common factors, then reports the Mean-Group (CCEMG) or Pooled (CCEP) slopes, which remain consistent where plain fixed effects is biased by the factor. | ✅ Full | Pesaran (2006, Econometrica) |
| Panel Quantile Regression (Canay) | Estimates fixed-effects panel quantile regression via Canay's (2011) two-step estimator -- removing each entity's location-shift fixed effect from a within mean regression, then running ordinary quantile regression at tau on the de-fixed data -- yielding slope effects on the conditional tau-quantile that are robust to entity fixed effects (unlike biased pooled quantile regression). | ✅ Full | Canay (2011, Econometrics Journal 14:368-386) |
| Error Components + AR(1) (Baltagi-Li) | One-way random-effects panel whose idiosyncratic error follows an AR(1) process: estimates the autocorrelation parameter rho, applies the Baltagi-Li Prais-Winsten transform and Sherman-Morrison FGLS, reports the variance components, the FGLS coefficient table, and a test of rho=0 (no serial correlation). | ✅ Full | Baltagi & Li (1991) |
| Pooled Mean Group (PMG) | Estimates a dynamic heterogeneous panel ARDL error-correction model with common (pooled) long-run coefficients and unit-specific short-run dynamics and adjustment speeds via the Pesaran-Shin-Smith concentrated-likelihood iteration, reporting pooled long-run coef/se/z/p, the average error-correction speed, per-unit speeds, and a Hausman MG-vs-PMG poolability test. | ✅ Full | Pesaran, Shin & Smith (1999, JASA) |
| MINQUE/MIVQUE Variance Components | Estimates the between-entity and idiosyncratic variance components of a one-way error-components panel by Rao's non-iterative Minimum-Norm/Minimum-Variance Quadratic Unbiased estimator (handles unbalanced panels cleanly, unlike ANOVA), reports the implied intraclass correlation, and forms the FGLS slope estimates. | ✅ Full | Rao (1971); Baltagi (2008) |
| Random-Trend Panel | Fixed-effects panel model that gives every entity its own intercept AND its own linear time trend (swept out via a double-within detrending transform), recovering the common predictor slopes purged of the unit-specific trends that would bias a plain one-way FE estimator. | ✅ Full | Wooldridge (2010, Econometric Analysis of Cross Section and Panel Data, Sec. 11.7.2) |
| BLUP of Random Effects | Predicts each entity's unobserved random effect after a one-way random-effects (GLS) panel fit by shrinking its mean composite residual toward zero with the Henderson BLUP factor theta_i = sigma_u^2/(sigma_u^2 + sigma_e^2/T_i), reporting per-entity BLUPs, the shrinkage factor, and the variance components. | ✅ Full | Henderson (1975); Baltagi (2008) |
| Two-Way Random Effects | Two-way error-components GLS panel model with random entity AND time effects, estimating the entity, time, and idiosyncratic variance components (Wallace-Hussain) and reporting the Fuller-Battese theta transforms and FGLS coefficients. | ✅ Full | Baltagi (2008); Wallace & Hussain (1969) |
| Panel Unit Root (IPS / LLC) | First-generation panel unit-root tests on a long panel: the Im-Pesaran-Shin W-bar statistic (standardised average of per-entity augmented Dickey-Fuller t-stats, allowing heterogeneous AR roots) plus the Levin-Lin-Chu pooled t* (common-rho, bias-adjusted), each returned with its N(0,1) p-value, the per-entity ADF t-stats and a stationary/unit-root verdict. | ✅ Full | Im, Pesaran & Shin (2003); Levin, Lin & Chu (2002) |
| Panel Cross-Sectional Dependence (BP-LM) | Tests panel errors for cross-sectional dependence from within-model residuals: the Breusch-Pagan LM (sum of T-weighted squared pairwise residual correlations ~ chi2(N(N-1)/2)), the Pesaran (2004) scaled LM, the Pesaran-Ullah-Yamagata (2008) bias-corrected scaled LM, and the reference Pesaran CD statistic, each with p-values and a verdict. | ✅ Full | Breusch & Pagan (1980); Pesaran, Ullah & Yamagata (2008) |
| CIPS Panel Unit Root (2nd-gen) | Pesaran (2007) cross-sectionally augmented IPS panel unit-root test, robust to cross-sectional dependence from a common factor: it averages per-entity CADF t-stats (each ADF regression augmented with the cross-section means of the lagged level and the differences) and compares the CIPS statistic against the non-standard Pesaran critical values. | ✅ Full | Pesaran (2007, J. Appl. Econometrics 22:265-312) |
| Panel Poolability (Chow-F) | Chow-type F test of panel poolability comparing restricted pooled-OLS SSR against the sum of unrestricted per-entity OLS SSRs to assess whether intercepts and slopes are homogeneous across entities, F~F((G-1)(k+1), N-G(k+1)). | ✅ Full | Baltagi (2008); Chow (1960) |
| Difference-in-Differences (DiD) | 2x2 DiD with cluster-robust or HC1 SEs; includes group means and specification. | ✅ Full | Card & Krueger (1994); Bertrand et al. (2004) |
| Regression Discontinuity (Sharp RDD) | Local polynomial with triangular or uniform kernel; ad-hoc 1.5*SD bandwidth (not MSE-optimal) or user-specified. | ⚠️ Limited | Seabold & Perktold (2010) |
| Propensity Score Matching (PSM) | Logistic propensity score with 1-NN matching on logit scale; caliper on logit scale (Austin 2011); naive paired SE (Abadie-Imbens not applied). | ⚠️ Limited | Rosenbaum & Rubin (1983) |
| Chow Structural Break Test | Tests equality of regression coefficients across two subsamples; F-statistic with df protection. | ✅ Full | Virtanen et al. (2020) |
| Synthetic Control Method | Weighted combination of donors minimizing pre-treatment MSE; RMSPE ratio and period-level treatment effects. | ✅ Full | Abadie et al. (2010); Abadie & Gardeazabal (2003) |
| Event-study (dynamic two-way fixed effects) | Conventional dynamic TWFE event study: two-way FE with relative-time dummies; pre-treatment trend test; reference period omitted. | ✅ Full | Sun & Abraham (2021) |
| Staggered DiD (Callaway & Sant'Anna 2021) | Group-time ATT estimates with not-yet-treated comparison group; bootstrap SEs; dynamic, group, and calendar aggregations. | ✅ Full | Callaway & Sant'Anna (2021); Goodman-Bacon (2021) |
| IV Diagnostics | First-stage F-tests, Cragg-Donald Wald F, Sargan over-identification, Durbin endogeneity test. | ✅ Full | Stock & Yogo (2005); Cragg & Donald (1993) |
| Inverse-Probability Weighting (IPW) | Logistic propensity score weighting; ATE, ATT, or ATU estimands. | ✅ Full | Rosenbaum & Rubin (1983); Horvitz & Thompson (1952) |
| Doubly Robust Estimation | Outcome model + propensity weighting; consistent if either model correct. | ✅ Full | Rosenbaum & Rubin (1983); Robins et al. (1994) |
| Local Average Treatment Effect (LATE) | IV-based LATE for compliers only; asymptotic SE under 2SLS. | ✅ Full | Imbens & Angrist (1994) |
| Classical Mediation Analysis | Classical Baron-Kenny path decomposition (direct/indirect effects) with a Sobel test and a percentile bootstrap CI for the indirect effect. | ✅ Full | Baron & Kenny (1986); Sobel (1982); Preacher & Hayes (2008) |
| Sensitivity Analysis | E-value or Rosenbaum bounds for unobserved confounding robustness. | ✅ Full | VanderWeele & Ding (2017); Rosenbaum (2002) |
| Lee Bounds | Nonparametric bounds under sample selection on unobservables. | ✅ Full | Lee (2009) |
| Manski Treatment Bounds | Worst-case partial-identification (Manski 1990) bounds on the average treatment effect of a binary treatment, with monotone-treatment-response and monotone-treatment-selection refinements that tighten the identified ATE interval. | ✅ Full | Manski (1990); Manski & Pepper (2000) |
| Sharp Regression Kink Design (RKD) | Sharp RKD: estimates the change in the outcome's slope at the threshold via piecewise-linear local regression (assumes a known unit kink in the assignment-to-policy map). | ✅ Full | Card et al. (2015) |
| Bunching Estimator (normalized excess mass) | Estimates excess mass at a policy threshold by fitting a counterfactual polynomial density excluding the bunching region; reports the normalized excess mass (bunching ratio). | ✅ Full | Saez (2010); Kleven (2016) |
Notes & limitations
- Regression Discontinuity (Sharp RDD) — Bandwidth selection is ad-hoc (not Imbens-Kalyanaraman or Calonico-Cattaneo-Titiunik data-driven optimal); local-linear only.
- Propensity Score Matching (PSM) — Uses naive paired SE; does not apply Abadie-Imbens (2006) variance correction for estimated scores and matching with replacement.