DynamicPanelModels.jl

DynamicPanelModels.jl is a Julia package for estimating linear dynamic panel data models — panel regressions with a lagged dependent variable — via Generalized Method of Moments (GMM). It provides the three standard estimators from the dynamic panel literature:

DifferenceGMM — Arellano & Bond (1991)
SystemGMM — Blundell & Bond (1998)
AndersonHsiao — Anderson & Hsiao (1981), as a simple IV baseline

Why this exists

Panel data with a lagged dependent variable ($y_{it} = \alpha y_{i,t-1} + x_{it}'\beta + \eta_i + \varepsilon_{it}$) cannot be consistently estimated with OLS or the standard fixed-effects (within) estimator: differencing or demeaning to remove the individual effect $\eta_i$ mechanically correlates the transformed lagged-dependent-variable regressor with the transformed error term (Nickell, 1981). GMM estimators built around instrumenting that lagged term — Difference GMM and System GMM — are the standard fix, widely used in applied macro/micro panel work (e.g. growth regressions, firm investment, labor dynamics) wherever T is short and N is large.

DynamicPanelModels.jl implements that estimation pipeline end to end: correct instrument construction (including the subtleties of unbalanced panels and forward orthogonal deviations), one-step and two-step GMM with cluster-robust and Windmeijer (2005) finite-sample-corrected standard errors, and the diagnostic tests (Sargan/Hansen, Arellano-Bond AR tests) needed to check whether the identifying assumptions actually hold on your data — because a dynamic panel GMM estimate without those checks is not trustworthy on its own.

Key features

Three estimators in one consistent interface: fit(DifferenceGMM(), df; ...).
Correct inference: one-step/two-step GMM, cluster-robust and Windmeijer-corrected standard errors — not just plug-in asymptotic SEs.
Diagnostics built in: Sargan/Hansen J-test, AR(1)/AR(2) serial correlation tests, instrument-proliferation check, Wald test, and a difference-in-Hansen test for nested instrument sets, all via diagnose.
Practical controls: instrument collapsing and min_lag/max_lag limits (xtabond2-style) for large-T panels where the instrument count can otherwise explode; forward orthogonal deviations for unbalanced panels.
Ecosystem-native: accepts any Tables.jl source, supports both string and StatsModels @formula syntax, and fitted models implement the standard StatsAPI (coef, vcov, stderror, confint, …) plus RecipesBase diagnostic plots.

Quick example

using DynamicPanelModels, DataFrames

# df must be in long format with :id and :time columns
model = fit(DifferenceGMM(robust=true), df;
            formula = "y ~ lag(y) + x1",
            id_col = :id,
            time_col = :time,
            exog = ["x1"])

println(model)      # Stata-like summary table
diagnose(model)      # Sargan, AR(1)/AR(2), normality tests

Where to go next

Getting Started — installation, input data format, a full worked example, and the methodology behind each estimator.
API Reference — every exported function, organized by category.

Scope

This package covers linear dynamic panel models (a continuous dependent variable with a lagged-dependent-variable regressor). Nonlinear dynamic panel models — binary choice or count data with a lagged dependent variable — are a distinct econometric problem without a widely-used reference implementation to validate against, and are out of scope here.