Getting Started

Installation

The package is currently unregistered and can be installed directly from GitHub:

using Pkg
Pkg.add(url="https://github.com/MichalS16/DynamicPanelModels.jl")

Input data

Panel data must be in long format, with one row per individual-period observation and separate ID and time columns:

Any Tables.jl-compatible source is accepted, so a DataFrame, a CSV.File, or any other Tables.jl source will work.

Fitting a model

using DynamicPanelModels
using DataFrames

model = fit(DifferenceGMM(robust=true), df;
            formula = "y ~ lag(y) + x1",
            id_col = :id,
            time_col = :time,
            exog = ["x1"])

Three estimators are available: DifferenceGMM (Arellano-Bond, 1991), SystemGMM (Blundell-Bond, 1998), and AndersonHsiao (1981). Regressors passed via exog are additionally used as their own GMM instruments; without it, non-lagged regressors are only weakly identified through their correlation with the lagged-dependent-variable instruments. Setting time_effects=true adds period dummies to absorb common time shocks, and transform=:fod switches DifferenceGMM from first differences to forward orthogonal deviations, which handles unbalanced panels better.

Methodology

All three estimators start from the same fixed-effects AR(1) model, $y_{it} = \alpha y_{i,t-1} + x_{it}'\beta + \eta_i + \varepsilon_{it}$, with $\eta_i$ an unobserved individual effect correlated with $y_{i,t-1}$ (so OLS/within estimation is biased — Nickell, 1981). Differencing removes $\eta_i$: $\Delta y_{it} = \alpha \Delta y_{i,t-1} + \Delta x_{it}'\beta + \Delta \varepsilon_{it}$.

• Difference GMM (DifferenceGMM, Arellano & Bond 1991) instruments $\Delta y_{i,t-1}$ with all valid lagged levels $y_{i,t-2}, y_{i,t-3}, \dots$, relying only on no serial correlation in $\varepsilon_{it}$. It performs poorly when $\alpha$ is close to 1 or the ratio $\mathrm{var}(\eta_i)/\mathrm{var}(\varepsilon_{it})$ is large, because lagged levels become weak predictors of $\Delta y_{i,t-1}$ in that regime.
• System GMM (SystemGMM, Blundell & Bond 1998) adds the levels equation back in, instrumented with lagged differences $\Delta y_{i,t-1}, \Delta x_{i,t-1}$ (not lagged levels — a common point of confusion, since simplified treatments sometimes state the level-equation moment condition symbolically as $E[(y_{it} - y_{i,t-1}) y_{i,t-1}] = 0$, which is actually the standard first-differenced moment condition rewritten in levels, not the level equation's own instrument set). This requires the extra mean-stationarity assumption $E[\eta_i \Delta y_{it}] = 0$ and improves efficiency exactly where Difference GMM struggles ($\alpha$ near 1).
• Anderson-Hsiao (AndersonHsiao, 1981) instruments $\Delta y_{i,t-1}$ with a single lagged level $y_{i,t-2}$, giving a consistent but less-efficient IV baseline (it is the $T=2$-instrument special case that Arellano-Bond generalizes).

Standard errors follow Windmeijer (2005): the naive two-step GMM covariance understates variability because it ignores the estimation error in the first-step weighting matrix; the correction restores accurate finite-sample inference. See diagnose for the accompanying Sargan/Hansen and AR tests that check the instrument and serial-correlation assumptions each estimator relies on.

Inspecting results

The fitted model supports the usual StatsAPI accessors:

println(model)      # Stata-like summary table
coef(model)         # coefficient vector
stderror(model)     # standard errors (Windmeijer-corrected, if applicable)
confint(model)      # confidence intervals

Diagnostics

diagnose(model)     # Sargan, AR(1), AR(2), and normality tests in one call
sargan_test(model)  # instrument validity (overidentifying restrictions)
ar_test(model, 2)   # serial correlation in the differenced errors

A significant AR(1) statistic is expected after first-differencing; a significant AR(2) statistic instead points to model misspecification.

Visualization

using Plots
plot(model)              # four-panel diagnostic dashboard
plot(model, :residuals)  # standardized residuals over time

The API Reference lists every exported function.