This note provides a brief overview about the methods suitable for dynamic panel data models with large T. In this case, the traditional go-to difference or system GMM leads to proliferation of instruments, the results become sensitive to the choice of the number of lags and there remain other problems such as endogeneity and cross-sectional dependence.

Dynamic panel data models and the Nickell bias

In dynamic panels, Nickell bias arises because removing fixed effects forces subtraction of time averages that contain past shocks, mechanically correlating lagged dependent variables with transformed errors.

Consider the standard dynamic panel model:

\[ y_{it} = \rho y_{i,t-1} + x_{it}\beta+ \alpha_i + u_{it} \]

where:

The Core Problem

To remove fixed effects, we apply the within (FE) transformation:

\[ y_{it} - \bar y_i = \rho (y_{i,t-1} - \bar y_{i,t-1}) + (u_{it} - \bar u_i) \]

But now the transformed regressor \((y_{i,t-1} - \bar y_{i,t-1})\) becomes correlated with the transformed error term \((u_{it} - \bar u_i )\).

Why this happens:

Thus even if:

\[ E(y_{i,t-1} u_{it}) = 0 \]

we still have:

\[ E[(y_{i,t-1} - \bar y_i)(u_{it} - \bar u_i)] \neq 0 \]

Result: Finite-T Bias

This induces bias in the FE estimator of \(\rho\):

This phenomenon is known as Nickell bias.

Large T Solves the Nickell bias asymptotically

As \(T \to \infty\):

Formally:

\(Bias ~ \hat \rho_{FE} = O(1/T)\)

(\(O(1/T)\) reads as “shrinks with the rate 1/T”)

So:

But other problems - endogeneity, cross-sectional dependence etc. remain an issue.

Why Large-T Changes Everything

Classic dynamic panel GMM (Arellano–Bond/System GMM) is designed for small-T settings. In macro and regional data where T is large, alternative estimators dominate because:

• Nickell bias vanishes as T grows

• Instrument proliferation becomes severe in GMM and the Hansen statistics become biased => the results become extremely sensitive on the choice of lags of variables used as internal instruments (Roodman, 2009, highlighted the impact of instrument proliferation)

• When variables are highly persistent and shocks serially correlated, lagged variables might remain correlated with current errors and the GMM with internal instruments becomes biased under endogeneity (Hayakawa 2009/2015)

• Cross-sectional dependence (CSD) becomes first-order (Chudik and Pesaran papers whowing that common factors are problem for GMM estimator)

So, for macro panels, persistent series, presence of global shocks and structural endogeneity one should consider other methods than GMM.

Also, we have now much longer time series available than a decade ago which make the large T methods feasible.

Large T - ideally more than 30, but GMM works well for low T (5–10), so with T above 20 the large T methods become feasible.

Methods for Large T dynamic panels

1. Bias-Corrected Fixed Effects (LSDV)

Core idea

Estimate dynamic FE and correct finite-sample bias analytically, via jackknife, or bootstrap. The method is an alternative to GMM when instrument proliferation makes the results unstable.

Key references

Kiviet (1995); Bruno (2005); Everaert & Pozzi (2007)

When to use

✔ Large T, moderate N
✔ Weak cross-sectional dependence (weak forms can be corrected via bootstrap - De Vos, Everaert, Ruyssen, 2015) ✔ Focus on dynamics, not global shocks

When NOT to use

✖ Strong common factors or global shocks
✖ Severe endogeneity beyond lag structure

Implementations

Implemented in Stata add-ons.

2. Fixed Effects IV / Large-T 2SLS

Core idea

When IV is needed and T is large, standard FE model becomes less biased because with large T the Nickell bias coverges to zero. Therefore, it could be reasonable to treat panel as standard FE model with external instruments.

Z_it → X_it → y_it

y_it ← ρ y_it-1 + x_it β + α_i + u_it (T large ⇒ bias ≈ 0)

Key references

Hsiao & Zhang (Journal of Econometrics, 2015) show that FE IV is unbiased when either N or T or both tend to infinity; Wooldridge (panel IV framework)

When to use

✔ Strong external instruments available
✔ CSD weak or handled via robust SE

When NOT to use

✖ Common-factor driven dependence
✖ Global shocks correlated with regressors

Implementations

Implemented in fixest R package.

3. Common Correlated Effects (CCE) Family

Core idea

The big issue in macro models is cross-sectional dependence driven by unobserved common factors. The CCE model adds cross-sectional averages of x and y to proxy those factors.

f_t ≈ avg(y_t), avg(x_t)

y_it ← ρ y_it-1 + x_it β_i + avg(y_t) + avg(x_t)

Key references

Pesaran (2006); Chudik & Pesaran (2015)

Variants

CCE pooled, CCE-MG (mean group, for heterogeneous slopes - often preferred in macroeconomic models), dynamic CCE, Cross-sectionally augmented ARDL (essentially ARDL model with fixed effects; useful when long-run effects are of interest and cointegration is needed).

When to use

✔ Global shocks or macro comovement
✔ Heterogeneous countries/regions
✔ Medium–large T

When NOT to use

✖ Endogeneity requiring strong external IV (at least I do not know implementations doing that)

Implementations

CCE-pooled and CCE-mean groupmplemented in plm package in R.

CS-ARDL needs to be implemented manually by constructing cross-sectional average and lags and estimating with plm or fixest packages.

For Stata xtdcce2 can be used.

4. Interactive Fixed Effects (Factor Models; alternative to CCE)

Core idea

Model errors explicitly as latent common factors to deal with cross-sectional dependence. Sequential method: estimation of common factors (principal components can be used), substract factors from variables (defactor them), run FE/FE-IV on defactored components.

u_it = λ_i’ f_t + ε_it

Key references

Bai (2009); Moon & Weidner (2015)

When to use

✔ Rich latent common shocks
✔ Need to estimate factor structure
✔ Strong cross-sectional dependence

When NOT to use

✖ Very small T
✖ When simpler CCE already works

Implementations

R implementation - package phtt, now removed from CRAN. FixedEffectjlr calling Julia from R exists.

5. Defactored Two-Stage IV (Large-T IV with Common Factors)

Core idea

Method, which handles both endogeneity and adds common factors to deal with cross-sectional dependence. Both internal instruments (lags) and external instruments are feasible. Ability to use external instruments makes this method appealing. Estimate factors → remove them → run IV on cleaned data.

Key references

Norkutė et al. (2021); Kripfganz & Sarafidis (2021)

When to use

✔ Endogeneity + global shocks
✔ External instruments available
✔ Large N and T

When NOT to use

✖ No credible instruments
✖ Very small T

Implementations

Implemented in Stata add-on xtivdfreg. In R, the method can be replicated piece by piece: (i) estimate factors by PC, (ii) defactor covariates/instruments, (iii) run FE-IV with fixest/ivreg.

6. Spatial Dynamic Panels with IV and Factors

Core idea

Extend defactored IV to spatial spillovers.

Key references

Cui, Sarafidis & Yamagata (Journal of Econometrics 2023); Kripfganz & Sarafidis (Journal of Statistical Software 2025)

When to use

✔ Peer effects or regional spillovers
✔ Endogeneity + common shocks

When NOT to use

✖ No spatial interaction structure
✖ Overly small panels

Implementations

Implemented in Stata add-on spxtivdfreg

Besides, new Panel VAR methods for large T have been developed. The most straightforward implementation is in Matlab BEAR Toolbox (https://www.ecb.europa.eu/press/research-publications/working-papers/html/bear-toolbox.en.html).

Quick Decision Guide

Problem Best Choice
Pure dynamics Bias-corrected FE
Strong IV, no CSD FE-IV
Global shocks CCEMG
Complex latent structure Interactive FE
IV + global shocks Defactored IV
Spillovers + IV Spatial defactored IV

Big Picture

Difference and system GMM can handle endogenous regressors in theory, but in practice internal lag instruments are often weak, invalid under persistence and common shocks, and unreliable in macro panels.

System GMM improves efficiency but does not solve the fundamental weak-instrument and cross-sectional dependence problems.

Large-T macro panels favor:

• Factor-aware methods
• Heterogeneous dynamics
• External IV when endogeneity is structural

GMM is no longer the default.