GitHub

Dynamic Panel GMM

Arellano-Bond and Blundell-Bond GMM for dynamic panels.

SpatialEconometrics.DynamicPanelSystemGMM.DifferenceGMM — Type
DifferenceGMM()

Arellano-Bond difference GMM: first-difference away the unit effects and instrument with lagged levels.

Consistent for a dynamic panel with fixed effects, but the lagged-level instruments become weak as the autoregressive parameter approaches 1 — a highly persistent series provides little information about its own differences. SystemGMM adds moment conditions to address exactly that.

References

Arellano, M. & Bond, S. (1991). Review of Economic Studies, 58(2).

source
SpatialEconometrics.DynamicPanelSystemGMM.SystemGMM — Type
SystemGMM()

Blundell-Bond system GMM: the difference equations of DifferenceGMM together with the levels equations, instrumented with lagged differences.

Much better behaved when the series is persistent, which is the usual case. The extra moment conditions require that changes in the regressors be uncorrelated with the unit effects — a real assumption, and the thing to examine if the Sargan test rejects.

References

Blundell, R. & Bond, S. (1998). Journal of Econometrics, 87(1).

source
SpatialEconometrics.DynamicPanelSystemGMM.SystemGMMModel — Type
SystemGMMModel

A fitted dynamic panel GMM model, returned by fit_dynamic_gmm. Implements the StatsAPI.RegressionModel interface.

Fields

  • variant: DifferenceGMM or SystemGMM.
  • coef_twostep, coef_onestep: the two-step and one-step estimates.
  • vcov_windmeijer: two-step covariance with the Windmeijer finite-sample correction — the one to report.
  • vcov_naive: uncorrected two-step covariance, kept for comparison. Without the correction two-step standard errors are severely biased downwards, so the gap between this and vcov_windmeijer is worth a look.
  • vcov_onestep: covariance of the one-step estimator.
  • hansen_j, hansen_df: Hansen J over-identification test.
  • ar1_z, ar2_z: Arellano-Bond tests for first- and second-order residual autocorrelation.
  • n_instruments, collapsed: how many instruments were used and whether the instrument matrix was collapsed.
  • N, T_total, coefnames.
Note

Read the three diagnostics together. ar1_z is expected to reject, since differencing induces first-order correlation by construction; ar2_z should not reject, or the lag structure is misspecified and the instruments are invalid. Then check hansen_j, bearing in mind the n_instruments caveat on fit_dynamic_gmm.

References

Windmeijer, F. (2005). Journal of Econometrics, 126(1).

source
SpatialEconometrics.DynamicPanelSystemGMM.fit_dynamic_gmm — Function
fit_dynamic_gmm(variant, Y_mat, X_ten; max_lag = 4, collapsed = false,
                varnames = nothing)

Fit a dynamic panel by Arellano-Bond or Blundell-Bond GMM.

Arguments

  • variant: DifferenceGMM or SystemGMM.
  • Y_mat: N x T matrix of the dependent variable — units by periods, not stacked as the spatial panel estimators expect.
  • X_ten: N x T x K array of covariates.

Keywords

  • max_lag: how many lags to use as instruments. More lags mean more moment conditions and, with many periods, an instrument count that grows quadratically and overfits.
  • collapsed: collapse the instrument matrix, holding the count down. Worth turning on whenever T is more than small.
  • varnames: covariate names.

Returns

A SystemGMMModel.

Warning

Instrument proliferation is the standard failure here: too many instruments relative to N makes the over-identification test lose all power, so a comfortable p-value can be meaningless. Keep the instrument count well below N, using max_lag and collapsed.

Note

Note the data layout: Y_mat is N x T and X_ten is N x T x K, unlike the stacked vectors the spatial panel estimators take.

References

Roodman, D. (2009). How to do xtabond2. Stata Journal, 9(1).

source