Title

xtdynestimb csdgmm -- GMM estimation of short dynamic panels with
error cross-sectional dependence (Sarafidis 2009)

(part of xtdynestimb. See also dd,
ablasso,
postestimation.)

Syntax

xtdynestimb csdgmm depvar [indepvars] [if] [in]
[, options]

Model
variant(type) difference or system; default
system

lags(#) autoregressive order p; default lags(1)

gmmlags(min max) lag window for the GMM instruments; default
gmmlags(2 .)

CSD robustness
partial use regressor-only instruments (drop all
lagged-y instruments); requires indepvars

nodemean do not time-demean (turns the CSD correction off;
for comparison only)

Estimator
twostep two-step efficient GMM (default)

onestep one-step GMM, robust variance

nowindmeijer no Windmeijer two-step correction

Reporting
graph coefficient plot

graphname(name) name for the graph

notable suppress the output table

level(#) confidence level; default level(95)

Description

xtdynestimb csdgmm estimates a short dynamic panel by GMM when the errors
are cross-sectionally dependent. Under a common-factor (strong) dependence
structure the standard Arellano-Bond / Blundell-Bond lagged-level instruments are
correlated with the errors and the estimator is inconsistent (Sarafidis 2009;
Sarafidis & Robertson 2009).

The command applies the Sarafidis (2009) remedy in two parts:

1. Cross-sectional (time) demeaning. Each variable is expressed in
deviations from its cross-sectional mean at each time period, which removes
common time effects and (approximately) the common-factor component of the
errors before the usual difference / system GMM moment conditions are formed.

2. Partial (regressor-only) instruments (partial). When the
dependence is heterogeneous, even demeaning may be insufficient; restricting the
instrument set to the strictly exogenous regressors (dropping all lagged-y
instruments) yields an estimator that Sarafidis, Yamagata & Robertson (2009) show
to be a reliable alternative under heterogeneous error CSD.

Pair this estimator with xtdyntest's syr and csd subcommands
to test for residual cross-sectional dependence after estimation.

Options

variant(type) selects difference (Sarafidis eq. 17) or
system (eq. 26) GMM on the demeaned data.

partial keeps only the regressor instruments. With system the
level equation is then instrumented by the regressors only. Requires at least one
indepvar.

nodemean disables the time-demeaning so you can see the size of the
CSD correction relative to ordinary difference/system GMM.

lags(), gmmlags(), twostep, onestep,
nowindmeijer, level() behave as in dd.

Stored results

In addition to the common e() results:

Scalars

e(j), e(j_df), e(j_p) Hansen J statistic, df, p-value

Macros

e(variant) variant used

e(demean) transform applied

e(partial) instrument set description

Examples

. webuse abdata

. xtset id year

CSD-robust system GMM (time-demeaned)

. xtdynestimb csdgmm n w k, variant(system)

Regressor-only (partial) instruments under heterogeneous CSD

. xtdynestimb csdgmm n w k, variant(system) partial

Test for residual CSD afterwards

. predict double e, residuals

. xtdyntest csd, residuals(e)

References

Sarafidis, V. 2009. GMM estimation of short dynamic panel data models
with error cross-sectional dependence. MPRA Paper 25176, University of Munich.

Sarafidis, V., T. Yamagata, and D. Robertson. 2009. A test of cross
section dependence for a linear dynamic panel model with regressors.
Journal of Econometrics 148: 149-161.

Author

Dr Merwan Roudane

merwanroudane920@gmail.com

github.com/merwanroudane