*! version 2.6.2 03aug2022

*! Sebastian Kripfganz, www.kripfganz.de

Title

xtdpdgmmfe -- GMM linear dynamic panel data estimation with fixed effects

Syntax

xtdpdgmmfe depvar [indepvars] [if] [in] [, options]

options

Model
lags(#) lags of the dependent variable; default is lags(1)

exogenous(varlist) exogenous variables in indepvars

predetermined(varlist) predetermined variables in indepvars

endogenous(varlist) endogenous variables in indepvars

orthogonal use orthogonal deviations instead of first differences

collapse collapse GMM-type into standard instruments

curtail(#) curtail the lag range for GMM-type instruments

serial(#) degree of serial correlation; default is serial(0)

iid independent and identically distributed errors

initdev weaker assumption on initial observations

stationary joint mean stationarity assumption

nonl do not use nonlinear moment conditions

* onestep|twostep use the one-step or two-step estimator

* igmm use the iterated GMM estimator, the default

* cugmm use the continuously-updating GMM estimator

teffects add time effects to the model

xtdpdgmm_options other options for xtdpdgmm estimation

Reporting
nocmdline supress xtdpdgmm command line

display_options control the display of the regression output

Minimization
igmm_options control the iterated GMM process; seldom used

minimize_options control the minimization process; seldom used

* You can specify at most one of these options. igmm is the default.

You must xtset your data before using xtdpdgmm; see [XT] xtset.

All varlists may contain factor variables; see fvvarlist.

depvar and all varlists may contain time-series operators; see tsvarlist.

xtdpdgmmfe is a wrapper for xtdpdgmm. See xtdpdgmm postestimation for features available after estimation.

Description

xtdpdgmmfe implements generalized method of moments (GMM) estimators for linear dynamic panel data models in the spirit of Anderson and Hsiao (1981), Arellano and Bond (1991), Ahn and Schmidt (1995), Arellano and Bover (1995),
Blundell and Bond (1998), Hayakawa, Qi, and Breitung (2019), and Chudik and Pesaran (2022).

The model can be estimated with the one-step, two-step, iterated, or continuously-updating GMM estimator. The two-step estimator uses an optimal weighting matrix which is estimated from the one-step residuals.
The iterated GMM estimator, suggested by Hansen, Heaton, and Yaron (1996), further updates the weighting matrix until convergence.
The continuously-updating GMM estimator, also proposed by Hansen, Heaton, and Yaron (1996), updates the weighting matrix jointly with the coefficients.

Options

Model

lags(#) specifies the lags of depvar to be used as regressors. The default is lags(1).

exogenous(varlist) specifies which of the variables in indepvars are strictly exogenous with respect to the idiosyncratic error component; see xtdpdgmm.

predetermined(varlist) specifies which of the variables in indepvars are predetermined with respect to the idiosyncratic error component; see xtdpdgmm.

endogenous(varlist) specifies which of the variables in indepvars are endogenous with respect to the idiosyncratic error component; see xtdpdgmm.

orthogonal requests instruments to be specified for the model in forward-orthogonal deviations instead of the model in first differences.
For exogenous variables, instruments are also specified for the model in deviations from within-group means; see xtdpdgmm.
In addition, when initdev is specified, backward-orthogonal deviations instead of first differences are used to transform instruments; see xtdpdgmm.

collapse requests to reduce the number of moment conditions by collapsing all GMM-type instruments into standard instruments and all nonlinear moment conditions into a single moment condition;
see xtdpdgmm.

curtail(#) requests to reduce the number of moment conditions by curtailing the lag range for GMM-type instruments such that # is the maximum lag used; see xtdpdgmm.
In combination with with option orthogonal, the maximum lag used is #-1. This ensures that the same number of instruments is used with or without option orthogonal.

serial(#) assumes that the idiosyncratic error component is serially correlated at most of order #. This affects which lags of predetermined and endogenous variables are valid instruments;
see xtdpdgmm. By default, serial(0), the idiosyncratic error component is assumed to be serially uncorrelated.
Depending on other assumptions made, additional nonlinear moment conditions proposed by Ahn and Schmidt (1995) or Chudik and Pesaran (2022) might be added which are valid under the absence of (higher-order) serial correlation;
see xtdpdgmm.

iid assumes that the idiosyncratic error component is homoskedastic and serially uncorrelated. This implies option serial(0).
Depending on other assumptions made, additional linear and nonlinear moment conditions might be added; see xtdpdgmm.

initdev assumes that the deviations of the initial observations of depvar from its long-run mean are uncorrelated with the first-differenced idiosyncratic error component, as considered by Chudik and Pesaran (2022).
By default, it is assumed that both the group-specific error component and the initial observations of varlist and indepvars are uncorrelated with the first-differenced idiosyncratic error component;
see xtdpdgmm.

stationary assumes that the initial observations of depvar and indepvars are jointly mean stationary. This allows to include additional instruments for the untransformed model, as proposed by Blundell and Bond (1998).
This implies option nonl because nonlinear moment conditions generally become redundant; see xtdpdgmm.

nonl requests not to include any nonlinear moment conditions.

onestep, twostep, igmm, and cugmm specify which estimator is to be used. At most one of these options can be specified.

onestep requests the one-step GMM estimator to be computed. In a model without nonlinear moment conditions and with the default weighting matrix, the one-step estimator corresponds to the two-stage least squares estimator.

twostep requests the two-step GMM estimator to be computed which is based on an unrestricted (cluster-robust) optimal weighting matrix.

igmm, the default, requests the iterated GMM estimator to be computed. At each iteration step, an unrestricted (cluster-robust) optimal weighting matrix is computed using the GMM estimates from the previous step.
Iterations continue until convergence is achieved for the coefficient vector or the weighting matrix, or the maximum number of iterations is reached.

cugmm requests the continuously-updating GMM estimator to be computed. As a function of the model's coefficients, the unrestricted (cluster-robust) weighting matrix is updated jointly with the coefficients.

teffects requests that time-specific effects in the form of time dummies are added to the model.

xtdpdgmm_options: iv(iv_spec), gmmiv(gmmiv_spec), wmatrix(wmat_spec),
center, norescale, nocons:tant, vce(vce_spec), small, and overid; see xtdpdgmm.
When adding further instruments with option iv() or gmm(), the suboption model(model_spec) should be specified because xtdpdgmmfe changes the default model.

Reporting

nocmdline suppresses display of the xtdpdgmm command line.

display_options: auxiliary, level(#), coeflegend, noheader, notable, and nofooter; see xtdpdgmm.
noci, nopvalues, noomitted, vsquish, noemptycells, baselevels, allbaselevels, nofvlabel, fvwrap(#), fvwrapon(style), cformat(%fmt), pformat(%fmt),
sformat(%fmt), and nolstretch; see [R] estimation options.

Minimization

igmm_options: igmmiterate(#), igmmeps(#), and igmmweps(#); see [R] gmm. These options are seldom used and only have an effect if the iterated GMM estimator is used.

minimize_options: noanalytic, from(init_spec), and nodots; see xtdpdgmm.
iterate(#), nolog, showstep, showtolerance, tolerance(#), ltolerance(#), nrtolerance(#), and nonrtolerance; see [R] maximize.
These options are seldom used.

Example

Setup

. webuse abdata

Anderson-Hsiao IV estimators with predetermined covariates

. xtdpdgmmfe n w k, pre(w k) c cur(1) nonl nocons one

. xtdpdgmmfe n w k, pre(w k) initd c cur(1) nonl nocons one

Arellano-Bond one-step GMM estimator with predetermined covariates and curtailed/collapsed instruments

. xtdpdgmmfe n w k, pre(w k) c cur(4) nonl nocons one

Arellano-Bover iterated GMM estimator with predetermined covariates and curtailed/collapsed instruments

. xtdpdgmmfe n w k, pre(w k) c cur(4) or nonl vce(r)

Ahn-Schmidt iterated GMM estimators with predetermined covariates and curtailed/collapsed instruments

. xtdpdgmmfe n w k, pre(w k) c cur(4) vce(r)

. xtdpdgmmfe n w k, pre(w k) iid c cur(4) vce(r)

Chudik-Pesaran iterated GMM estimator with predetermined covariates and curtailed/collapsed instruments

. xtdpdgmmfe n w k, pre(w k) initd c cur(4) nocons vce(r)

Blundell-Bond two-step, iterated, and continuously-updating GMM estimators with predetermined covariates and curtailed/collapsed instruments

. xtdpdgmmfe n w k, pre(w k) sta c cur(4) two vce(r)

. xtdpdgmmfe n w k, pre(w k) sta c cur(4) igmm vce(r)

. xtdpdgmmfe n w k, pre(w k) sta c cur(4) cu vce(r)

Hayakawa-Qi-Breitung IV estimator with predetermined covariates

. xtdpdgmmfe n w k, pre(w k) initd or c cur(1) nonl nocons one

Replication of a static fixed-effects estimator

. xtdpdgmmfe n w k, la(0) exo(w k) or c cur(1) nores one

. xtreg n w k, fe

Author

Sebastian Kripfganz, University of Exeter, http://www.kripfganz.de

References

Ahn, S. C., and P. Schmidt. 1995.
Efficient estimation of models for dynamic panel data.
Journal of Econometrics 68: 5-27.

Anderson, T. W., and C. Hsiao. 1981.
Estimation of dynamic models with error components.
Journal of the American Statistical Association 76: 598-606.

Arellano, M., and S. R. Bond. 1991.
Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations.
Review of Economic Studies 58: 277-297.

Arellano, M., and O. Bover. 1995.
Another look at the instrumental variable estimation of error-components models.
Journal of Econometrics 68: 29-51.

Blundell, R., and S. R. Bond. 1998.
Initial conditions and moment restrictions in dynamic panel data models.
Journal of Econometrics 87: 115-143.

Chudik, A., and M. H. Pesaran. 2022.
An augmented Anderson-Hsiao estimator for dynamic short-T panels.
Econometric Reviews 41: 416-447.

Hansen, L. P., J. Heaton, and A. Yaron. 1996.
Finite-sample properties of some alternative GMM estimators.
Journal of Business & Economic Statistics 14: 262-280.

Hayakawa, K., M. Qi, and J. Breitung. 2019.
Double filter instrumental variable estimation of panel data models with weakly exogenous variables.
Econometric Reviews 38: 1055-1088.