*! version 1.3.0 26may2022

*! Sebastian Kripfganz, www.kripfganz.de

*! Jörg Breitung, wisostat.uni-koeln.de/en/institute/professors/breitung

Title

xtdpdbc postestimation -- Postestimation tools for xtdpdbc

Postestimation commands

The following postestimation commands are of special interest after xtdpdbc:

Command Description

estat serial perform test for autocorrelated residuals

estat overid perform test of overidentifying restrictions

estat hausman perform generalized Hausman test

The following standard postestimation commands are available:

Command Description

estat VCE and estimation sample summary

predict predictions, residuals, influence statistics, and other diagnostic measures

Syntax for predict

predict [type] newvar [if] [in] [, statistic]

predict [type] {stub*|newvar1 ... newvarq} [if] [in] , scores

statistic

Main
xb calculate linear prediction; the default

stdp calculate standard error of the prediction

ue calculate the combined residual

* xbu calculate prediction including unit-specific error component

* u calculate the the unit-specific error component

* e calculate the idiosyncratic error component

* scores calculate parameter-level scores

Description for predict

predict creates a new variable containing predictions such as fitted values, standard errors, and residuals.

Options for predict

Main

xb calculates the linear prediction from the fitted model; see [R] predict. This is the default.

stdp calculates the standard error of the linear prediction; see [R] predict.

ue calculates the prediction of u_i + e_it, the combined residual; see [XT] xtreg postestimation.

xbu calculates the linear prediction including the group-specific error component; see [XT] xtreg postestimation.

u calculates the prediction of u_i, the estimated group-specific error component; see [XT] xtreg postestimation.

e calculates the prediction of e_it; see [XT] xtreg postestimation.

scores calculates the parameter-level scores for all independent variables, the first derivatives of the criterion function with respect to the coefficients.
This option requires that the length of the new variable list be equal to the number of independent variables including the constant term, if any.

Syntax for estat

Arellano-Bond test for autocorrelated residuals

estat serial [, ar(numlist)]

Sargan-Hansen test of overidentifying restrictions

estat overid

Generalized Hausman test for model misspecification

estat hausman name [(varlist)] [, df(#)]

Description for estat

estat serial reports the Arellano and Bond (1991) test for autocorrelation of the first-differenced residuals. A robust version is computed if vce(robust) is specified with xtdpdbc.

estat overid reports the Sargan (1958) or Hansen (1982) J-statistic which is used to determine the validity of the overidentifying restrictions.

estat hausman reports a generalized Hausman (1978) test for model misspecification by comparing the coefficient estimates of varlist from the most recent xtdpdbc estimation results
to the corresponding coefficient estimation results stored as name by using estimates store. By default, the coefficients of all indepvars are contrasted, excluding the constant term.
This generalized test uses the cluster-robust variance-covariance estimator for the test statistic suggested by White (1982), which is computed using the parameter-level scores; see [R] suest.

Options for estat

ar(numlist) with estat serial specifies the orders of serial correlation to be tested. The default is ar(1 2).

df(#) with estat hausman specifies the degrees of freedom for the test.
The default is the difference in the number of overidentifying restrictions from the two estimations or the number of contrasted coefficients, whichever is smaller.

Remarks for estat

Even though the bias-corrected estimator does not transform the model into first differences, the serial correlation test is performed on the first-differenced residuals as originally suggested by Arellano and Bond (1991).
If the untransformed idiosyncratic error component is serially uncorrelated, then there will be first-order but no higher-order serial correlation in the first-differenced errors.

The Sargan-Hansen test is only available for random-effects or hybrid models because the fixed-effects estimator is just-identified.
The Sargan test after the one-step estimator is asymptotically invalid, unless there are no unobserved group-specific effects. The Hansen test after the two-step estimator should be considered instead.

Under a random-effects assumption, when the panel data set is unbalanced and time effects are included, time dummies will be used as instruments both for the model in deviations from within-group means and the model in levels.
The additional instruments for the model in levels are asymptotically redundant, even though some of them are not numerically redundant in finite samples.
When xtdpdbc is specified with option teffects, estat overid adjusts the degrees of freedom accordingly by ignoring the time dummy instruments for the model in levels.

The generalized Hausman test can be used as an asymptotically equivalent test to the Sargan-Hansen test if a random-effects (or hybrid) estimator is constrasted with a fixed-effects estimator.
This test statistic is guaranteed to be nonnegative but it might have poor coverage in finite samples.

Example

Setup

. webuse psidextract

Bias-corrected fixed-effects estimator with AR(2) dynamics

. xtdpdbc lwage wks south smsa ms exp exp2 occ ind union, lags(2)

. estimates store fe

Arellano-Bond test for autocorrelation of the first-differenced residuals

. estat serial, ar(1/3)

Bias-corrected random-effects estimator with AR(2) dynamics

. xtdpdbc lwage wks south smsa ms exp exp2 occ ind union, re lags(2)

Hansen test for the validity of the overidentifying restrictions

. estat overid

Generalized Hausman test

. estat hausman fe

Authors

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

Jörg Breitung, University of Cologne, https://wisostat.uni-koeln.de/en/institute/professors/breitung

References

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.

Hansen, L. P. 1982.
Large sample properties of generalized method of moments estimators.
Econometrica 50: 1029-1054.

Hausman, J. A. 1978.
Specification tests in econometrics.
Econometrica 46: 1251-1271.

Sargan, J. D. 1958.
The estimation of economic relationships using instrumental variables.
Econometrica 26: 393-415.

White, H. L. 1982.
Maximum likelihood estimation of misspecified models.
Econometrica 50: 1-25.