*! version 1.2.3 04aug2020

*! Sebastian Kripfganz, www.kripfganz.de

Title

xtseqreg postestimation -- Postestimation tools for xtseqreg

Postestimation commands

The following postestimation commands are of special interest after xtseqreg:

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 options]

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

scores is not available after xtseqreg with two equations.

options

Options
equation(eqno) specify equation

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 unit-specific error component; see [XT] xtreg postestimation.

u calculates the prediction of u_i, the estimated unit-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 (scaled by -0.5);
see [R] gmm postestimation. 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.
A finite-sample correction term is added after two-step GMM estimation with the Windmeijer (2005) correction. This option is not available after xtseqreg with two equations.

Options

equation(eqno) specifies the equation to which you are referring; see [R] predict.

Syntax for estat

Arellano-Bond test for autocorrelated residuals

estat serial [, ar(numlist)]

Hansen's J-test of overidentifying restrictions

estat overid

Difference-in-Hansen test of overidentifying restrictions

estat overid name

Generalized Hausman test for model misspecification

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

where name is a name under which estimation results were stored via estimates store.

Description for estat

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

estat overid reports the Hansen (1982) J-statistic, which is used to determine the validity of the overidentifying restrictions.
The moment functions are evaluated at the two-step estimates after xtseqreg with option twostep, and at the one-step estimates otherwise.
An optimal weighting matrix based on the one-step estimates is used, irrespective of whether the two-step GMM estimator is computed or not.

estat overid name reports a difference-in-Hansen statistic, which is used to determine the validity of a subset of overidentifying restrictions.
It is computed as the difference between the respective J-statistics from the most recent xtseqreg estimation results and the estimation results stored as name by using estimates store.

estat hausman reports a generalized Hausman (1978) test for model misspecification by comparing the coefficient estimates of varlist from the most recent xtseqreg 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 deterministic model components such as the constant term and time dummies, if specified with option teffects of xtseqreg. This generalized test does not require one of the estimators to be efficient.
It uses the cluster-robust variance-covariance estimator for the test statistic suggested by White (1982) that 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.

nonested with estat hausman specifies that the two estimators are not nested in terms of the moment conditions they employ. This option implies that the degrees of freedom for the test equal the number of contrasted coefficients.

Remarks for estat

For the difference-in-Hansen test statistic to be valid, the two estimators need to be nested in terms of the moment conditions they employ. It is the user's responsibility to verify that this is indeed the case.
The test statistic is computed as the difference of Hansen's J-test statistics from the two estimations, subtracting the J-statistic with the smaller degrees of freedom from the one with the larger degrees of freedom.
In finite samples, the difference-in-Hansen statistic can become negative. This indicates that the excluded instruments received a large weight but the test cannot be used to determine their validity.

The generalized Hausman test can be used as an asymptotically equivalent test to the difference-in-Hansen test if the two estimators are nested
and the number of the excluded overidentifying restrictions does not exceed the number of contrasted coefficients. This test statistic is guaranteed to be nonnegative but it might have poor coverage in finite samples.

Example

Setup

. webuse abdata

Two-step difference-GMM estimator with strictly exogenous covariates

. xtseqreg L(0/1).n w k, gmmiv(L.n, c m(d)) iv(w k, d m(d)) teffects twostep vce(robust)

. estimates store ab

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

. estat serial

Hansen's J-test for the validity of the overidentifying restrictions

. estat overid

Two-step system-GMM estimator with strictly exogenous covariates

. xtseqreg L(0/1).n w k, gmmiv(L.n, c m(d)) iv(w k, d m(d)) iv(L.n, d m(l)) teffects twostep vce(robust)

Generalized Hausman test for the additional level moment condition

. estat hausman ab

Author

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

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.

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

Windmeijer, F. 2005.
A finite sample correction for the variance of linear efficient two-step GMM estimators.
Journal of Econometrics 126: 25-51.