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help for ^ivgmm0^ (Statalist distribution)
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Instrumental variables via Generalized Method of Moments
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^ivgmm0^ depvar [varlist1] ^(^varlist2^=^varlist_iv^)^ [^if^ exp] [^in^ range]
[^,^ ^noc^onstant ]
depvar, varlist1, varlist2, and varlist_iv may contain time-series operators;
see help @varlist@.
^ivgmm0^ shares the features of all estimation commands; see help @est@.
Description
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^ivgmm0^ estimates a linear regression model containing endogenous regressors
via a generalized method of moments instrumental variables estimator (GMM-IV)
that allows for heteroskedasticity of unknown form. The relationship modelled
is that of depvar explained by varlist1 (exogenous variables) and varlist2
(endogenous variables), identified by an additional set of instruments
(varlist_iv), with a command syntax matching that of ^ivreg^. If the equation
is overidentified by an abundance of instruments, a test of overidentifying
restrictions--Hansen's "J" statistic (1982)--is provided to evaluate the
validity of the model. If this statistic (distributed Chi-squared in the number
of overidentifying restrictions) rejects the null hypothesis that the
additional moment conditions are approximately satisfied, the validity of the
model is called into question.
The specification of this routine as ^ivgmm0^ is meant to highlight its ability
to deal with a heteroskedastic error process (at lag 0), but not with
autocorrelation of unknown form (which would require that a Newey-West
procedure be embedded in its logic, rather than the White "sandwich"
estimator). That extension may be provided in further development.
Although this estimator is restricted to models linear in the parameters,
it is relatively more efficient than ^ivreg^ (with or without the ^robust^
option, which invokes the White procedure to calculate a heteroskedasticity-
consistent covariance matrix). The efficiency gain is derived from GMM-IV's
use of an optimal weighting matrix (rather than the identity weighting
matrix implicit in any least squares estimator) to define the appropriate
combination of moment conditions. In this context, the moment conditions
are the orthogonality conditions of each instrument with the error process.
A discussion of the development of the estimator is given in Hayashi
(2000, Chapter 3) and Greene (2000, Chapter 11).
Hansen (1982) showed that W, the optimal weighting matrix for this class of
estimators, is the inverse of S = AsyVar[1/N Z'e], where Z is the N x L matrix
of instruments and e is the N x 1 matrix of the GMM residuals. For ^ivgmm0^
on N observations the optimal W is given by:
N
W = inv [ (1/N^^2) SUM z_i z_i' e_i^^2 ]
i=1
where z_i is the ith row of Z and e_i is the ith element of e.
^ivgmm^ saves W in e(W).
Options
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^noconstant^ suppresses the constant term (intercept) in the regression. If
^noconstant^ is specified, the constant term is excluded from both the
final regression and the first-stage regression.
^gres^ specifies that the GMM residuals are to be used to calculate the
variance-covariance matrix of the parameters, rather than the first
round (IV) residuals.
Examples
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. ^* Hayashi (2000) p.255^
. ^use http://fmwww.bc.edu/ec-p/data/hayashi/griliches76.dta^
. ^xi i.year^
. ^ivgmm0 lw expr tenure rns smsa _I* (iq s = med kww mrt age)^
. ^ivgmm0 lw expr tenure rns smsa _I* (iq s = med kww mrt age), gres^
References
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Greene, W., Econometric Analysis. 4th Ed., 2000. New York: Prentice-Hall.
Hansen, L., "Large Sample Properties of Generalized Methods of Moments
Estimators," Econometrica, 50, 1982, 1029-1054.
Hayashi, F., Econometrics. 1st Ed., 2000. Princeton: Princeton University Press.
Authors
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Christopher F Baum, Boston College, USA
baum@@bc.edu
David M. Drukker, StataCorp
ddrukker@@stata.com
Also see
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On-line: help for @ivreg@, @ivreg2@ (if installed)