Instrumental variables via Generalized Method of Moments --------------------------------------------------------
^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@.
^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).
^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 --------
. ^* 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^
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 > .
Christopher F Baum, Boston College, USA baum@@bc.edu
David M. Drukker, StataCorp ddrukker@@stata.com Also see --------
On-line: help for @ivreg@, @ivreg2@ (if installed)