Estimate @probit@ with one endogenous variable via instrumental variables -------------------------------------------------------------------------
^prob1nx^ depvar [varlist1] ^(^endog^=^varlist_iv^)^ [^if^ exp] [^in^ range]
Description -----------
^prob1nx^ estimates a probit model in which one explanatory variable is presumed endogenous via instrumental variables, as proposed by Smith and Blundell (1986). They demonstrate that in the case of a single auxiliary instrumental variables regression, the correlation between the errors in the probit equation and the auxiliary regression may be manipulated to avoid the use of the bivariate normal distribution. Their test for endogeneity of the specified explanatory variable (calculated by ^probexog^) is also generated by ^prob1nx^.
^prob1nx^ test requires specification of the suspected endogenous variable (^endog^) as well as a list of instruments (^varlist_iv^), in the same format as Stata's ^ivreg^ command. The set of instruments is taken to be those specified plus all other explanatory variables (i.e. those not suspected of endogeneity, in ^varlist1^). The standard order condition for identification of the model applies: there must be at least as many instruments excluded from the model as there are suspected endogenous variables.
The model is estimated by maximum likelihood. The parameter ^rho^ is the estimated correlation between the errors of the probit and auxiliary regression equations.
^prob1nx^ shares the features of all estimation commands, see help ^est^.
Example -------
. ^use auto^ . ^prob1nx foreign price (mpg=displ weight)^
References ----------
Smith, Richard J., Blundell, Richard W., An exogeneity test for a simultaneous equation Tobit model with an application to labor supply. Econometrica, 1986, 54:4, 679-686. Acknowledgements ----------------
We are grateful to Richard Blundell, and to Nick Cox for his ^matdelrc^ routine, a version of which is included herein. Errors remaining are our own.
Authors -------
Christopher F Baum, Boston College, USA baum@@bc.edu Peter Gottschalk, Boston College, USA gottscha@@bc.edu
Also see --------
Manual: ^[R] probit^, ^[R] ivreg^ On-line: help for @probit@, @ivreg@, @probexog@ (if installed)