Calculate Smith-Blundell test for effects of endogeneity after @probit@, @tobit > @ ----------------------------------------------------------------------------
^probexog^ depvar [varlist1] ^(^varlist2^=^varlist_iv^)^ [^if^ exp] [^in^ rang > e] [weight] [, noconstant] ^tobexog^ depvar [varlist1] ^(^varlist2^=^varlist_iv^)^ [^if^ exp] [^in^ rang > e], ^ll^[(#)] ^ul^[(#)]
^fweights^, ^pweights^, and ^iweights^ are allowed with probexog; ^aweights^ and ^fweights^ are allowed by tobexog. See ^help weights^. In ^tobexog^, one or both of the limits (^ll^, ^ul^) must be specified, but a limit value need not be given; see ^help tobit^.
Description -----------
^probexog^ (^tobexog^) computes a test of exogeneity for a probit (tobit) model proposed by Smith and Blundell (1986). The test involves specifying that the exogeneity of one or more explanatory variables is under suspicion. Under the null hypothesis, the models are appropriately specified with all explanatory variables as exogenous. Under the alternative hypothesis, the suspected endogenous variables (in ^varlist2^) are expressed as linear projections of a set of instruments, and the residuals from those first-stage regressions are added to the model. Under the null hypothesis, these residuals should have no explanatory power.
This test is related to an auxiliary regression test for exogeneity in a regression context (see ^ivendog^), which in turn is a convenient alternative to the commonly employed Hausman test (^hausman^).
The ^probexog^ (^tobexog^) test requires specification of the suspected endogen > ous variables (^varlist2^) as well as a list of instruments (^varlist_iv^), in the same format as Stata's ^ivreg^ command or the Baum-Schaffer-Stillman (20 > 03) ^ivreg2^ 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 conditio > n 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 residuals from each first-stage instrument regression are included in a probit (tobit) model. Estimation of the model gives rise to a test for the joint hypothesis that each of the coefficients on the residual series are zero. The ^probexog^ test statistic, under the null, is distributed Chi-squared(m), where m is the number of explanatory variables specified as endogenous in the model. The ^tobexog^ test statistic, under the null, is distributed as F(m,N-k), where m is the number of explanatory variables specified as endogenous in the model. A rejection indicates that the standard probit (tobit) estimator should not be employed.
The command displays the test statistic, degrees of freedom and P-value, and places values in the return array. ^return list^ for details.
Examples --------
. ^use auto^ . ^probexog foreign price (mpg=displ weight)^ . ^use hsng^ . ^replace rent=250 if rent<250^ . ^tab region,gen(reg)^ . ^tobexog rent popgrow (hsngval=faminc reg2-reg4),ll(250)^
References ----------
Baum, C.F., Schaffer, M.E., and Stillman, S. 2003. Instrumental Variables and G > MM: Estimation and Testing. The Stata Journal, Vol. 3, No. 1, pp. 1-31. Workin > g paper version: Boston College Department of Economics Working Paper No 545. http://ideas.repec.org/p/boc/bocoec/545.html
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 ----------------
I am grateful to Ronna Cong of StataCorp for critical review of this module, and to Nick Cox for assistance with syntax. Errors remaining are my own.
Author ------
Christopher F Baum, Boston College, USA baum@@bc.edu
Also see --------
Manual: ^[R] probit^, ^[R] tobit^, ^[R] ivreg^, ^[R] hausman^ On-line: help for @probit@, @tobit@, @ivreg@, @ivreg2@ (if installed), @ivendo > g@ (if installed)