equation (i.e. be able to meaningfully estimate its parameters). A necessary condi-
tion for identiWcation, the order condition, requires that the number of exogenous
variables excluded from an equation must be at least as large as the number of
endogenous variables included in the equation (Greene 1993 : 592 ). (A condition
suYcient for identiWcation, the rank condition, is beyond the scope of the present
discussion, but is deWned in most econometrics texts.) In our example, the perf
equation is likely identiWed, even though hr is included, becausex 2 is excluded and
serves as an instrument for hr.
The key is that the IV/ 2 SLS procedure, if successfully implemented, results in
hrhat (unlike hr) being independent ofv, eliminating the source of the problem.
The IV/ 2 SLS estimator is consistent, rather than unbiased. The Hausman ( 1978 )
test for endogeneity is often used. The logic is that if endogeneity is a problem,
then the IV/ 2 SLS estimator should diVer from the OLS estimator. The test involves
adding the residual,uhat, from the HR equation to the perf equation (and
keeping HR in the perf equation also). If the standardtorzstatistic for the
coeYcient onuhat is signiWcant, there is evidence of endogeneity (Wooldridge
2002 : 118 – 20 ).
The success of the IV/ 2 SLS procedure depends on the theoretical justiWcation for
the instrument (i.e. the credibility of the assumption that cov(perf=x 2 jhr)¼ 0 )or
equivalently that cov(u, x 2 )¼ 0 , as well as a suYciently large partial R^2 (i.e.
partialing the other exogenous variables) between the instrument,x 2 , and the
variable being replaced using theWrst-stage regression, hr (Bound et al. 1995 ;
Larcker and Rusticus 2005 ; Staiger and Stock 1997 ). This has two clear implications
for researchers. First, a convincing conceptual rationale must be made for using the
instrument. Second, the full results of the equation used to obtain the predicted/
instrumental variable values must be reported. Bound et al. ( 1995 : 449 ) conclude
that ‘the use of instruments that jointly explain little of the variance in the
endogenous variable can do more harm than good’ and note that their results
‘emphasize the importance of examining characteristics of theWrst-stage estimates’,
especially the ‘partial R^2 and F statistic on the excluded instruments in theWrst-
stage regression.’ Both Bound et al. and Staiger and Stock ( 1997 ) also note that
despite the consistency property (a large-sample or asymptotic property) of
IV/ 2 SLS, even large samples cannot compensate for a low R^2 , as demonstrated by
their re-analysis of the Angrist and Krueger ( 1991 ) study, which used IV/ 2 SLS in a
sample of 300 , 000 to 500 , 000 observations.
In the HR and performance literature, a search turned up three studies (Bae and
Lawler 2000 ; Huselid 1995 ; Huselid et al. 1997 ) that have taken the possibility of
simultaneity between HR (practices) and performance seriously enough (and
judged instruments to be available) to use IV/ 2 SLS.^14 The latter two studies
(^14) IV/ 2 SLS is rare in the psychological literature. An introduction (James and Singh 1978 ) and an
example (Schmitt and Bedeian 1982 ) appeared years ago, but as recently as 1996 ,Psychological Methods
568 b a r r y g e r h a r t