perft 1 ¼hrt 1 bþvt 1 þuSubtract the second equation from theWrst:
(perftperft 1 )¼(hrthrt 1 )bþ(vtvt 1 )The key result is thatu, the omitted, time-invariant (i.e. ‘Wxed’) component, is
eliminated. Thus, any bias due to time-invariant omitted variables is also elimin-
ated. With more than two waves of data, it is mathematically equivalent to pool
cross-sections and include dummy variables for eachWrm (in this example).
Huselid and Becker ( 1996 ) used aWxed eVects model and reasoned that if this
estimate for the HR–performance coeYcient was similar to the estimate based on
cross-sectional data, it would reduce any concern about omitted variable bias in
studies that have used cross-sectional data. Recognizing thatWxed eVects estimates
(operationalized as diVerence scores with two waves of data) are often smaller than
the cross-sectional estimates because of more serious measurement error problems
in the former,^13 Huselid and Becker ( 1996 ) wisely corrected for unreliability in their
Wxed eVects estimates. However, they did not correct their cross-sectional esti-
mates. Gerhart ( 1999 ) found that upon additionally correcting the coeYcient
derived from the cross-sectional data, it was nearly twice as large (. 240 ) as the
comparableWxed eVects coeYcient of. 125. This suggests, in contrast to Huselid and
Becker’s conclusion, that omitted variables may be a problem in cross-sectional
studies.
There are (other) costs (beyond measurement error) in usingWxed eVects. One is
that time-invariant variables fall out of the model described. Another is that
degrees of freedom are lost from the denominator. This is most easily seen in the
dummy variable speciWcation wheren 1 dummy variables are added to the
equation (wheren¼number ofWrms). This leads to less eYciency. Thus, it is
recommended that a test be conducted to determine whetherWxed eVects belong in
the model before using the estimates from theWxed eVects model. If not, the
recommended model is the error components model (Hausman 1978 ) and is
estimated using generalized least squares (GLS), which accounts for the depend-
ence of the disturbance terms across time.
- 4 Control Variables: Sometimes ‘Too Much of a Good Thing’
Because omitted variable bias arises from using a model that omits relevant
variables, the natural inclination may be to add ‘control’ variables to a model
(^13) It has long been known that reliability problems are exacerbated by using diVerence scores
(Cronbach and Furby 1970 ), though these can be corrected for unreliability using structural equation
models (e.g. Gerhart 1988 ). Other studies probably underestimate the magnitude of the HR per
formance relationship because they use diVerence scores without correcting for measurement error
(e.g. Cappelli and Neumark 2001 ).
modeling hrm and performance linkages 565