Oxford Handbook of Human Resource Management

statistical challenge in HR and performance research. They suggest, for example,
that ‘Wrms that understand the advantages of high performance HR are also good
at other types of management (e.g., marketing, operations)’ (p. 851 ). Another
variable that must be included in research on HR and performance is industry,
with narrower (three-digit or four-digit SIC code) being preferable to more coarse
categories (one-digit or two-digit SIC code). The use of ‘industry studies’ in
automobile assembly plants (MacDuYe 1995 ), telecommunications (Batt 2002 ),
andWnancial services (Hunter and Lafkas 2003 ) uses single industry samples as a
way to control omitted variables and to understand the industry-speciWc institu-
tional workings of HR and performance. Recent evidence provides further support
for the idea that this relationship may vary by industry (Datta et al. 2005 ).
To estimate the magnitude of bias from omitting a relevant variable (e.g.
industry, management quality/expertise in non-HR areas), call it ‘control,’ take
the fully (i.e. correctly) speciWed equation to be (Kmenta 1971 : 392 – 93 ):

perf¼b 0 þbperfhr:controlhrþbperfccntrol:hrcontrolþe,

but we omit control and estimate instead:

perf¼a 0 þbperfhrhrþe

Then the expected value of bperfhrwill equal not bperfhr.control, but rather:

bperfhr¼bperfhr:controlþbperfcontrol:hrdcontrolhr

where dcontrolhris the regression coeYcient from the auxiliary regression of control
on the included independent variables (hr only in this example):

control¼d 0 þdcontrolhrhrþresidual:

The bias in estimating bperfhr:control grows more severe as dcontrolhr and
bperfcontrol:hr become more diVerent from. 00. In this two-variable example,
dcontrolhrhr is a direct function of æcontrolhr. However, with more independent
variables, it would be mathematically possible foræcontrolhrto be ‘large,’ but for
dcontrolhrto be ‘small’ due to the inclusion of other independent variables. This then
means that it is incorrect to say that omitted variable bias exists when the omitted
variable ‘is correlated with’ the dependent variable and any of the included
independent variables. Rather, it is thepartialrelationship of the omitted variable
with the included variable that matters.
There are two traditional approaches to reducing omitted variable problems.
The Wrst is the randomized experiment, which has the major advantage, in
suYciently large samples, of achieving what Cook and Campbell ( 1979 ) refer
to as equivalent groups. By deWnition, cov(hr,e)¼ 0 under successful random
assignment. Moreover, this equivalence can be achieved without any knowledge

modeling hrm and performance linkages 561