72 K. Li and N.R. Prabhala
the diversification discount. If not, the diversification discount could not be due to di-
versification. Under the assumption that the error terms in equations(67) and (68)are
bivariate normal, the system is akin to and is estimated just like the basic Heckman
selection model.^27
In the empirical application, Campa and Kedia measure the LHS variable in equa-
tion(68), as the difference between the actual value of the firm and the sum of the
imputed value of each of its segments. Segment imputed values are estimated using
multipliers based on market value to sales or market value to book value of assets of
peer firms. The explanatory variables for equation(68)include profitability, size, capi-
tal expenditure, and leverage. The additional instruments used in the probit specification
equations(66) and (67)include industry instruments such as the fraction of firms (or
their sales) in an industry that are diversified, time instruments, macroeconomic indi-
cators such as the overall economic growth and economic expansion/contraction, and
firm specific instruments such as being listed on a major exchange or being included in
a stock index. Campa and Kedia extensively discuss their choices for instruments.
Campa and Kedia show that in OLS specifications,d 2 is negative, so that diversified
firms do appear to trade at a discount. However, once they include the inverse Mills
ratio to correct for self-selection, the coefficientd 2 becomes positive. The negative sign
seen in OLS estimates is soaked up by the coefficient for the inverse Mills ratio. This
indicates that diversified firms possess private information that makes them self-select
into being diversified. The information is negatively associated with value and leads to
the diversification discount. After accounting for unobserved private information, there
is no diversification discount: in fact, there is a premium, implying that diversification
may well be in shareholders’ best interests.
The flip in the sign ofd 2 when the selection term is introduced does raise the question
of robustness of results, particularly with respect to potential collinearity between the
dummy variable for diversification and the inverse Mills ratio that corrects for selec-
tion. Campa and Kedia address this issue by reporting several other models, including
a simultaneous questions system that instruments the diversification dummyDitand
evidence based on a sample of refocusing firms. The main results are robust: there is
indeed a diversification discount as found byLang and Stulz (1994)orBerger and Ofek
(1995)when using OLS estimates. However, this discount is not due to diversification,
but by private information that leads firms to become diversified. In fact, the Campa and
Kedia self-selection estimates suggest that diversified firms trade at a premium relative
to their value had they not diversified.
(^27) Compared to the standard Heckman model, there is one additional variable in the second stage equation
(68), specifically, the dummy variableDit. The Heckman model with the additional dummy variable is called
a “treatment effects” model. The panel data setting also requires the additional assumption that the unobserved
errors be i.i.d. period by period. Campa and Kedia estimate fixed effects models as an alternative to Heckman-
style selection models to handle the panel structure of the data.