Ch. 2: Self-Selection Models in Corporate Finance 73
10.2. Observables and the discount:Villalonga (2004)
WhileCampa and Kedia (2002)attribute the diversification discount to unobservables
causing firms to diversify,Villalonga (2004)offers an explanation based on differences
in observables. Villalonga uses a longitudinal rather than cross-sectional analysis, fo-
cusing onchangesin excess value around diversification rather than the level of the
excess value itself.
Villalonga’s main sample comprises 167 cases where firms move from being one
segment to two segments. She tracks the changes in the diversification discount around
the diversification event compared to a control group of non-diversifying firms, using
propensity score (PS) based matching to construct matched control firms. Following
the methods discussed in Section4.3.2, Villalonga fits a probit model to estimate the
probability that a given firm will diversify using variables similar to those inCampa and
Kedia (2002). She matches each diversifying firm with a non-diversifying firm with a
similar propensity score, i.e., diversifying probability. Her final sample has five quintiles
of firms based on their estimated propensity scores and having a common support.
Villalonga estimates the “treatment effect” caused by diversification as the difference
between the change in excess value of a diversifying firm and the excess value change
of a comparable non-diversifying firms with the closest propensity score. She reports
that while the treatment effect is negative, it is not significant whether she uses the
Dehejia and Wahba (1999)or theAbadie and Imbens (2004)technique for estimation.
Villalonga also reports similar findings when using a Heckman correction, presumably
a treatment effect model on the lines ofCampa and Kedia (2002).^28
Two aspects of Villalonga’s results deserve comment. One issue is perhaps seman-
tic, the use of the termcausal inference. In reading the work, one could easily come
away with the impression that matching methods somehow disentangle causality from
correlation. This is incorrect. Matching methods rule out correlation by arbitrary fiat:
causality is anassumptionrather than a statistically tested output of these methods. This
fact is indeed acknowledged by Villalonga but easy to overlook given the prominence
attached to the term “causal inference” in the paper.
A second issue is that some point estimates of treatment effects are insignificant but
not very different in economic magnitude from those inLang and Stulz (1994)and
Berger and Ofek (1995)—and indeed, from the baseline industry-adjusted estimates that
Villalonga herself reports. Thus, in fairness to Lang and Stulz and Berger and Ofek, Vil-
lalonga’s results do not necessarily refute their earlier work. Nevertheless, Villalonga’s
(^28) In reviewing applications, we often found references to “the” Heckman model or “standard” Heckman
models to be quite confusing.Campa and Kedia (2002)andÇolak and Whited (2005)use it to denote a
treatment effects model, and focus on the coefficient for the diversification dummy variable. However, the
Heckman (1979)model is not a treatment effects model. Also, it is not clear from the papers whether the
coefficient of interest is the coefficient for the dummy variable in a treatment effects model or for the inverse
Mills ratio term. It is perhaps a better practice not to use labels but instead describe fully the specification
being estimated.