Ch. 2: Self-Selection Models in Corporate Finance 41
we focus on applications published in the last decade or so, and on articles in which
self-selection is a major component of the overall results.^1
I. MODELING SELF-SELECTION
This portion of our review discusses econometric models of self-selection. Our in-
tention is not to summarize the entire range of available models and their estimation.
Rather, we narrow our focus to models that have been applied in the corporate finance
literature, and within these models, we focus on the substantive assumptions made by
each specification. From the viewpoint of the empirical researcher, this is the first order
issue in deciding what approach suits a given application in corporate finance. We do
not touch upon asymptotic theory, estimation, and computation. These important issues
are well covered in excellent textbooks.^2
We proceed as follows. Section1 describes the statistical issue raised by self-
selection, the wedge between the population distribution and the distribution within
a selected sample. Sections2–6develop the econometric models that can address selec-
tion. Section2 discusses a baseline model for self-selection, the “Heckman” selection
model analyzed inHeckman (1979), a popular modeling choice in corporate finance.^3
We discuss identification issues related to the model, which are important but not fre-
quently discussed or justified explicitly in corporate finance applications. Because the
Heckman setting is so familiar in corporate finance, we use it to develop a key point
of this survey, the analogy between econometric models of self-selection and private
information models in corporate finance. Section3 considers switching regressions and
structural self-selection models. While these models generalize the Heckman selection
model in some ways, they also bring additional baggage in terms of economic and sta-
tistical assumptions that we discuss.
We then turn to other approaches towards modeling selection. Section4 discusses
matching models, which are methodsdu jourin the most recent applications. The
popularity of matching models can be attributed to their relative simplicity, easy inter-
pretation of coefficients, and minimal structure with regard to specification. However,
these gains come at a price. Matching models make the strong economic assumption
that unobservable private information is irrelevant. This assumption may not be realistic
in many corporate finance applications. In contrast, selection models explicitly model
and incorporate private information. A second point we develop is that while matching
(^1) Our attempt is to capture the overall flavor of self-selection models as they stand in corporate finance as of
the writing. We apologize to any authors whose work we have overlooked: no slight is intended.
(^2) The venerable reference,Maddala (1983), continues to be remarkably useful, though its notation is often
(and annoyingly, to the empirical researcher) different from that used in other articles and software packages.
Newer material is covered inWooldridge (2002)andGreene (2003).
(^3) Labeling any one model as “the” Heckman model surely does disservice to the many other contributions
of James Heckman. We choose this label following common usage in the literature.