40 K. Li and N.R. Prabhala
Introduction
Corporate finance concerns the financing and investment choices made by firms and
a broad swathe of decisions within these broad choices. For instance, firms pick their
target capital structure, and to achieve the target, must make several choices including
issue timing of security issues, structural features of the securities issued, the investment
bank chosen to underwrite it, and so on. These choices are not usually random, but are
deliberate decisions by firms or their managers toself-selectinto their preferred choices.
This chapter reviews econometric models of self-selection. We review the approaches
used to model self-selection in corporate finance and the substantive findings obtained
by implementing selection methods.
Self-selection has a rather mixed history in corporate finance. The fact that there is
self-selection is probably not news; indeed, many papers at least implicitly acknowledge
its existence. However, the literature differs on whether to account for self-selection us-
ing formal econometric methods, and why one should do so. One view of self-selection
is that it is an errant nuisance, a “correction” that must be made to prevent other para-
meter estimates from being biased. Selection is itself of little economic interest under
this view. In other applications, self-selection is itself of central economic interest, be-
cause models of self-selection represent one way of incorporating and controlling for
unobservable private information that influences corporate finance decisions. Both per-
spectives find expression in the literature, although an increasing emphasis in recent
work reflects the positive view in which selection models are used to construct interest-
ing tests for private information.
Our review is organized into two parts. Part I focuses on econometric models of
self-selection. We approach selection models from the viewpoint of a corporate fi-
nance researcher who is implementing selection models in an empirical application. We
formalize the notion of self-selection and overview several approaches towards model-
ing it, including reduced form models, structural approaches, matching methods, fixed
effect estimators, and Bayesian methods. As the discussion clarifies, the notion of se-
lection is not monolithic. No single model universally models or accounts for all forms
of selection, so there is no one “fix” for selection. Instead, there are a variety of ap-
proaches, each of which makes its own economic and statistical assumptions. We focus
on the substantive economic assumptions underlying the different approaches to illus-
trate what each can and cannot do and the type of applications a given approach may be
best suited for. We do not say much on estimation, asymptotic inference, or computa-
tional issues, but refer the reader to excellent texts and articles on these matters.
Part II of our review examines corporate finance applications of self-selection mod-
els. We cover a range of topics such as mergers and acquisitions, stock splits, equity
offerings, underwriting, analyst behavior, share repurchases, and venture capital. Our
objective is to illustrate the wide range of corporate finance settings in which selec-
tion arises and the different econometric approaches employed in modeling it. Here,