80 K. Li and N.R. Prabhala
Cheng (2003)andLi and Zhao (2006)emphasize that PS methods are merely sub-
stitutes for characteristic-by-characteristic matching of observables. This perspective is
probably appropriate. The main issue in these applications is the data driven nature of
the exercise in fitting probit models. Characteristics and interaction terms are added as
needed to achieve balance in characteristics and propensity scores. While we recognize
that a reasonable probit model seems necessary to place faith in treatment effect esti-
mates, the search required to achieve balance, however transparent, nevertheless raises
data dredging concerns and even inconsistency of estimates (Heckman and Navarro-
Lozano, 2004). The general use of PS methods in studies of long-term stock return or
operating performance as an alternative to methods studied inBarber and Lyon (1996,
1997), Barber, Lyon and Tsai (1999), andKothari and Warner (1997)remains an open
question.
- Bayesian methods
13.1. Matching:Sørensen (2005)
Investors differ in their abilities to select good investments, and in their ability to take a
given investment and monitor and manage it so as to add value to what they invest in.
A key question in the venture capital literature is the differentiation of selection from
value-addition. To what extent are better performing venture capitalists more successful
because of their ability to select good investments rather than their ability to value-add
to their investments?Sørensen (2005)employs a matching-selection model to separate
these two influences, using Bayesian MCMC (Markov Chain Monte Carlo) methods to
estimate it.
In Sørensen’s model, there is a set of venture capital investors indexed byi. Each
investor evaluates a set of potential investments indexed byjand ultimately invests
(i.e., becomes the lead investor) in a subset of these. Once an investment occurs, its
outcome is specified as the variableIPOwhich equals one if the investment results
in a public offering and zero otherwise. In Sørensen’s model, feasible investments for
each investor are partly determined by the characteristics of the other agents in the
market. These characteristics are related to the investment decision but unrelated to the
investment outcome, so they provide the exogenous variation used for identification
of the model. On the other hand, this type of sorting also causes interaction between
investment decisions by different venture capitalists, which leads to a dimensionality
problem and considerable numerical difficulties in estimation. Bayesian methods offer
feasible routes for estimation.
Sørensen specifies normally distributed and diffuse prior beliefs with prior variances
that are over 300 times the posterior variance. He assumes that error terms for different
deals are independent. There are three sets of exogenous variables. The characteristics of
the company includes the stage of development of the company and industry dummies.
The characteristics of the venture capital investor include his experience and amount of