Ch. 2: Self-Selection Models in Corporate Finance 75
10.4. Discussion
A key advantage of the diversification discount literature is that it has reasonably similar
datasets, so it is easier to see the changes due to different econometric approaches. By
the same token, it becomes easier to raise additional questions on model choice. We raise
these questions here for expositional convenience, but emphasize that the questions are
general in nature and not particular to the diversification discount literature.
One issue is statistical power. The diversification discount is significant using conven-
tional industry-size matching but it is insignificant using PS based matching methods. Is
this because the latter lack power? Çolak and Whited offer some welcome Monte Carlo
evidence with respect to their application, simulating data with sample sizes, means,
covariance matrix, and covariates with third and fourth moments equal to that observed
in the actual data. They confirm that their tests have appropriate size, and at the level of
the treatment effects in the sample, there is a better than 20% chance of detecting the
observed treatment effect. More on these lines would probably be useful.
A second issue is the use of PS based matching methods as primary means of infer-
ence about treatment effects. There are good reasons to be uncomfortable with such an
approach. The main issue is that propensity score methods assume that private informa-
tion is irrelevant. However, this assumption is probably violated to at least some degree
in most corporate finance applications. In fact, in the diversification literature, private
information does empirically matter. Thus, using PS methods as the primary specifica-
tion seems inappropriate without strong arguments as to why firms’ private information
is irrelevant.Heckman and Navarro-Lozano (2004)stress and show explicitly that even
small deviations from this assumption can introduce significant bias. Thus, the practice
followed in the finance literature of reporting private information specifications in con-
junction with matching models is probably appropriate, although more full discussion
on reconciling the results from different approaches would be useful.
A final comment is about the self-selection specifications used to control for private
information. While the literature has used versions of the baselineHeckman (1979)
model, we emphasize that this restriction is neither necessary nor desirable. Other
models, such as switching regressions and structural models are viable alternatives for
modeling self-selection and private information. Because these models come with their
own additional requirements, it is not clear that they would always be useful, but these
issues are ultimately empirical.
- Other applications of selection models
11.1. Accounting for R&D:Shehata (1991)
Shehata (1991)applies self-selection models to analyze the accounting treatment of
research and development (R&D) expenditures chosen by firms during the period of the
introduction of FASB ruling SFAS No. 2. This ruling pushed firms to expense rather