82 K. Li and N.R. Prabhala
p∗ 1 =X 1 β 1 + 1 , (70)
p∗ 2 =X 2 β 2 + 2 , (71)
y 1 ∗=W 1 α 1 +v 1 , (72)
R∗ 1 =V 1 θ 1 +u 1 , (73)
R∗ 2 =V 2 θ 2 +u 2 , (74)whereI∗is an unobserved latent variable representing the incremental utility of tender
offers over open market repurchases,p∗ 1 ,y∗ 1 ,R 1 ∗are the percentage of shares sought, ten-
der premium and announcement effects under the tender offer regime, andp∗ 2 ,R∗ 2 are
the proportion sought and announcement effects in an open market repurchase regime.
The error terms in equations(69)–(74)are assumed to have a multivariate normal dis-
tribution.
The system of equations(69)–(74)represents a switching regression system dis-
cussed in Section3.1, but with more than one regression in each regime. The key issue
in estimating the system is the lack of information on unobserved counterfactuals. We
observe outcomes in the repurchase technique actually chosen by a firm but do not ex-
plicitly observe what would happen if the firm had chosen the alternative technique
instead. Li and McNally employ MCMC methods that generate counterfactuals as a
natural by-product of the estimation procedure. This approach involves a data augmen-
tation step in which the observed data are supplemented with counterfactuals generated
consistent with the model structure. The priors about parameters are updated and poste-
riors obtained using standard simulation methods after which the additional uncertainty
due to the data augmentation step can be integrated out. Observations on counterfactual
choices and outcomes are generated as part of the estimation procedure. These can be
directly used to examine the impact of choosing a given type of repurchase mechanism
not just in isolation, but also relative to the impact of choosing the unchosen alternative.
The sample in Li and McNally comprises 330 fixed price tender offers, 72 Dutch
auction tender offers, and 1,197 open market repurchases covering time periods from
1962 to 1988. In terms of findings, Li and McNally report that firms choose the tender
offer mechanism when they have financial slack and large shareholders that monitor
management. Firms prefer the open market repurchase in times of market turbulence
or weak business conditions. Unobserved private information affects both the type of
the repurchase program and the repurchase terms and is reflected in the stock market
announcement effects. The estimates of counterfactuals are quite interesting. For in-
stance, if the open market repurchasers had opted for tender offers, the proportion of
shares sought would have been 36% (versus actual of about 7%) and the tender pre-
mium would have been 33% compared to 0% actuals, and the five-day announcement
effect would be 16% compared to the actual announcement effect of 2.2%. Likewise,
tender offer firms would have repurchased 10.6% (actual= 19 .7%) and experienced
announcement effects of 3.7% (actual= 10 .2%). Firms appear to have a comparative
advantage in their chosen repurchase mechanisms.