60 K. Li and N.R. Prabhala
EorNE, markets update expectations. If the private information affects stock prices,
the stock price reactionyto the firm’s choice should be related to the updated value
of private information. Assuming that(η, y)are bivariate normal with mean, variances,
and correlation equal to( 0 , 0 , 1 ,σy^2 ,ρ), we can write
E(y|E)=πE(ηi|ηi>−Z′iγ)=πλE(Z′iγ), (33)whereπ =ρσandλE(Z′iγ)=πφ(Z′iγ)/Φ(Z′iγ), the inverse Mills ratio. Equa-
tion(33)gives theconditionalannouncement effect associated with eventE.Itisa
specialized version of theHeckman (1979)model (e.g., equation(10)) in which there
are no regressors other than the inverse Mills ratio.^20
The empirical application inAcharya (1988)is conversion-forcing calls of convert-
ible bonds (eventE) whileNEdenotes the decision to delay forced conversion. Acharya
finds that the coefficientπin equation(33)is statistically significant, suggesting that the
markets do react to the private information revealed in the call. The coefficient is nega-
tive, consistent with theHarris and Raviv (1985)signaling model. A legitimate question
is whether testing for the significance of unconditional announcement effects and run-
ning a linear regression on characteristicsZcould yield inferences equivalent to those
from Acharya’s model.Acharya (1993)offers simulation evidence and the question is
formally analyzed inPrabhala (1997). Self-selection models add most value when one
has samples of firms that chosenotto announceEbecause these methods offer a natural
way of exploiting the information in samples of silent non-announcers.
7.2. Two announcements on the same date:Nayak and Prabhala (2001)
In the Acharya model, there is one announcement on an event-date.Nayak and Prabhala
(2001)analyze a specification in which two announcements are made on the same date.
They present a model to recover the individual impact of each announcement from the
observed announcement effects, which reflect the combined impact of both announce-
ments made on one date.
The empirical application in Nayak and Prabhala is to stock splits, 80% of which
are announced jointly with dividends. Nayak and Prabhala model the joint decisions
about whether to split a stock and whether to increase dividends using a bivariate probit
model, which can be specified as
SPLi=γsZsi+ψsi, (34)
DIVi=γdZdi+ψdi. (35)IfSPLiexceeds zero, a firm splits, and ifDIViexceeds zero, it increases dividends.
The private information components of these two latent variables areψsiandψdi, and
these have potentially non-zero correlationρsd. The announcement effect from the two
(^20) The absence of other regressors is dictated by the condition that announcement effects should not be related
to ex-ante variables under the efficient markets hypothesis.