…cation would ignore the strategic considerations of each player. Second, one potential
problem is an independent error assumption, i.e. uncorrelated private information for
each player. Although the Heckman bivariate probit analysis resolves this problem, it
does not consider strategic decision-making seriously (Signorino 2002).
27
Third, I can
divide the game into separate stages that would represent each decision node, rather
than testing the whole structure of the model. Then, it would be possible to estimate
from the bottom of the tree upwards using a simultaneous equations model. However,
since the sender moves twice and the two players update their beliefs, the simultaneous
equations model cannot re‡ect the complicated interactions as e¤ectively as shown in
the equilibrium probabilities of outcomes. Consequently, the fully structural model …ts
best with the data-generating process of sanctions.
Based on the PBE probabilities of each outcome, the likelihood function is
L =
N
Y
i=1
P
Y
S Q i
SQ
i
P
Y
C w i
C
w
i
P
Y
B d w i
Bd
w
i
P
Y
D lw i
Dl
w
i
P
Y
C si
C
s
i
P
Y
B d si
Bd
s
i
P
Y
D lsi
Dl
s
i
;
where P
outcome
le ve l
s are the PBE probabilities of outcomes de…ned in the Appendix.
Y
outcome
le ve l
s are binary dependent variables. The log-likelihood function is maximized
with respect to the parameters.
4.3
Results
The results are shown in Table 3.
28
I brie‡y summarize the results from sender’s and
target’s perspectives.
Not surprisingly, the sender receives a positive payo¤ of compliance (V
A
) and this
payo¤ increases as the issue becomes important. When the sender backs down after the
target’s resistance, she receives negative mean payo¤s (a
W
and a
S
). Also, the sender is
worse o¤ if she backs down from strong sanctions than weak sanctions. The fact that
the back-down outcome leaves the sender with signi…cantly negative payo¤s implies
2 7
Moreover, it is di¢ cult to say that the strategic aspects of my model (and true utilities representing
them) are dominated by the error term.
2 8
While I report only one result that I believe is the best to test the hypotheses, I ran di¤erent
combinations of covariates to check if the result in Table 3 is sensitive to addition or deletion of other
variables. For example, in Table 3, I estimate the deadlock payo¤ of the sender using only allies. I
tried other variables such as the sender’s economic dependence and the hostility level between sender
and target. The sender’s economic dependence had no meaningful variation over the outcomes and was
not statistically signi…cant. With all the di¤erent versions, however, both directions and signi…cance
of the results in Table 3 remained robust.
17
Convention