Estimating State Preference in International Crises:

An Application

• Question: What are the sources of state preferences in international crises?

• Challenge: • Preferences are unobserved, so we need to infer them from observed choices• In a strategic setting, the mapping between preferences and choices is complicated by (a) interdependence and (b) uncertainty

Motivation

A

B

A

ChallengeNot

Challenge

ResistNot

Resist

FightNot

Fight

SQSQA, SQB

ACQACQA, ACQB

BDBDA, BDB

SFSFA, SFB

The Crisis Bargaining Game

Information Structure:• B does not know SFA and BDA

• A does not know SFB

• All other payoffs common knowledge

A

B

A

ChallengeNot

Challenge

ResistNot

Resist

FightNot

Fight

From Theoretical to Empirical Model

A ABD BDX AA SFSFX

BB SFSFX

Information Structure:• SFA

, BDA, SFB

~N(0,1)

• A observes SFA, BDA

• B observes SFB

•X common knowledge

BBDX

ASQX

BSQX

AACQX

BACQX

The Equilibrium Probabilities

( )Pr(Resist) B B B BBD ACQ F SF BD

RF

X X p X Xp

p

( ) ( )Pr(Challenge) 1 A A A A A A A ASQ ACQ R ACQ SF SQ ACQ R ACQ BD

CR R

X X p X X X X p X Xp

p p

2

( ) 1Pr(Fight|Challenge) , ,

2 2A A A A A ASF BD ACQ SQ R SF ACQ

C FR

X X X X p X Xp p

p

Outcome Probabilities:

Pr(SQ)=1

Pr(ACQ)= (1 )

Pr(BD) (1 )

Pr(SF)

C

C R

C R F

C R F

p

p p

p p p

p p p

Normalizations/Constraints

1. Normalize SQA and BDB to have zero mean by demeaning the covariates and including no constants in these expressions.

2. Constrain the constant in ACQA to be greater than zero, and the constant in ACQB to be less than zero. This ensures that, on average, • ACQA > SQA and ACQB < BDB

• i.e., the “good” is actually a good.

Why Do This?

1. Captures the strategic nature of choices and the role of asymmetric information in a crisis interactions.

2. Strategic interaction can lead to non-monotonic relationships and other oddities that are not easy to capture in linear models.

3. Allows us to estimate the effects of covariates on specific payoffs, rather than on outcomes.

A Possible Non-Monotonic Effect

The Pitfalls of Standard PracticeSchultz, “Do Democratic Institutions Constrain or Inform?” (1999 International Organization):

Theoretical Prediction:• If democracy decreases WA, then democracy in A should increase the probability that B resists.• If democracy decreases BDA, then democracy in A should decrease the probability that B resists.

Empirical Result: Democratic initiators face lower probability of reciprocation in militarized disputes.

Conclusion: Democracy decreases BDA.

But…A correlation between democracy in A and an increased probability of ACQ by B can be the product of more than one thing:

Equilibrium Probability of the ACQ Outcome

WA WB BDA

Caveat Emptor

1. Do we believe that this stylized, theoretical model actually generated the data?

2. Data demands• Data need to reflect game outcomes• The SQ problem• Large number of observations are needed to

avoid empirical under-identification

The Data• Cases drawn from

– International Crisis Behavior (ICB)– Militarized Interstate Dispute (MID)

• Definition of Challenge:– “Any act that is made deliberately by a central state

authority with the intent of altering the pre-crisis relationship between itself and at least one other state and that is backed by the threat of military force. The threat of force may take the form of a diplomatic ultimatum, a show of force, or a limited use of force.”

• For each case, we identify – State A (Challenger)– State B (Target)– Outcome (SQ, ACQ, BD, SF)

The Data

• In the period 1919-1939, we identified 93 dyadic challenges.

• Outcome distribution:

Outcome ICB MID Total

ACQ 28 16 44

BD 5 7 12

SF 33 4 37

The Status Quo Problem

• What is the correct population of SQ cases?– We can only be sure that a play of the game took place if

the outcome is not SQ.– How often do crisis opportunities arise?

• We generated 4188 SQ observations meeting the following criteria:

– No challenge occurred in a three-year period– The dyad consisted of

• Contiguous states, or• major powers with other major powers and states in their

geographic region.– For each dyad that met this criterion, there are two

observations, since each state has a turn to be the challenger. These observations were given weight ½.

Empirical Under-Identification

( )Pr(Resist) B B B BBD ACQ F SF BD

RF

X X p X Xp

p

Even if a parameter is theoretically identified, it may be hard in practice to distinguish the effects of two parameters that have similar effect on behavior in the game.