Running head: DATA LOGIT MODEL.
Data Logit Model.
Student Name.
Institution Affiliation.
Date.
, DATA LOGIT MODEL.
Data Logit Model.
Consider the following panel data logit model
Y =1{X′β+a−u >0} it it i it
for i = 1,2,··· ,N and t = 1,2. uit is i.i.d over (i,t) with a logistic distribution. The regressors X are
strictly exogenous with respect to the transitory shock uit. However, the individual effects ai can
be correlated with the regressors. Define Yi ≡ {Yi1,Yi2},Xi ≡ {Xi1, Xi2} and Si ≡ Yi1 + Yi2.
a. Obtain the closed-form CCP of Yit given both Xit and ai for each t = 1, 2.
When we consider the law of conditional probability (Zhang, 2017, December)., Pr(Yi,Si |Xi,αi) =
Pr(Yi |Si,Xi,αi) Pr(Si |Xi,αi). Therefore,
b. Obtain the closed-form CCP of Yi given Xi, ai and Si for Si = 0 and Si = 2. Show this does not
depend on ai.
We are going to obtain the probabilities Pr(Yi |Si = 0,Xi,αi), Pr(Yi |Si = 1,Xi,αi), and Pr(Yi |Si =
2,Xi,αi).
When Si = 0, the only possible value of Yi = (0,0). This means that
Data Logit Model.
Student Name.
Institution Affiliation.
Date.
, DATA LOGIT MODEL.
Data Logit Model.
Consider the following panel data logit model
Y =1{X′β+a−u >0} it it i it
for i = 1,2,··· ,N and t = 1,2. uit is i.i.d over (i,t) with a logistic distribution. The regressors X are
strictly exogenous with respect to the transitory shock uit. However, the individual effects ai can
be correlated with the regressors. Define Yi ≡ {Yi1,Yi2},Xi ≡ {Xi1, Xi2} and Si ≡ Yi1 + Yi2.
a. Obtain the closed-form CCP of Yit given both Xit and ai for each t = 1, 2.
When we consider the law of conditional probability (Zhang, 2017, December)., Pr(Yi,Si |Xi,αi) =
Pr(Yi |Si,Xi,αi) Pr(Si |Xi,αi). Therefore,
b. Obtain the closed-form CCP of Yi given Xi, ai and Si for Si = 0 and Si = 2. Show this does not
depend on ai.
We are going to obtain the probabilities Pr(Yi |Si = 0,Xi,αi), Pr(Yi |Si = 1,Xi,αi), and Pr(Yi |Si =
2,Xi,αi).
When Si = 0, the only possible value of Yi = (0,0). This means that
