2. The logit model for binary data was introduced in Exercise 1 of Chapter 6. A way of representing the logit model is:

y i

= x

iβ + ui i = 1, ..., n (7.12)

ui ∼ logistic(mean zero)

where the logistic (mean zero) distribution for u is defined by the pdf f (u) = exp(u)

[1 + exp(u)]2

−∞< u < ∞ (7.13)

Consider the ordered logit model, defined in exactly the same way as the ordered probit model, except for the assumption concerning the distribution of u. Derive the likelihood function for the ordered logit model. Note that the ordered logit model can be estimated in STATA with the command ologit.