Consider the censored regression or Tobit model (see Section 16.3) where y = x
Question:
Consider the censored regression or Tobit model (see Section 16.3) where iid , and is observed when but is not observed (censored) when . There are censored observations on , and refers to them. Introduce a latent variable that corresponds to the censored observations such that if the th observation belongs to the censored set. The data augmentation method can be used to draw latent variables , a set of independent random variables distributed as truncated normal, with support and pdf , , where and are, respectively the normal pdf and cdf. Use a normal prior for and a gamma prior for .
(a) Show that it is possible to specify a full set of conditionals for , and .
(b) Use the results of part
(a) to outline the Gibbs algorithm for simulating , and .
(c) Explain how suitable initial values of and may be obtained.
Step by Step Answer:
Microeconometrics Methods And Applications
ISBN: 9780521848053
1st Edition
Authors: A.Colin Cameron, Pravin K. Trivedi