Consider the censored regression or Tobit model (see Section 16.3) where y = x

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Consider the censored regression or Tobit model (see Section 16.3) where y=xβ+ε,ε iid N[0,σ2], and y is observed when y>0 but is not observed (censored) when y0. There are N0 censored observations on y, and y0 refers to them. Introduce a latent variable z that corresponds to the censored observations such that zi0 if the i th observation belongs to the censored set. The data augmentation method can be used to draw latent variables zi, a set of independent random variables distributed as truncated normal, with support (,0) and pdf ϕ(ziyi,β,σ2)/(1Φ(xiβ/σ)), zi0, where ϕ and Φ are, respectively the normal pdf and cdf. Use a normal prior for β and a gamma prior for σ2.

(a) Show that it is possible to specify a full set of conditionals for zi,β, and σ2.

(b) Use the results of part

(a) to outline the Gibbs algorithm for simulating zi,β, and σ2.

(c) Explain how suitable initial values of β and σ2 may be obtained.

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Microeconometrics Methods And Applications

ISBN: 9780521848053

1st Edition

Authors: A.Colin Cameron, Pravin K. Trivedi

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