6. The posterior simulator for the stochastic frontier model (see Section 7.7.4) used an exponential inefficiency distribution (i.e. zi G.z ; 2/). Derive a

6. The posterior simulator for the stochastic frontier model (see Section 7.7.4)

used an exponential inefficiency distribution (i.e. zi ¾ G.¼z ; 2/). Derive a posterior simulator for the case where zi ¾ G.¼z ; 4/ and zi ¾ G.¼z ; 6/.

Note: The Gamma distribution with (known) degrees of freedom equal to an even integer (i.e. ¹ D 2; 4; 6; : : : ) is referred to as the Erlang distribution.

Bayesian inference in stochastic frontier models with Erlang inefficiency distribution using importance sampling is described in van den Broeck, Koop, Osiewalski and Steel (1994). Inference using Gibbs sampling is described in Koop, Steel and Osiewalski (1995). Bayesian inference in the unrestricted Gamma case (zi ¾ G.¼z; ¹/ where ¹ is an unknown parameter) is described in Tsionas

(2000). If you are having difficulty with this question you may wish to take a look at some of these references.