## Bayesian inference

In order to define the sampling model,5 we make the following assumptions about and zi for i = 1 … N:

1. p(vi | h_1) = f N(vi |0, h_1) and the vis are independent;

2. vi and z; are independent of one another for all i and l;

3. p(zt | ^-1) = fG(zi |1, ^-1) and the zis are independent.

The first assumption is commonly made in cross-sectional analysis, but the last two require some justification. Assumption 2 says that measurement error and inefficiency are independent of one another. Assumption 3 is a common choice for the nonnegative random variable, zi, although others (e. g. the half-normal) are possible. Ritter and Simar (1997) show that the use of very flexible one-sided distributions for zi such as the unrestricted gamma may result in a problem of weak identification...

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