Bayesian evaluation of non-admissible conditioning

Virtually all econometric models are conditional models. Nevertheless many of such models lose information by involving non-admissible conditionings. In this article we analyse, from a Bayesian point of view, the problem of admissible conditioning. Next, we design a methodology to evaluate the loss of information when a non-admissible conditioning is used as an approximation of the exact posterior distribution. Considering the Fisher test as a case study we conclude that, in the usual situations of multinomial or of independent binomial samplings, conditioning on the two margins involves a loss of information which does not decrease when the sample size increases.