Dependence and Conditional Independence in Economic Models ∗

De Finetti’s Theorem asserts that a sequence of exchangeable variables are conditionally independent, that is, dependence under exchangeability is nothing but conditionally independence. However, de Finetti’s theorem is valid only with a infinite number of random variables, which makes this result unsuitable for application in many economic models. In this paper, we prove that dependence is conditionally independence in a completely general setting (even without exchangeability). Moreover, we prove the existence of a minimally informative random variable that makes types conditionally independent. If this variable is known by all privately informed individuals, then all results that are valid under independence are also valid for such a model. JEL Classification Numbers: C62, C72, D44, D82.