Semi-parametric specification tests for mixing distributions

We present a semi-parametric method for testing mixing distributions in the mixed Poisson model. The proposed method, which is based on the generalized method of moments, does not demand the complete specification of the probability function but only requires a specification of a set of moment conditions which the model should satisfy. We demonstrate that an explicit expression for moment relations between the mixing and the mixed distributions provides a natural way in selecting moment restrictions and model parameterization. The Monte Carlo evidence suggests that the test has satisfactory performance for moderate size samples.