Two-Part Models for Fractional Responses Defined as Ratios of Integers

This paper discusses two alternative two-part models for fractional response variables that are defined as ratios of integers. The first two-part model assumes a Binomial distribution and known group size. It nests the one-part fractional response model proposed by Papke and Wooldridge (1996) and thus, allows to apply Wald, LM and/or LR tests in order to discriminate between the two models. The second model extends the first one by allowing for overdispersion. Monte Carlo studies reveal that, for both models, the proposed tests are equipped with sufficient power and are properly sized. Finally, we demonstrate the usefulness of the proposed two-part models for data on the 401(k) pension plan participation rates used in Papke and Wooldridge (1996).