Greene (1994) Accounting for Excess Zeros and Sample Selection in Poisson and Negative Binomial Regression Models

Summary

Develops modifications of the Poisson and negative binomial (NB) count-data models to handle excess zeros and sample selection. Greene stresses that excess zeros can masquerade as over-dispersion, and provides a test to distinguish genuine zero inflation from over-dispersion. He also formulates a sample-selection model for counts — a count-data analogue of the Heckman selection specification for continuous outcomes — in which the count is observed only for a selected subsample whose selection is correlated with the count's unobservables. An application to consumer loan (default) behaviour shows both zero inflation and selection present.

Key Claims

• Excess zeros ≈ apparent over-dispersion. A surplus of zeros inflates the sample variance relative to the mean and can be mistaken for over-dispersion; the two mechanisms must be disentangled, not conflated.
• A test for zero inflation vs. over-dispersion. Greene proposes a test procedure distinguishing zero-inflated (ZIP/ZINB) departures from plain over-dispersion (NB), rather than relying on fit statistics alone.
• Zero-inflated Poisson/NB (ZIP/ZINB). Mixtures of a point mass at zero with a Poisson or NB count component (following Lambert 1992 / Mullahy 1986) are set out in a unified econometric treatment.
• Count-data sample selection (Heckman analogue). A selection equation (probit) governs whether the count is observed; correlation between the selection error and the count process biases naive estimates, corrected by jointly modelling selection and the count — the count analogue of the Heckman continuous-outcome selection model.
• Empirical relevance. In consumer-loan data both excess zeros and sample selection are clearly present, and ignoring either distorts the estimated covariate effects.

Concepts Introduced or Extended

• Count-Data Regression
• Selection Model

Entities Mentioned

• William H. Greene

Quotes

"We present several modifications of the Poisson and negative binomial models for count data to accommodate cases in which the number of zeros in the data exceed what would typically be predicted by either model. The excess zeros can masquerade as overdispersion. We present a new test procedure for distinguishing between zero inflation and overdispersion. We also develop a model for sample selection which is analogous to the Heckman style specification for continuous choice models."

My Take

The paper that turned the excess-zeros toolkit into standard econometric practice — its ZIP/ZINB treatment and, above all, the insistence that excess zeros and over-dispersion are distinct and testably separable are exactly the entanglement the count-data regression page flags as an open question; Greene supplies the test. Its second contribution, a Heckman-style selection model for counts, is the less-cited but conceptually neat half: it ports the selection-correction idea from continuous outcomes to counts, extending the selection model beyond its Gaussian home. As a working paper from the author of Econometric Analysis and LIMDEP/NLOGIT, it also did much of the work of making these estimators routinely available to applied researchers.