Marginal effects and incremental effects in two-part models for endogenous healthcare utilization in health services research

Xueyan Liu, Wencong Chen, Tian Chen, Hui Zhang*, Bo Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In health services research, endogenous healthcare utilization refers to the notion that the choice of utilizing health services is endogenous due to its correlation with the intensity of utilization outcomes, such as the number of emergency room visits. Greene in (Empir Econ 36:133–173, 2009) extended four conventional two-part models for zero-abundant count utilization to the two-part models that account for endogenous utilization. However, statistical inference on the (average) marginal and incremental effects in these models has not been carefully studied. The present article provides the estimation formulations for (average) marginal and incremental effects of the four two-part models: zero-inflated Poisson and negative binomial models, and hurdle Poisson and negative binomial models with correlated errors that characterize endogenous healthcare utilization. The variance estimation derived from the delta method is provided to facilitate the statistical inference of these effects. We then perform simulation studies to numerically justify our methodology. An empirical study is presented to investigate the average effects of household income and health insurance status on healthcare utilization with the German Scocioeconomic Panel data. The four models give consistent results regarding interpretations for moral hazards and adverse selection in the study.

Original languageEnglish (US)
Pages (from-to)111-139
Number of pages29
JournalHealth Services and Outcomes Research Methodology
Issue number2-3
StatePublished - Sep 1 2020


  • Endogeneity
  • Endogenous participation
  • Healthcare utilization
  • Hurdle models
  • Zero-inflated models

ASJC Scopus subject areas

  • Health Policy
  • Public Health, Environmental and Occupational Health


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