Paarlberg, L., & Zuhlke, S. (2019). Revisiting the Theory of Government Failure in the Face of Heterogenous Demand. Perspectives on Public Management and Governance, 2(2): 103-124.

What explains the development of the nonprofit sector? The classic theory of demand heterogeneity posits the nonprofit sector provides services for those unsatisfied by government service delivery. However, formal tests of this theory have produced conflicting results. This article revisits the theory of demand heterogeneity, refining it to include the mediating effects of government wherein increased diversity leads to lower levels of government funding, which are associated with a larger nonprofit sector. The test results do not support this refined model, and instead generally support theories of government and nonprofit interdependencies, whereby increased diversity leads to a larger nonprofit sector through larger government. We condition our results by the type of good being produced, and call for future empirical tests to identify processes by which demand heterogeneity influences the development of the nonprofit sector.

Cook, S. J., Niehaus, J., & Zuhlke, S. (2018). A warning on separation in multinomial logistic models. Research & Politics5(2), 2053168018769510.

Oppenheim et al. (2015) provides the first empirical analysis of insurgent defection during armed rebellion, estimating a series of multinomial logit models of continued rebel participation using a survey of ex-combatants in Colombia. Unfortunately, many of the main results from this analysis are an artifact of separation in these data – that is, one or more of the covariates perfectly predicts the outcome. We demonstrate that this can be identified using simple cross tabulations. Furthermore, we show that Oppenheim et al.’s (2015) results are not supported when separation is explicitly accounted for. Using a generalization of Firth’s (1993) penalized-likelihood estimator – a well-known solution for separation – we are unable to reproduce any of their conditional results. While our (re-)analysis focuses on Oppenheim et al. (2015), this problem appears in other research using multinomial logit models as well. We believe that this is both because the discussion on separation in political science has primarily focused on binary-outcome models, and because software (Stata and R) does not warn researchers about separation in multinomial logit models. Therefore, we encourage researchers using multinomial logit models to be especially vigilant about separation, and discuss simple red flags to consider.