Abstract
We introduce three new commands—nop, ziop2, and ziop3—for the estimation of a three-part nested ordered probit model, the two-part zero-inflated ordered probit models of Harris and Zhao (2007, Journal of Econometrics 141: 1073–1099) and Brooks, Harris, and Spencer (2012, Economics Letters 117: 683–686), and a three-part zero-inflated ordered probit model of Sirchenko (2020, Studies in Nonlinear Dynamics and Econometrics 24: 1) for ordinal outcomes, with both exogenous and endogenous switching. The three-part models allow the probabilities of positive, neutral (zero), and negative outcomes to be generated by distinct processes. The zero-inflated models address a preponderance of zeros and allow them to emerge in different latent regimes. We provide postestimation commands to compute probabilistic predictions and various measures of their accuracy, to assess the goodness of fit, and to perform model comparison using the Vuong test (Vuong, 1989, Econometrica 57: 307–333) with the corrections based on the Akaike and Schwarz information criteria. We investigate the finite-sample performance of the maximum likelihood estimators by Monte Carlo simulations, discuss the relations among the models, and illustrate the new commands with an empirical application to the U.S. federal funds rate target.
Highlights
We introduce the commands nop, ziop2, and ziop3, which fit the two-level nested and zero-inflated ordered probit (OP) models for ordinal outcomes, including the zero- and middle-inflated OP models of Harris and Zhao (2007), Bagozzi and Mukherjee (2012), Brooks, Harris, and Spencer (2012), and Sirchenko (2020)
The Nested Ordered Probit (NOP) model provides a substantial improvement of the likelihood and is preferred to the standard OP model according to Akaike information criteria (AIC) and the Vuong test
The Vuong tests for zero inflation favor the ZIOP-3 model over the OP model at the 0.001 and 0.01 level, respectively
Summary
We introduce the commands nop, ziop, and ziop, which fit the two-level nested and zero-inflated ordered probit (OP) models for ordinal outcomes, including the zero- and middle-inflated OP models of Harris and Zhao (2007), Bagozzi and Mukherjee (2012), Brooks, Harris, and Spencer (2012), and Sirchenko (2020). The model of Harris and Zhao (2007) is suitable for explaining decisions such as the levels of consumption, when the upper hurdle is naturally binary (to consume or not to consume), the responses are nonnegative, and the inflated zeros are situated at one end of the ordered scale (see the bottom left panel of figure 1). Bagozzi and Mukherjee (2012) and Brooks, Harris, and Spencer (2012) modified the model of Harris and Zhao (2007) and developed the middle-inflated OP model for an ordinal outcome, which ranges from negative to positive responses, and where an abundant outcome is situated in the middle of the choice spectrum (see the bottom right panel of figure 1). The zero-inflated models, estimation of which is currently implemented in Stata, include the zeroinflated Poisson model (the zip command), the negative binomial model (the zinb command), and the binomial model (the zib command) and the beta-binomial model (the zibbin command) both developed by Hardin and Hilbe (2014)
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