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Abstract
The ordered probit and logit models, based on the normal and logistic distributions, can yield biased and inconsistent estimators when the distributions are misspecified. A generalized ordered response model is introduced which can reduce the impact of distributional misspecification. An empirical exploration of various determinants of life satisfaction suggests possible benefits of allowing for diverse distributional characteristics. These improvements are confirmed using a Monte Carlo study to contrast the performance of the flexible parametric specifications to the probit and logit specifications.
Acknowledgements
We would like to thank Daniel Gardner for his instructive comments and help with the estimation procedure. We would also like to thank an anonymous referee for detailed comments and Bryan Chia for additional assistance in finalizing the paper.
Notes
1 The publically available scripts used for estimation include programs that do not require parallel processing and is available at https://bitbucket.org/cjohnst5/generalizedorderedprobit/src/master/. Under the restriction that the code do not run in parallel, the authors are still working on optimizations for the SGT. Estimation in both programs imposes monotonicity of the cut points.
2 The Monte Carlo approximations with four cutoffs and 10,000 observations collectively took 3,677 processor-hours. With 64 of these approximations, each having 10,000 replications, the implied average computational time for an ordered response model with 10,000 observations and four cutoffs is 20.7 seconds.