A Generalized Ordered Response Model

• Activity Number: 246
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Carla Johnston*+ and James McDonald
• Companies: Brigham Young University and Brigham Young University
• Keywords: Semiparametric estimation ; ordered response ; heteroskedasticity ; sgt distribution

Abstract

The ordered probit and logit models are the standard models used to analyze categorical data. The use of a normal or logistic distribution to estimate parameters removes nonsensical parameter results and mitigates heteroskedasticity. Yet, the normal or logistic distributional assumptions for the errors pose a threat of misspecification. When using MLE to estimate marginal effects, misspecification of the error terms can lead to biased parameter estimates. To avoid this danger, the generalized ordered response model allows the error terms to take on more flexible distributions and reduce the consequences of misspecification. In particular, the SGED and ST allow for varying skewness and kurtosis in the error distribution. An empirical application examining the effect of income on life satisfaction exhibits the improvement in estimate results when increasing the flexibility of error distribution assumptions. Standard errors on parameters decreased and the log-likelihood functions increased with each step in increasing flexibility. Estimation methods accounting for heteroskedasticity and more flexible error distributions are also applied to the data.