Single-variable threshold effects in ordered response models with an application to estimating the income-happiness gradient

This short article extends well-known threshold models to the ordered response setting. We consider the case where the sample is endogenously split to estimate regime-dependent coefficients for one variable of interest, while keeping the other coefficients and auxiliary parameters constant across the threshold. We use Monte Carlo methods to examine the behavior of the model. In addition, we derive the formulae for the partial effects associated with the model. We apply our threshold model to the relationship between income and self-reported happiness using data drawn from the U.S. General Social Survey. While the findings suggest the presence of a threshold in the income-happiness gradient at approximately U.S. $76,000, no evidence is found in support of a satiation point. Supplementary materials for this article are available online.