A Fixed Effects Ordered Choice Model with Flexible Thresholds with an Application to Life-Satisfaction

Abstract

In many contexts reported outcomes in a rating scale are modeled through the existence of a latent variable that separates the categories through thresholds. The literature has not been able to separate the e¤ect of a variable on the latent variable from its effect on threshold parameters. We propose a model which incorporates (1) individual fixed effects on the latent variable, (2) individual fixed effects on the thresholds and (3) threshold shifts across time depending on observables. Importantly, the latent variable and the threshold specifications can include common variables. In order to illustrate the estimator, we apply it to a model of life satisfaction using the GSOEP dataset. We demonstrate that important differences can arise depending on the choice of the model. Our model suggests that threshold shifts are statistically and quantitatively important. Factors which increase reported life-satisfaction are due both to positive effects on the latent variable AND to shifting thresholds to the left, while factors which decrease reported life satisfaction are due to negative e¤ects on the latent variable AND to shifting thresholds to the right.