A new paper by Cunha, Heckman and Navarro examines the unobserved components of thresholds in ordered choice models.
They extend the ordered discrete choice model to "allow for thresholds that depend on observables and unobservables to jointly analyze discrete choices and associated choice outcomes and to accommodate uncertainty at the agent level".According to the authors, the defning feature of the classical ordered choice model is that choices are generated by ordered sections of the support of a scalar latent continuous random variable (e.g. durations or hours of work).
"In a number of contexts, it is plausible that the cutoff values differ among persons depending on variables that cannot be observed by the econometrician". The issue of hereogeneity in cutoff points is also being considered by researchers at the Geary Institute, but the approach being taken is somewhat different.
Cunha et al develop conditions for nonparametric identification of ordered choice models with stochastic thresholds. Researchers at the Geary Institute are using "anchoring vignettes" to re-weight the thresholds in ordered models of multiple response categories (in the context of self-reported status). Cunha et al do not examine self-reported sttaus in any of their applications, so it would be interesting to see how their approach compares to the use of anchoring vignettes in an application involving self-reported status.
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