Semi-parametric Dynamic Models for Ordinal Categorical Panel Data

We consider a general multinomial dynamic logits model in a semi-parametric setup first to analyze nominal categorical panel data in a semi-parametric setup, and then modify this model to analyze ordinal categorical panel... [ view full abstract ]

We consider a general multinomial dynamic logits model in a semi-parametric setup first to analyze nominal categorical panel data in a semi-parametric setup, and then modify this model to analyze ordinal categorical panel data. The ordinal responses are fitted by using a cumulative semi-parametric multinomial dynamic logits model.  A kernel-based semi-parametric weighted likelihood approach is used for the estimation of the non-parametric function. This weighted likelihood estimate for the non-parametric function is shown to be consistent. The regression and dynamic dependence parameters of the model are estimated by maximizing an approximate semi-parametric likelihood function for the parameters, which is constructed by replacing the non-parametric function with its consistent estimate. Asymptotic properties including the proofs for the consistency of the likelihood estimators of the regression and dynamic dependence parameters are discussed.