This dissertation focuses on the semiparametric estimation of a panel data model without monotonicity or separability and the nonparametric estimation of a generalized transformation model.

The first chapter considers a generalized single index panel data model without monotonicity or separability. Although monotonicity and/or separability assumptions are commonly imposed in a panel data model to identify the parameters of interest, they usually fail and thus are unideal in practice. For the generalized model, we analyze its identified features under a stationary condition on the idiosyncratic errors, and provide sufficient conditions for point identification of β in several cases. We also establish a matching approach to estimate β under the point identification. The proposed estimat...[ Read more ]

This dissertation focuses on the semiparametric estimation of a panel data model without monotonicity or separability and the nonparametric estimation of a generalized transformation model.

The first chapter considers a generalized single index panel data model without monotonicity or separability. Although monotonicity and/or separability assumptions are commonly imposed in a panel data model to identify the parameters of interest, they usually fail and thus are unideal in practice. For the generalized model, we analyze its identified features under a stationary condition on the idiosyncratic errors, and provide sufficient conditions for point identification of β in several cases. We also establish a matching approach to estimate β under the point identification. The proposed estimator is shown to be asymptotically normal with a convergence rate approaching √n. In addition, a dimension free estimator is developed for the stayers' local average response (LAR) by employing the estimate of β. The basic idea of our method can also apply to a binary choice model. A series of Monte Carlo studies are conducted and verify that our estimator has a good performance in a finite sample. An empirical study of Engel curve suggests the pratical implication of our proposed method.

The second chapter considers a panel data generalized transformation model with an additive structure, Λ(y_it)=∑^d_k=1m_k(X_itk)+α_i+ε_it in which both the structural functions, m_k ,k=1,⋅⋅⋅,d, and the transformation function, Λ, are unspecified. We propose an estimation procedure to nonparametrically estimate m_k in the model. Our estimator has an explicit expression and is easily computed. It is shown to be uniformly consistent and asymptotically normal. We also extend our method to the model without an additive structure and a cross-sectional case. In addition, an alternative method, two stage estimation, is developed for the cross-section generalized transformation model without an additive structure. Monte Carlo simulations are conducted to illustrate our estimator in the panel data case with an additive structure.