| Existing research shows that, since the middle period of last century, the Panel Data model has been widely applied in economics research, due to the advantage of model setting and data structure in economics researchs, it has become an important branch of econometrics research at present, of which the Nonlinear Panel model is the focus and cutting-edge of current Panel model research. Nonlinear panel model, refers to the relative to the linear panel model, the model structure for model parameters is essentially non-linear, such as discrete selection panel model, counting panel model, truncation panel model, etc. The advantage of panel model compared with the general time series model and cross-section model is that it can effectively control unobserved individual heterogeneity in the model, for these characteristics there are two settings with random effects and fixed effects. Due to the structure particularity of nonlinear panel model, traditional linear panel model analysis methods applied in this model have some problems at this point. This paper systematically research the analysis methods of nonlinear panel model, focuses on the parameter estimation theory of nonlinear panel model with fixed effects, and takes advantage of the empirical analysis to examine the the application of nonlinear panel model in the empirical research. In this paper, the main research works and research conclusions can be summed up in the following aspects:Firstly, systematically research the basic theory of the nonlinear panel model and the parameter estimation of this kind of model, analysis and summary the existing problems when various commonly used parameter estimation methods are applied to nonlinear panel model. Research results show that traditional data conversion method between group and group in a nonlinear panel model is not feasible because the nonlinear characteristics of the nonlinear panel model of; The condition maximum likelihood estimation method applied in linear panel model is only suit to a handful of special nonlinear panel model, because this method requires that the sufficient statistic of the individual effect exists, but in general nonlinear panel model this condition is unable to satisfy; Semiparametric estimation method and generalized moment estimation can obtain the consistency structural parameters estimators of nonlinear panel model under certain conditions, but they cann’t estimate other induced parameters constructed from the model structure parameters and individual effects, such as the average marginal effect, etc. Maximum likelihood estimator is a full information estimator, can estimate all structural parameters, incidental parameters and induced parameters similar to the average marginal effect in the model, but in the settings of T fixed, N tends to infinity, or N, T tends to infinite with the some order, these estimators are biased and not consistent under fixed effects settings because of incidental parameters problems.Secondly, this paper considers the parameter estimation theory and bias correction problem based on different setting of nonlinear panel model.For static nonlinear panel model, focuses on the bias correction problems in the maximum likelihood estimators of model structure parameters with fixed effects, researches the bias correction methods aim at the model structure parameters and the induced parameters through the analytical bias correction, orthogonality of parameter information bias correction, a priori information bias correction and bootstrap bias correction, while studying the connection and difference between different bias correction methods, providing instructions and guidance for the application of these methods in the actual. Nonlinear dynamic panel model is one of the forefront issues in current panel model research, this paper study parameter estimation and bias correction problem in this kind of model from two aspects, first of all, for a specific dynamic discrete selection panel model with fixed effects, under the setting of T fixed, N tend to be infinite, set research fixed effects parameter estimation problem in the set of this kind of model, and focuses on the modified maximum likelihood estimation method, the research conclusion shows that this method can effectively reduce the bias of structure parameters’maximum likelihood estimators of the dynamic discrete selection panel model from O(T-1) to O(T-2). Again, based on the general nonlinear dynamic panel model under the setting of N,T tends to infinite in the same order, research the related parameter estimation theory.Finally, this paper introduces time effect to the nonlinear panel model contains only of the individual effect in general to constitute the double effects nonlinear panel model, analysis the model setting and parameter estimation theory of this kind of model, for the bias of model parameters and induced parameters of two-factors error nonlinear model with fixed effects, through studying the gradual extension of the maximum likelihood estimator of various parameters of the model under the fixed effects setting, analysis analytical bias correction method and two types of bootstrap methods based on these extensions.Thirdly, in terms of empirical analysis, this paper using the China health and nutrition survey (CHNS) micropanel data, using ordered Probit model panel to examine the influence factors of residents’Self-Assessed Health in our country.In micro data investigation, such as China health and nutrition survey (CHNS), often ask respondents to evaluate themself health status, the self assessment is often used as a proxy variable for personal health research in the literature related health problems. Self-Assessed Health has all been influenced by same subjective factors and objective factors, this paper establishes the nonlinear panel empirical analysis models, the error terms are used to control the unobserved factors and the individual effects are use to control the unobserved individual heterogeneity, analyzes the influence of society, economy factors on Self-Assessed Health, such as income level, marital status, age and disease, and study the different influence between the male Self-Assessed Health and female Self-Assessed Health. |
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