Theoretical And Empirical Analysis Of Specification, Estimation And Tests In Binary Choice Models Of Panels

This dissertation is supported by National Natural Science Funds—Stationary and Unstationary Linear Panel Data Modeling Research under Cross-sectional Dependence and Non-spherical Disturbances Conditions(No.71071130).More and more empirical works on response of individuals have arised with continuously accumulated individual-level data on the economics behavior of individuals or firms. But it is more difficult to study nonlinear models than linear ones. So many issues of nonlinear models are still left to be researched. The specification, estimation and test for binary panel data models are discussed in this dissertation. We hope make some contributions in these areas.In chapter1, we introduce the problems researched in this dissertation and the background of our study.We give a review in the specification, estimation, test and empirical research systematically in chapter2.For estimation,we introduce some usually used methods including direct estimation,conditional maximum likelihood estimation, bias correction estimation and maximum score estimation. We also review the methods to test the cross sectional dependence and the specification tests in binary panel models.Besides these areas.In the third chapter the specification error tests for binary choice panel data models are considered. The first section of this chapter introduces the common methods in great detail for specification tests in cross sectional data models, including heteroscedasticity tests, variable omission tests and distribution tests. Except for these specific tests we also introduce the RESET tests. And in the second part we discuss the RESET tests for binary choice panel data models, In the following we extend the specification tests used in cross sectional models to panel models and compare these tests with the RESET test.And in chapter4, we consider the estimation for binary panel models with heterogeneous linear trend mainly. Firstly the small sample properties of bias-corrected estimator for Gumbit model are discussed. And then we give a sufficient and necessary condition for the existence of the sufficient statistics in binary panel logit models with serial correlation disturbances. Lastly bias correction estimators for the binary panel models with heterogeneous linear trends are proposed to remedy the shortback of the conditional estimator.The cross-sectional independence tests are considered in the fifth chapter. Firstly we introduce the ideas and deficiencies in the current main methods to test cross section independence proposed for linear panel data models. And then a new statistics for cross-sectional independence test is proposed. Secondly these statistics are extended to binary choice panel data models..The chapter6shows the estimation methods for binary choice panel models with cross-sectional dependence. We use Copula functions to construct the likelihood functions with cross-sectional structure and estimate the parameters of interested in pooled models and fixed effect models by maximizing these likelihood functions.In chapter7, the methods proposed above are applied to research the behavior of cash dividends payment of the listed companies, including bias-corrected estimator for binary choice panel data model with heterogeneous linear trend, cross-sectional dependence test for binary choice panel data model and estimation for binary choice panel data model with cross-sectional dependence.And lastly in the chapter8, we give a conclusion on this dissertation and present some areas which are worthy of being studied for future.Concretely, the following several points are included in our dissertation:1. Domestic literature pays little attention to the theory research in discrete choice models, especially in discrete choice panel data models. This dissertation summarizes systematically the research on specification, estimation and test, and introduces the new research results in binary choice panel models. We discuss the advantages and disadvantages of main methods to hope provide some new ideas for future study.2. Specification tests.We expand the RESET test proposed by Ramsey (1969) to binary choice panel models. The size and power performance of RESET test is considered for heteroscedasticity test, variable omission test and distribution assumption test respectively. Small sample experiments manifest:(1) the actual size is very close to the nominal size for these models;(2) the power performs well wholly, especially when the omitted variable is highly correlated with some explanatory variable;(3) the power of the test to distinguish standard normal distribution and standard logistics distribution is very low. The special specification tests (include heteroscedasticiy test and variable omission test proposed by Davidson&Mackinno and distribution specification error test proposed by Silva) introduced above are also extended to binary panel models directly. However, the performance is very bad except for variable omission test.3. Estimation. The big problem mainly mentioned in binary choice panel models is the bias of maximum likelihood estimators caused by nuisance parameters. The small sample properties of the bias-corrected estimator of gumbit models are discussed firstly. We find that the bias of this estimator in gumbit models is corrected greatly. Then we focus on the estimation of binary choice panel models with heterogeneous linear trends. With respect to logit models, we obtain a sufficient and necessary condition for the existence of sufficient statistics of these models with serially correlated disturbance. For those models in which sufficient statistics don’t exist such as probit models, the leading bias of the maximum likelihood estimator is obtained. Through this bias structure, we get bias-corrected estimators of binary choice panel models with heterogeneous linear trends. At the same time, we get the bias correction estimators of the average marginal effects of explanatory variables. Monte Carlo simulation shows these estimators can correct the bias of maximum likelihood estimators almost completely. In logit panel models the MAE (mean absolute error) performance is even better than that of conditional likelihood estimators.4. Cross-sectional dependence test. After introducing the latest methods to test cross-sectional independence for panel data models, we put forward a new statistics called MCD statistics for cross-sectional independence test, which follows asymptotically standard normal distribution.Monte Carlo experiments show the MCD statistics performs very well. At the same time, we discuss the cross section dependence test when the disturbance terms are correlated serially in linear panel data models, and find those statistics introduced above manifest serious size distortion with serially correlated disturbance terms. But if we eliminate the serial correlation, the size and power still perform well just as no serial correlation. In addition, we extend the modified LM statistics proposed by Baltige et. al. to binary choice panel models. Its small sample properties perform like the MCD statistics here. Using these statistics we get the empirical evidence that there is dependence between the cash dividends payment behaviors of the listed firms.5. Estimation for binary choice panel models with cross-sectional dependence.It is still a hot research area to estimate binary choice panel models with cross-sectional dependence. A two-step maximum likelihood estimation method and a three-step maximum likelihood estimation method are proposed for pooled models and fixed effect models respectively. The asymptotic properties are obtained and the small sample properties are discussed as well. The difference between these two methods is that the nuisance parameters need to be estimated in three-step estimation method, In three-step maximum likelihood estimation method, we first estimate the common parameters under the assumption of cross-sectional independence. Using this result to estimate the nuisance parameters is the second step. Then the general residuals of the model are obtained. The correlation coefficients of the general residuals are looked as the correlation parameters in Copula likelihood function. Thus the third step is to maximize this likelihood function to get the final estimation results of common parameters. The asymptotic properties of the estimators are given including the asymptotic distribution and covariance matrix. Monte Carlo simulation shows the estimators proposed here have good MAE than ordinary MLE estimators that ignore cross-sectional dependence, not only improving the convergence speed but the efficiency. The empirical study also shows that these multiple-step maximum likelihood estimators can make better the efficiency of the estimators in binary panel models with cross sectional dependent disturbance.The following three innovations are achieved in this dissertation after study on the estimation and tests of binary choice panel data models.1. To estimate binary panel models with linear trends, a bias-corrected estimator is proposed which have very good small sample properties. This estimator is prior to the conditional logit method and maximum score estimator and is very helpful to empirical study. Comparing with these two estimators, this estimator proposed here has the following two advantages.(1)The distribution of the disturb term need not to be specified as logistics, and the samples used in estimation are more than conditional likelihood estimator.(2) We need not to specify artificial parameters such as bandwidth in maximum score estimation, and the estimator is much easier relatively.2. After studying the cross-sectional dependence tests for panel data models, a new statistics for these models is proposed which follows aymtoticly standard normal distribution. Monte Carlo simulation shows this new statistics has good small sample properties. This statistics can avoid grealy the low power situation of Pesaran’s CD statistics (2004), and is much simpler than the statistics proposed by Pesaran et.al.(2008). Then, this statistics is extended to binary choice panel models with another statistics for linear panel models.3. For the pooled models and fixed effect models in binary panel models with cross-sectional dependence, a two-stage maximum likelihood estimator and three-stage maximum likelihood estimator are proposed separately. The consistency, asymptotic normality and asymptotic variance are obtained. Monte Carlo simulation shows these two estimators are more efficient than ordinary maximum likelihood estimators and conditional likelihood estimators obviously. In some situations the convergance speed is faster.