Research On Nonparametric Model Specification Test With Mixed Discrete And Continuous Data

Model specification research is an core and important issue of econometric. Econometric model is based on economic theory, economic theory can only tell us the influence of one variable on others variable, but can’t determines the form of econometric model. The correct model specification is the premise of empirical research, the reliability of both mathematical derivation and statistical inference rely on the correct model specification. The description of economic laws with econometric model also require the correct model specification. When a theoretical hypothesis is rejected in statistical tests, it doesn’t mean that the economic theory is wrong, maybe we choose the incorrect function form in hypothesis. This phenomenon is called misspecification when assumed function form is inconsistent with economic laws. If the model is misspecification, then the improvement of statistical techniques can not reduce bias of empirical results and the estimation or statistical inference based on incorrect model, so it’s important to pay close attention to the research of model specification test. This paper discussed the statistics construction from the perspective of model specification, and wish to give some useful theoretical and application contribution to this field.Model specification test is a widely research field, this paper mainly focus on the problem of the specification test of parametric regression model. Most parametric regression model specification tests assume that the variables are continuous. However, many economic data such as income and ages are continuous, but some economic data are discrete, such as family size、 gender race and the choices made by the economic agents etc, and in micro-data based econometric models, the discrete variable are more common. On the other hand, sometimes economic models both include continuous and discrete variables, so the study of consistency model specification test with discrete or mixed data is theoretical and practical significance.This paper review the research literature about the estimate and tests of nonparametric model specification test, especially for models include discrete and continuous mixed variables. On this basis, the paper draw Hsiao, Li & Racine(2006)’s ideas, and used integrated squared difference metrics proposed by Hardle & Mammen(1993), construct an consistent parametric regression model specification test statistic with mixed data, we also derived the limit distri-bution of statistics and study the size and power of test with simulation methods.The main thesis of the paper include:Proof the asymptotic norm distribution of test statistic with mixed data based on the integrated squared error. In the finite sample Monte Carlo simulation, the paper compare the size and power of the test under different critical value and different smoothing parameter and compare the results with Hsiao, Li & Racine(2006). Simulation result show that there has no significant difference between empirical size and nominal size, the performance of test almost same as Hsiao, Li & Racine(2006). However, the empirical size of the test is not sensitive to smoothing parameter, the test is more powerful than Hsiao, Li & Racine(2006) with high frequency data and less powerful than Hsiao, Li & Racine (2006) with low frequency data. In addition, the smoothing parameter selected by cross-validation has better performance than selected by nonparametric frequency estimation method and can improve the power of test.The empirical research of the paper is focus on the relationship among corporate performance、ownership structure and industry characteristics of listed companies by establishing a linear parametric model and a nonparametric model that can smooth the discrete and continuous data. The estimation of both models show that there is a negative correlation between corporate performance and state-owned equity proportion. There has a positive correlation between corporate performance and ownership concentration and exist a significant "range effect". The relationship between corporate performance and the ownership has a significant industry differences. In addition, the model specification test show that nonparametric model has better performance than parametric model. The result above not only provide the information about corporate performance、ownership structure and industry characteristics, but also provide empirical evidence for the test.The innovations of the paper reflected in three aspects. First, there has not enough attention to the theory research of the nonparametric model specification and no comprehensive collation of literature, this paper systematic review the literature about this topic, especially comparison and summary the literature about nonparametric specification test with discrete and continuous data, above work can provide systematic reference for related researchers. Secondly, the paper proposed a new model specification test with parametric model based on integrated squared error method proposed by Hardle & Mammen(1993), this test is different from residuals regression test proposed by Hsiao, Li & Racine(2006). The test is based on nonparametric kernel estimation and least squares cross-validation methods and can be applied to model with mixed data, we also proposed a wild bootstrap test statistic and study the empirical size and power of the test, compared the reliability of different tests. Above work can give some theoretical support and methodology development for the research of regression model specification test. Finally, this paper employ the consistent model specification test to the empirical research of corporate performance、ownership structure and industry characteristics of listed companies, and compared the results of both parametric linear model and nonparametric model specification test with mixed data, this provides both new ideas and empirical evidence for the research of nonparametric model specification test.