Effective Estimation Of Partial Linear Models With Fixed Effects Under Panel Data

With the advent of the era of “big data”,people's economic activities become increasingly complex,compared with the traditional time series data and cross section data,panel data can reflect the dynamic change trend of economic variables,which shows people's complex activities.With the continuous development of panel data,it has become a new focus in the data model analysis and statistics.Panel data can effectively overcome the factors such as time series analysis by the autocorrelation sequence,to improve the accuracy of the estimation,contains more practical significance.This article mainly discusses the partial linear models with fixed effects under panel data,we consider the parametric and nonparametric components under the function and further study the large sample properties of the parameter.According to the panel data models,this paper puts forward a new method: on the premise of not to underestimate the nonparametric function,we prove the parameter is semiparametric efficient.Specifically,first of all,due to the endogenous of fixed effect in panel data models,it will affect the accuracy of the estimation,this paper adopted a kind of effective method to eliminate the fixed effect;Secondly,in the estimation of nonparametric functions,this paper improves the marginal quasi-likelihood method,which not only using the local observations near the target point,but also using the observations out of the neighborhood of the target point.It avoids the omission of the relevant information,and improves the estimation accuracy.Finally,in terms of the estimation of parameter,we use the full-quasi-likelihood method,in this method,the asymptotic properties and semiparametric efficiency can be guaranteed theoretically without assuming the distribution of the random error.Furthermore,this paper considers two different types of simulations.Simulation 1 assumes that data in the group are interchangeable related structures,through the adjustable parameters ?,we can see our method's performances under both random effects model and fixed effects model.The result shows that it has a good robustness of bandwidth under both models.In addition,compared with the methods in the literature,this paper has a slightly larger mean square error in the estimation of regression coefficient and a smaller mean square error in the estimation of non-parametric functions.Simulation 2 has a more complex structure,it shows that our method also performs well on it.Indicating that the proposed method has a wide range of application and feasibility.In the empirical study,this paper selects the GDP data of various provinces and cities published in China's statistical yearbook from 2000 to 2011,and emphatically selects the added value of the primary and secondary industries,residents' consumption level and total energy consumption as vectors to measure.The results show that: Four indexes play a role of promoting the development of GDP,the added value of secondary industry is our country is the main driver of GDP growth,it also conforms to the rapid industrial development in our country.At the same time,through the out-of-sample test,we found that the method has smaller prediction error,reflected the practical value of our method.