The Estimation And Statistical Computational Realization Of The Parameters In Panel Data Autoregressive Models With Spatial Dependent Errors

Classical statistics deal with problems arising in relations between variables instead of exploring the spatial dependency of them. Take panel data for instance. For every individual, after it is fixed we in fact have a time series of this particular individual. Generally we considered the interrelations among observations, errors, variances of errors, etc, so that classical statistics, to say time series analysis was well established including AR,MA,ARCH models and so on, which have well explained and predicted some of the data existing in social and econometrical research.However, with the development of the social economy and theoretical research, more and more literatures and research attention have been attached to exploring the spatial dependency of variables, such as the similar or opposite properties of regional development in economy or society, or to say whether the variables with similar properties would tend to concentrate, even they would tend to disperse. For panel data, after a certain moment is fixed or appointed, what we have are not time series data. In fact they are one observation for all variables at one time. The purpose of spatial statistics is to find out the essential relations in variables and measure this kind of relation. The most significant difference between spatial and classical statistics lies in the concept of"contiguity"and the way of measuring the levels of contiguity. Spatial contiguity can refer to both regional neighborhoods and similarity in some properties.Much like those models such as AR, MA, ARCH in time series analysis, the bulk of models applied in spatial statistical analysis are those called Spatial Autoregressive models (SAR), Spatial Moving Average models (SMA) and Spatial Error Component models (SEC) proposed by Kelejian and Robinson(1998)[16]. Based on the great efforts and achievement that have been made, we propose a spatial autoregressive models with order 1 and spatial dependency in error terms and elaborate the estimating methods in two steps. The most important step is step two where we estimate the unknown parameter which represents the spatial dependency by applying the estimator proposed by Kelejian and Prucha(1999)[14], GMM in name. Also we use Monte Carlo simulation to realize the algorithm in R program with large sample size in N and large time dimension in T, all of which are 1000. We show in our paper that OLS is inefficient than GMM when estimating the parameter in the model with spatial dependence in explanatory variables by comparison with the two methods in small autoregressive parameter and large one. We show in figure that GMM may be erroneous when the standard deviation of innovations is rather small compared with the regressive coefficient. At last we explore the property of the GMM estimates in our models with relatively small sample size, to say, 50, and large time dimension, also 1000.The paper is organized as follows. First, we give a short introduction about spatial statistics in terms of their obvious properties in our introduction. Second, in Chapter 1, we recall 3 kinds of the mostly seen models in spatial statistics. In Chapter 2 we propose a new model with autoregressive order 1 and spatial dependent error terms and then describe the whole process of estimating a model, including unit root test for both independent panels and spatial correlated ones, estimation algorithms, significant test for models. At last in Chapter 3, we present the simulation results for estimation and show OLS is inefficient in our models. In appendix we give the R programs for estimation, significant tests and comparison with OLS and GMM.