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In this paper, we introduce the one-step generalized method of moments (GMM) estimation methods considered in Lee (2007a) and Liu, Lee, and Bollinger (2010) to spatial models that impose a spatial moving average process for the disturbance term. First, we determine the set of best linear and quadratic moment functions for GMM estimation. Second, we show that the optimal GMM estimator (GMME) formulated from this set is the most efficient estimator within the class of GMMEs formulated from the set of linear and quadratic moment functions. Our analytical results show that the one-step GMME can be more efficient than the quasi maximum likelihood (QMLE), when the disturbance term is simply i.i.d. With an extensive Monte Carlo study, we compare its finite sample properties against the MLE, the QMLE and the estimators suggested in Fingleton (2008a).
In this paper, we introduce the one-step generalized method of moments (GMM) estimation methods considered in Lee (2007a) and Liu, Lee, and Bollinger (2010) to a spatial autoregressive model that has a spatial moving average process in the disturbance term (for short SARMA (1,1)). First, we determine the set of the best linear and quadratic moment functions for the GMM estimation. Second, we show that the GMM estimator (GMME) formulated from this set is the most efficient estimator within the class of GMMEs formulated from the set of linear and quadratic moment functions. Our analytical results show that the GMME can be asymptotically equivalent to the maximum likelihood estimator (MLE), when the disturbance term is i.i.d. Normal. When the disturbance term is simply i.i.d., the one-step GMME can be more efficient than the quasi MLE (QMLE). With an extensive Monte Carlo study, we compare its finite sample properties against the MLE, the QMLE and the estimators suggested in Fingleton (2008).
In this study, I investigate the necessary condition for consistency of the maximum likelihood estimator (MLE) of spatial models with a spatial moving average process in the disturbance term. I show that the MLE of spatial autoregressive and spatial moving average parameters is generally inconsistent when heteroskedasticity is not considered in the estimation. I also show that the MLE of parameters of exogenous variables is inconsistent and determine its asymptotic bias. I provide simulation results to evaluate the performance of the MLE. The simulation results indicate that the MLE imposes a substantial amount of bias on both autoregressive and moving average parameters.
This is the most recently developed book in Spatial Econometrics which cover important models and estimation methods. Its coverage is rather broad, and some of the topics covered have only been developed in the recent econometric literature in spatial econometrics.The book summarizes our devoted efforts on spatial econometrics that represent joint contributions with former PhD advisees from the Ohio State University in Columbus, Ohio, USA.The coverage is comprehensive and there are a total of sixteen chapters from basic statistics and statistical theory of linear-quadratic forms, law of large numbers (LLN) and central limit theory (CLT) on martingales to nonlinear spatial mixing and spatial near-epoch dependence theories, which can justify the statistic inferences for various spatial models and their estimation. New estimation and testing approaches in empirical likelihood and general empirical likelihood, and Bootstrapping are presented. Model selection is also discussed in this book. In addition to the popular spatial autoregressive models, there are chapters on multivariate SAR models, simultaneous SAR models, and panel dynamic spatial models. Recent econometric developments on intertemporal spatial models with rational expectations and flows data in trade theory will also be included. In terms of statistics, classical estimation, testing and inference are the main concerns, and we provide classical inference for the justification of Bayesian simulation approaches.
Providing an authoritative assessment of the current landscape of spatial analysis in the social sciences, this cutting-edge Handbook covers the full range of standard and emerging methods across the social science domain areas in which these methods are typically applied. Accessible and comprehensive, it expertly answers the key questions regarding the dynamic intersection of spatial analysis and the social sciences.
This book provides an overview of three generations of spatial econometric models: models based on cross-sectional data, static models based on spatial panels and dynamic spatial panel data models. The book not only presents different model specifications and their corresponding estimators, but also critically discusses the purposes for which these models can be used and how their results should be interpreted.
Most of the estimators suggested for the estimation of spatial autoregressive models are generally inconsistent in the presence of an unknown form of heteroskedasticity in the disturbance term. The estimators formulated from the generalized method of moments (GMM) and the Bayesian Markov Chain Monte Carlo (MCMC) frameworks can be robust to unknown forms of heteroskedasticity. In this study, the finite sample properties of the robust GMM estimator are compared with the estimators based on the Bayesian MCMC approach for the spatial autoregressive models with heteroskedasticity of an unknown form. A Monte Carlo simulation study provides evaluation of the performance of the heteroskedasticity robust estimators. Our results indicate that the MLE and the Bayesian estimators impose relatively greater bias on the spatial autoregressive parameter when there is negative spatial dependence in the model. In terms of finite sample efficiency, the Bayesian estimators perform better than the robust GMM estimator. In addition, two empirical applications are provided to evaluate relative performance of heteroskedasticity robust estimators.
This conference serves as a means of presenting and discussing various research results among academics, researchers, and practitioners in the fields of statistics, analytics, computing, data science, and its application. Based on 110 papers that have been presented there are three main topics as the focus of the discussion, namely Statistical Modeling, Predictive Analytics, and Pattern Learning. The approach is in the form of a study to obtain a valid methodology for extracting, collecting, storing, analyzing, and visualizing data including those derived from big data. The application studies cover various fields such as agriculture, climate, energy, industry, business, social, and so on. The conference is expected to be able to provide solutions to various problems in various fields through statistical and analytical approaches.
Cross sectional spatial models frequently contain a spatial lag of the dependent variable as a regressor, or a disturbance term which is spatially autoregressive. In this paper we describe a computationally simple procedure for estimating cross sectional models which contain both of these characteristics. We also give formal large sample results.