Essays On Multivariate And Simultaneous Equations Spatial Autoregressive Models

Databases with cross-sectional interdependent variables have highlighted the need for new data analysis techniques to model interdependence patterns cross-sectional units. Among various models to describe the interdependence, spatial autoregressive models (SAR) have attracted much attention. The theory and practice of single dependent variable SAR have been well established. Although a large number of economic theories may concern about interrelations among several economic variables, econometric studies regarding multivariate and simultaneous equations SAR models are limited. This dissertation is filling in this gap. This dissertation is composed of two chapters, the first chapter focuses on models with cross-sectional data, while the second chapter is on models in panel data which incorporates both intertemporal dynamics and spatial interdependence. The first chapter investigates a simultaneous equations spatial autoregressive model which incorporates simultaneity effects, own-variable spatial lags and cross-variable spatial lags as explanatory variables, and allows for correlation between disturbances across equations. In exposition, this chapter also discusses a multivariate spatial autoregressive model that can be treated as a reduced form of the simultaneous equations model. For a multivariate model, we provide identification conditions in terms of the existence of instruments for spatial lags and regularities of the weight matrix structure. Rank conditions and order conditions are provided for identification of structural parameters in the simultaneous equations model. In this chapter we study parameter spaces, the parameter identification, asymptotic properties of the quasi-maximum likelihood estimation, and computational issues. Monte Carlo experiments illustrate the advantages of the QML, broader applicability and efficiency, compared to instrumental variables based estimation methods in the existing literature. The second chapter introduces multivariate and simultaneous equations dynamic panel spatial autoregressive models in the cases of stability and spatial cointegration. A spatial unit is assumed to depend on its lagged term, and to respond to its neighbours' or peers' behaviour in the current period (spatial lags), and in the previous period (space-time lags). The disturbances in the model are specified with time fixed effects and individual fixed effects in addition to idiosyncratic disturbances. This chapter investigates identification for the model with simultaneous effects, time dynamic effects, and spatial effects. In the estimation of stable and spatially cointegrated models, we investigate QMLE and establish asymptotic properties of the estimator. Convergence rates of parameters may change depending on variables being stable or unstable. We analyze asymptotic biases and suggest bias-corrected estimates. We also study a robust estimation method which can be applied to stable case, spatial cointergration case and some spatial explosion cases. We apply the model to study the grain market integration using a unique historical dataset of rice and wheat prices of 65 cities in 49 years in Yangtze River Basin. The empirical result shows that rice and wheat prices are spatially cointegrated across cities. These results provide evidences of interregional and intertemporal grain market integration and trading network in the eighteenth-century Yangtze River basin.

Volume 36 of Advances in Econometrics recognizes Aman Ullah's significant contributions in many areas of econometrics and celebrates his long productive career.

Abstract: My research focuses on the extension of the spatial autoregressive (SAR) model into a system of simultaneous equations. The resulting new model is useful in studying problems involving multiple networks where individuals are not only linked to members of the same network but also interact with members of the other networks. The behavior of each individual is affected by the behavior of those to whom he is linked. The magnitude of such effects, which are referred to as spatial effects, depends on the strength of the links.

Abstract: This dissertation is composed of three essays on spatial econometric models with missing data. Spatial models that have a long history in regional science and geography have received substantial attention in various areas of economics recently. Applications of spatial econometric models prevail in urban, developmental and labor economics among others. In practice, an issue that researchers often face is the missing data problem. Although many solutions such as list-wise deletion and EM algorithm can be found in literature, most of them are either not suited for spatial models or hard to apply due to technical difficulties. My research focuses on the estimation of the spatial econometric models in the presence of missing data problems. The first chapter develops a GMM method based on linear moments for the estimation of mixed regressive, spatial autoregressive (MRSAR) models with missing observations in the dependent variables. The estimation method uses the expectation of the missing data, as a function of the observed independent variables and the parameters to be estimated, to replace the missing data themselves in the estimation. The proposed GMM estimators are shown to be consistent and asymptotically normal. Feasible optimal weighting matrix for the GMM estimation is given. We extend our estimation method to MRSAR models with heteroskedastic disturbances, high order MRSAR models and unbalanced spatial panel data models with random effects as well. From these extensions, we see that the proposed GMM method has more compatibility, compared with the conventional EM algorithm. The second chapter considers a group interaction model first proposed by Lee (2006); this model is a special case of the spatial autoregressive (SAR) models. It is a first attempt to estimate the model in a more general random sample setting, i.e. a framework in which only a random sample rather than the whole population in a group is available. We incorporate group heteroskedasticity along with the endogenous, exogenous and group fixed effects in the model. We prove that, under some basic assumptions and certain identification conditions, the quasi maximum likelihood (QML) estimators are consistent and asymptotically normal when the functional form of the group heteroskedasticity is known. Two types of misspecifications are considered, and, under each, the estimators are inconsistent. We also propose IV estimation in the case that the group heteroskedasticity is unknown. A LM test of group heteroskedasticity is given at the end. The third chapter considers the same group interaction model as that in the second chapter, but focuses on the large group interaction case and uses a random effects setting for the group specific characters. A GMM estimation framework using moment conditions from both within and between equations is applied to the model. We prove that under some basic assumptions and certain identification conditions, the GMM estimators are consistent and asymptotically normal, and the convergence rates of the estimators are higher than those of the estimators derived from the within equations only. Feasible optimal GMM estimators are proposed.

This Advanced Introduction provides a critical review and discussion of research concerning spatial statistics, differentiating between it and spatial econometrics, to answer a set of core questions covering the geographic-tagging-of-data origins of the concept and its theoretical underpinnings, conceptual advances, and challenges for future scholarly work. It offers a vital tool for understanding spatial statistics and surveys how concerns about violating the independent observations assumption of statistical analysis developed into this discipline.

Estimation of Spatial Panels provides some recent developments on the specification and estimation of spatial panel models.

Spatial Econometrics provides a modern, powerful and flexible skillset to early career researchers interested in entering this rapidly expanding discipline. It articulates the principles and current practice of modern spatial econometrics and spatial statistics, combining rigorous depth of presentation with unusual depth of coverage. Introducing and formalizing the principles of, and ‘need’ for, models which define spatial interactions, the book provides a comprehensive framework for almost every major facet of modern science. Subjects covered at length include spatial regression models, weighting matrices, estimation procedures and the complications associated with their use. The work particularly focuses on models of uncertainty and estimation under various complications relating to model specifications, data problems, tests of hypotheses, along with systems and panel data extensions which are covered in exhaustive detail. Extensions discussing pre-test procedures and Bayesian methodologies are provided at length. Throughout, direct applications of spatial models are described in detail, with copious illustrative empirical examples demonstrating how readers might implement spatial analysis in research projects. Designed as a textbook and reference companion, every chapter concludes with a set of questions for formal or self--study. Finally, the book includes extensive supplementing information in a large sample theory in the R programming language that supports early career econometricians interested in the implementation of statistical procedures covered. Combines advanced theoretical foundations with cutting-edge computational developments in R Builds from solid foundations, to more sophisticated extensions that are intended to jumpstart research careers in spatial econometrics Written by two of the most accomplished and extensively published econometricians working in the discipline Describes fundamental principles intuitively, but without sacrificing rigor Provides empirical illustrations for many spatial methods across diverse field Emphasizes a modern treatment of the field using the generalized method of moments (GMM) approach Explores sophisticated modern research methodologies, including pre-test procedures and Bayesian data analysis

This volume presents some of the most influential papers published by Rabi N. Bhattacharya, along with commentaries from international experts, demonstrating his knowledge, insight, and influence in the field of probability and its applications. For more than three decades, Bhattacharya has made significant contributions in areas ranging from theoretical statistics via analytical probability theory, Markov processes, and random dynamics to applied topics in statistics, economics, and geophysics. Selected reprints of Bhattacharya’s papers are divided into three sections: Modes of Approximation, Large Times for Markov Processes, and Stochastic Foundations in Applied Sciences. The accompanying articles by the contributing authors not only help to position his work in the context of other achievements, but also provide a unique assessment of the state of their individual fields, both historically and for the next generation of researchers. Rabi N. Bhattacharya: Selected Papers will be a valuable resource for young researchers entering the diverse areas of study to which Bhattacharya has contributed. Established researchers will also appreciate this work as an account of both past and present developments and challenges for the future.

Despite spatial statistics and spatial econometrics both being recent sprouts of the general tree "spatial analysis with measurement"—some may remember the debate after WWII about "theory without measurement" versus "measurement without theory"—several general themes have emerged in the pertaining literature. But exploring selected other fields of possible interest is tantalizing, and this is what the authors intend to report here, hoping that they will suscitate interest in the methodologies exposed and possible further applications of these methodologies. The authors hope that reactions about their publication will ensue, and they would be grateful to reader(s) motivated by some of the research efforts exposed hereafter letting them know about these experiences.