Kai Yang
Published: 2016
Total Pages: 196
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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.