Estimation of Spatial Autoregressive Econometric Models with Continous and Limited Dependent Variables

空间计量经济学领域涉及使用统计和计量经济学技术来处理多区域经济模型中的空间效应以及空间中各主体之间的经济相互作用。需要开发适当的空间计量经济学模型，以实证验证现代空间经济理论。地理信息系统(地理信息系统)在区域和城市政策分析中的重要性与日俱增，推动了进一步的经验发展。该项目为估计和测试复杂的空间计量经济学模型，包括因变量有限的空间模型，开发了计量经济学方法。这个项目在几个方向上进行。文献中一些流行的估计方法的统计性质往往是假设的，而没有详细调查空间计量经济模型可能的显著特征。虽然一些说法在某些空间情景下是正确的，但在其他情况下可能不是这样。现有的空间计量经济学文献主要关注小群体相互作用的模型，但大群体相互作用的模型有许多有趣的潜在应用。本项目继续研究具有大群体相互作用的空间自回归模型的常用估计量的统计性质。具有大群体交互作用的空间模型的估计器与具有小群体交互作用的模型具有非常不同的统计特性。这个项目探索了捕捉社会互动效应的替代模型，并解决了空间模型中随机样本和可能的不完全空间互动的问题。此外，还开发了区分空间模型和社会效应模型的统计程序。具有交互离散选择的空间模型对于研究创新扩散过程是有用的。由于离散选择模型的似然函数涉及高维积分，因此空间相互作用的离散选择模型的估计可能是相当具有挑战性的。积分的维度可以与样本观测的数量一样大。为了充分发挥这些模型的能力，必须开发出便于计算的方法。该项目开发了基于模拟估算方法的估算方法。研究了各种模拟估计方法的有效性，包括模拟极大似然法、模拟EM算法、模拟计分方法和Gibbs采样器。研究了这些估计量的统计性质。除了估计外，还开发了用于空间相关性和诊断的检验统计。这个项目发展了计算上容易处理的广义矩方法，用于估计有或没有外生变量存在的任何有限阶的空间自回归模型。研究了这类估计量的渐近性质。动态离散选择模型捕捉了面板数据环境中动态效应、状态相关性、异质性和虚假相关性的各种概念。该项目概括了现有的模型，以纳入可能的同时期和跨时间的空间相互作用效应。离散选择中的空间动力学特别令人感兴趣。对这种面板数据模型的规范和估计给予了特别的关注。尽管计量经济学方法的发展是本项目的主要重点，但利用发展中国家的面板数据进行的实证研究说明了新模型的用处和方法的可行性。

The field of spatial econometrics is concerned with the use of statistical and econometric techniques to handle spatial effects in multiregional economic models and economic interaction of agents located in space. Proper spatial econometric models need to be developed to empirically validate modern spatial economic theories. Further empirical developments are motivated by the growing importance of Geographic Information Systems (GIS) in regional and urban policy analyses. This project develops econometric methodologies for the estimation and testing of complex spatial econometric models including spatial models with limited dependent variables. This project proceeds in several directions. Statistical properties of some popular estimation methods in the literature are often assumed without detailed investigation into possibly distinctive features of a spatial econometric model. While some claims are correct under certain spatial scenarios, they might not be so in others. The existing literature on spatial econometrics has mainly focused on models with small group interaction but models with large group interaction have many interesting potential applications. This project continues the investigation of statistical properties of popular estimators for spatial autoregressive models with large group interaction. Estimators for spatial models with large group interaction have quite different statistical properties from those of models with small group interaction. This project explores alternative models to capture social interaction effects and addresses issues of random sample and possible incomplete spatial interactions in spatial models. In addition, statistical procedures are developed for distinguishing spatial models from social effect models.Spatial models with agents making interactive discrete choices are useful for research on innovation diffusion processes. The estimation of a discrete choice model with spatial interaction can be quite challenging as its likelihood function involves high dimensional integral. The dimension of integration can be as large as the number of sample observations. In order to develop these models to their full capacities, computationally tractable methods must be developed. This project develops estimation methods based on simulation estimation methodologies. The effectiveness of various simulation estimation methods, which include the method of simulated maximum likelihood, the method of simulated EM algorithm, the method of simulated scores, and the Gibbs sampler, are investigated. Statistical properties of those estimators are studied. In addition to estimation, test statistics for spatial correlations and diagnostics are also developed. This project develops computationally tractable generalized method of moments for the estimation of spatial autoregressive models of any finite order with or without the presence of exogenous variables. Asymptotic properties of such estimators are investigated.Dynamic discrete choice models capture various notions of dynamic effects, state dependence, heterogeneity, and spurious correlation in a panel data setting. This project generalizes existing models to incorporate possible contemporaneous and intertemporal spatial interaction effects. Spatial dynamics in discrete choices are of special interest. Special attention is paid to the specification and estimation of such panel data models. Even though the development of econometric methods is the main focus of this project, empirical studies with panel data from developing countries illustrate the useful of the new models and the feasibility of the methodologies.