空间计量经济学导论及GeoDa的应用 An Introduction to Spatial Econometrics with GeoDa 孙铁山 北京大学政府管理学院 中国区域科学协会学术年会青年学者培训 内容提要 空间计量经济学及其发展 空间数据及其特性 空间自相关及其测度 空间回归模型：设定、估计与解释 GeoDa应用演示 空间计量经济学及其发展 spatial econometrics and its development 什么是空间计量经济学？ Spatial Econometrics: Definitions Three Definitions Paelinck-Klaassen, 1979 Spatial Econometrics Anselin, 1988 Spatial Econometrics: methods and models Anselin, 2006 in Handbook of Econometrics 什么是空间计量经济学？ Spatial Econometrics: Definitions the definition provided in Paelinck-Klaassen (1979) role of spatial interdependence asymmetry in spatial relations importance of factors in other spaces differentiation ex post and ex ante interaction explicit modeling of space 什么是空间计量经济学？ Spatial Econometrics: Definitions the definition provided in Anselin (1988) “the collection of techniques that deal with the peculiarities caused by space in the statistical analysis of regional science models”. dealing with “the specific spatial aspects of data and models in regional science that preclude a straightforward application of standard econometric methods”. limiting the definition to the realm of regional science. the modeling perspective was comprehensively treated, which distinguishes spatial econometrics from the broader field of spatial statistics or spatial data analysis. Emphasizing specification, estimation and specification tests of spatial regression models. 什么是空间计量经济学？ Spatial Econometrics: Definitions the definition provided in Anselin (2006) “a subset of econometric methods that is concerned with spatial aspects present in cross-sectional and space-time observations. Variables related to location, distance and arrangement (topology) are treated explicitly in model specification; estimation; diagnostic checking and prediction”. the limiting context of urban and regional modeling and regional science is removed and the definition of spatial econometrics is placed squarely within the methodological toolbox of (applied) econometrics. 空间计量经济学的发展 Development of Spatial Econometrics 发展于1970年代，起初作为空间统计和空间数据分析的一个分支，其理论与应用研究大多源于空间统计、区域科学和定量地理，被主流经济学和计量经济学所忽视。 近20年，经历了快速发展，已成为现代计量经济学的重要分支。the field moves “from the margins in applied urban and regional economic analysis to the mainstream of economics and other social science” (Anselin, 2010). 1990年代以来，空间计量经济学理论得到较大发展，方法开始得到普遍应用，理论与应用研究呈现爆发式的增长，除了出现在区域科学和空间分析期刊上，也开始大量出现在主流计量经济学期刊和应用经济学各领域的期刊上。但大多数计量经济学教材仍未能包括相关内容。 空间计量经济学的发展 Development of Spatial Econometrics 这主要归因于： the ready availability of increasing volumes of geo-referenced data; a user friendly technology to manipulate these in geographic information systems; the growing attention to a spatial perspective stimulated by an important shift in theoretical focus. 国内对空间计量模型方法的应用 Application of Spatial Econometrics in China 核心期刊，主题或关键词或摘要中含“空间计量”，共有363篇。 2010年后，迅速增加。 国内对空间计量模型方法的应用 Application of Spatial Econometrics in China 2005年，首先在地理类和软科学类刊物上 空间数据:性质、影响和分析方法，地球科学进展 我国高校R&D知识溢出的实证研究——以高技术产业为例，中国软科学 2006年，数量经济技术经济研究刊发3篇 中国地区经济σ-收敛的空间计量实证分析 中国省域R&D溢出的空间模式研究 中国省域经济增长趋同的空间计量经济分析 主要是应用研究，早期主要集中在区域经济增长与收敛、创新和知识溢出等经典主题。其他主题包括：FDI溢出、空间集聚、区域差异、地方财政与税收竞争、能源消费与环境问题等。 空间数据及其特性 spatial data and spatial effects 空间数据=截面数据？ Spatial Data or Cross-sectional Data 什么是空间数据 What is Spatial Data Generally speaking, observations such as these, for which the absolute location and/or relative positioning (spatial arrangement) is taken into account are referred to as spatial data. 空间数据的类型 Types of Spatial Data Lattice data Point data Geostatistical data 空间数据的特性 Spatial Data and Spatial Effects Spatial effects is a catchall term referring to both spatial dependence and spatial heterogeneity. Spatial dependence (or autocorrelation) is a fundamental property of attributes located in space. Tobler’s First Law of Geography "attribute values in space are not random" Student (1914) "near things are more related than distant things" Fisher (1935) 时间与空间的自相关 Autocorrelation in space and in time time series (“time line”) vs. spatial data (map) dependence in time vs. dependence in space: Time: one-directional between two observations Space: two-directional among several observations Spatial autocorrelation is more complicated, relative to the time series case, by the second dimension (dependency might not be the same in all directions) and by the lack of directionality (time has a natural uni-directional flow from past to present, simultaneous dependence in spatial data). 为什么需要发展空间计量模型方法？ Why spatial econometrics? 为什么需要发展空间计量模型方法？ Why spatial econometrics? 由于空间数据具有空间依赖、空间异质的特性，打破了经典计量分析中样本相互独立的基本假设，导致OLS估计不再是有效的估计，通常的统计推断不再适用。 因此，在处理空间数据时，要引入一些合适的空间计量方法，即对经典计量技术加以修改以适于空间数据分析。 空间计量经济学的范畴 Spatial Econometrics: Four Dimensions Four Dimensions Specifying the structure of Spatial Dependence/Heterogeneity Testing for the Presence of Spatial Effects Estimating Models with Spatial Effects Spatial Prediction 空间自相关及其测度 measures and tests of spatial autocorrelation 空间权重矩阵 Spatial Weight Matrix The spatial arrangement of spatial units is directly related to spatial dependence between units of observation. Impose structure in terms of what are the neighbors for each location. A relevant “neighborhood” is defined as those locations surrounding it that are considered to interact with it. Formally, the membership of observations in the neighborhood set for each location is expressed by means of a spatial weights matrix. 一个简单的示例 Spatial Weight Matrix: A Simple Example Spatial Arrangement of Units Contiguity as a Graph Spatial Weight Matrix 空间滞后变量 Spatial Lag No Direct Counterpart to Time Series Lag Operator. Spatial Lag as a Smoother is the Weighted Average of Neighboring Values Lagged y = Wy 空间自相关的测度 Measure of Spatial Autocorrelation：Moran’I Moran’s I Moran’s I - slope of linear Moran scatter plot smoother 空间自相关的检验 Test of Spatial Autocorrelation Null Hypothesis: No Spatial Autocorrelation (spatial randomness) Alternative Hypotheses: Positive/Negative Spatial Autocorrelation Negative Autocorrelation None Positive Autocorrelation 空间自相关的检验 Test of Spatial Autocorrelation Inference: Randomization Strategy Construct Artificial Reference Distribution 全局与局部空间自相关 Global and Local Spatial Autocorrelation Global – Moran’s I - one statistic to summarize pattern - clustering - homogeneity Local – Local Moran’s I (LISA) - location-specific statistics - clusters - heterogeneity 局部空间自相关与空间数据探索 Local Spatial Autocorrelation and ESDA Identify Hot Spots: suggest interesting locations and “significant” spatial structure - significant local clusters - significant local outliers Indicate Local Instability - local deviations from global pattern of spatial autocorrelation 空间回归模型：设定、估计与解释 Spatial Regression: Specification, Estimation and Interpretation 空间自回归 The Spatial Autoregressive (SAR) Process the simultaneous nature of the spatial autoregressive process 空间回归模型的形式 Specification of Spatial Regression Models three interaction effects (Manski, 1993): (i) endogenous interaction effects; (ii) exogenous interaction effects; (iii) correlated effects. 空间滞后与空间误差模型 Spatial Lag and Spatial Error Model traditional approach, following Anselin ,1988 focus on two specifications: Spatial lag model (SAR) and Spatial error model (SEM) SAR SEM 空间滞后与空间误差模型 Spatial Lag and Spatial Error Model Specification tests: LM test and Robust LM test 空间回归模型的估计 Methods of Estimation Estimation of spatial models via least squares can lead to inconsistent estimates of the regression parameters for models with spatially lagged dependent variables, inconsistent estimation of the spatial parameters, and inconsistent estimation of standard errors. In contrast, maximum likelihood is consistent for these models (Lee, 2004). Three main estimation methods: one is based on maximum likelihood (ML) one on instrumental variables or generalized method of moments (IV/GMM) one on the Bayesian Markov Chain Monte Carlo (MCMC) approach 解释参数估计值 Interpreting Parameter Estimates Linear regression parameters have a straightforward interpretation, which arises from linearity and the assumed independence of observations in the model. Interpretations of parameters become much more complicated in the spatial regression. The diagonal elements of the n × n matrix Sr(W) contain the direct impacts, and off-diagonal elements represent indirect impacts Lesage and Pace (2009)