Sesion1_Introduccion Geoespecial Econometria

Anlisis Economtrico Geoespacial

Profesora: Coro Chasco YrigoyenUniversidad Autnoma de Madrid

17 a 21 de mayo, 2010

2010, Coro Chasco YrigoyenAll Rights Reserved

@ 2010 Coro Chasco YrigoyenAll Rights Reserved 2

Overview and Goals Overview: 24 hours Intensive Course

lectures + PC training sessions Goals: 1. Sound understanding of basic and more advanced

principles of spatial econometrics2. Offer tools for practical application of the methodology3. Commonly available software products used in the GIS

framework (GeoDa) will be introduced and practised in the PC training sessions.

Materials:http://www.uam.es/coro.chasco/courses/Geoespacial/geoespacial.html


ndice del Curso S1: Introduccin a la Econometra Espacial SP1: IntroducciSP1: Introduccin al programa GeoDan al programa GeoDa S2: Efectos espaciales: dependencia espacial S3: Anlisis Exploratorio de Datos Espaciales (AEDE): tcnicas bsicas SP2: AEDE en GeoDa: tcnicas bsicas S4: Contrastes de dependencia espacial: tcnicas avanzadas de AEDE S5: Anlisis confirmatorio de datos espaciales: especificacin de los

modelos de dependencia espacial SP3: AEDE en GeoDa: tSP3: AEDE en GeoDa: tcnicas avanzadascnicas avanzadas S6: Estimacin y contrastes de un modelo de regresin espacial por el

mtodo de Mnimos Cuadrados Ordinarios S7: Estimacin y contraste de los modelos de dependencia espacial SP4: El mSP4: El mdulo de regresidulo de regresin espacial en el programa GeoDan espacial en el programa GeoDa S8: Estimacin y contraste del modelo del error espacial y estrategias

de modelizacin espacial. SP5: AplicaciSP5: Aplicacin de la estrategia de modelizacin de la estrategia de modelizacin cln clsica a sica a

casos prcasos prcticos con el programa GeoDacticos con el programa GeoDa


Sesin 1: Introduccin a la Econometra Espacial

Fundamentals of spatial econometrics Spatial econometrics history Spatial data problems Some applications in spatial econometrics

. CHASCO, C. (2003), Econometra espacial aplicada a la prediccin-extrapolacin de datos microterritoriales.

Comunidad de Madrid; pp.7-26 .


1.1. Fundamentals of spatialeconometrics (I) Subfield of classical econometrics Spatial interaction = autocorrelation Spatial instability (heteroskedasticity, regimes) =

heterogeneity Spatial effects: autocorrelation & heterogeneity Spatial effects do affect regression models Spatial econometrics spatial statistics

Session 1

Regional & urbaneconomics

Physical phenomena: biology & geology


1.1. Fundamentals of spatialeconometrics (II)

Session 1

Spatialheterogeneity

Core

Spatialautocorrelation


1.2. Spatial econometrics history Early 70s: Paelink coins the term spatial econometrics 1979: Paelinck & Klaasen book - Spatial econometrics 1975/1981: Cliff and Ords books 1988: Anselins book- Spatial econometrics: Methods and

models 1991/1995/1998/2001: Anselin SpaceStat versions 1995: Anselin & Florax (eds) New directions in spatial

econometrics First 2000s : LeSages Spatial Econometrics Toolbox

(Matlab), Bivands spdep (R) y Reys STARS (Python) 2004: Anselin, Florax & Rey (eds) Advances in spatial

econometrics 2003: Anselins GeoDa and others 2006, 2009: Arbia and Le Sage Spatial econometrics

Session 1


Session 1

1.3. Spatial data

Spatial data nature Spatial data problems Spatial data empirical

applications


1.3.1. Spatial data nature TimeTime: continousand unidimensionalPast (t-1)

Future (t+1)

SpaceSpace: continuous andbidimensional

i

North

South

EastWest

NortheastNorthwest

SoutheastSouthwest

Present (t)

Session 1


1.3.1. Spatial data nature (II)

How discretize space? GIS: Raster & vector data Raster data or field view:

considers de world as a field, a continuous variation

Session 1HAINING, R. (1995), Data problems in spatial

econometric modeling. In L. Anselin and R. Florax(ed.), New directions in spatial econometrics.

Springer-Verlag, Berlin; pp. 156-171.

Vector data or object view: discrete objects Discretization results in a set of regular or irregular

contours, sample points or a spatial partition

In the object view the world is depicted as an empty space populated by points, lines and areas


1.3.1. Spatial data nature (III)

Year

Year

Time series:Trim.

Month

Country Region

Province

Spatial data:

FRECUENCIES

SCALES

Session 1


1.3.1. Spatial data nature (IV)

FUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROFUENTE DEL BERROGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYAGOYA

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A

M-30

Type of time series data:

Type of spatial data:

Polygons(e.g. districts)

Points(e.g. outlets)

Lines(e.g. roads)

Points(e.g.months)

Session 1


1.3.1. Spatial data nature (V)

Year 0

B.C.

A.C.

2 spatial references:

Axis X:

Longitude

Axis Y: Latitude

Spain: coordinates(-300,4200) EquatorEquator::

latitudelatitude 00

Greenwich: Greenwich: longitudelongitude 00

(0,0)

Session 1

1 temporal reference:


Session 1

1.3.2. Spatial data problems

AggregationAggregation andand spatialspatial arrangementarrangement ChangesChanges ofof supportssupports IdentificationIdentification

- Micro-macro aggregation problem Econometrics- Modifiable Areal Unit Problem (MAUP) - Geography- Ecological fallacy - Sociology- Change of Support Problem (COSP) - Geostatistics


Session 11.3.2. Spatial data problems (II)

ModifiableModifiable ArealAreal Unit Unit ProblemProblem (MAUP)(MAUP)

ANSELIN, L (1988), Spatial econometrics: methods and models, Kluwer Academic Publishers

A B

a1 a2 b1 b2

The statistical measures for cross-sectional data are sensitive to theway in which the spatial units are organised. The level ofaggregationaggregation andand thethe spatialspatial arrangementarrangement in zones (i.e., combinations of contiguous units) affects the magnitude of variousmeasures of association, such as spatial autocorrelation coefficientsand parameters in a regression model.

Spatial data aggregation only lead to sensical conclusions when theunderlying phenomenon is homogeneous.

If not, the inherent spatialheterogeneiy and structuralinstability should be accounted for in the variousaggregation schemes.


Session 1

1.3.2. Spatial data problems (III) The different types of

spatial data (point, line, area, surface), occurringnaturally or as a result ofthe measurement process, potentially allow many waysof integrating these data.

Changing the support ofa spatial variable (volume, geometrical size, shape & spatial orientation) -typicallyby aggregation/averaging-creates a new variable.

GOTWAY, CA and LJ YOUNG (2002), Combining incompatible spatial data. Journal of the American

Statistical Association 97, 632-648


Session 1

1.3.2. Spatial data problems (IV)

From an econometric standpoint, MAUP is also an identificationidentificationproblemproblem, since there is insufficient information in the data to allowfor the full specification of the simultaneous interaction over space.

In this sense, a formulation of linear spatial association can be considered as a special case of a system of simultaneous linear equations, with one observation for each equation.

1

N

i ij ii

y w y

1

N

i i ij ii

y w y

SYSTEM OF SIMULTANEOUS

LINEAR EQUATIONSLINEAR SPATIAL

AUTOREGRESSIVE MODEL


Session 1

1.3.3. Spatial data empiricalapplications

Empirical applications with spatialdata imply the use of:

Statistical dataGIS & digital maps Spatial econometrics software


1.3.3. Spatial data empiricalapplications (II)

StatisticalStatistical datadata: Primary data: from private or public surveys... Secondary data. E.g. in Spain:

Regional data: INE, IVIE-BBVA, la Caixa... Municipal data: INE, la Caixa-LR Klein Institute... Districts, census tracts: INE, Regional Statistics

Offices Others: Exprian, Mosaic, Data Segmento, Sitesa...


1.3.3. Spatial data empiricalapplications (III)

GIS:: Managment, analysis and visualization of spatial data. It isestructures in interactive maps, spatial data, geoprocessingmodels, data models and metadata


Digital Digital mapsmaps:Instituto Nacional de Estadstica:

regions, provinces, municipalities, districts, census tracts, streets...

ESRI: Muniview, Censalview, ArcpolisMapInfoOthers: Maptel...

1.3.3. Spatial data empiricalapplications (IV)


Focused on ESDA:GEODAGEODA: http://geodacenter.asu.edu/software/downloadsSTARSSTARS: http://regionalanalysislab.org/index.php/Main/STARS

Focused on confirmatory analysis:SpaceStatSpaceStat: http://www.terraseer.comSpatialSpatial EconometricsEconometrics ToolboxToolbox (Matlab):

http://www.spatial-econometrics.comspdepspdep (R): http://cran.r-project.orgPySALPySAL (Python): http://geodacenter.asu.edu/pysal

1.3.3. Spatial data empiricalapplications (V)

SpatialSpatial econometricseconometricssoftware:software:


GEODAGEODA:http://geodacenter.asu.edu/software/downloads

Created by Luc Luc AnselinAnselin, Arizona State University


GIS + ESDA + Spatial regression Exploratory Spatial Data Analysis (AEDE):

- Data managment- Mapping and descriptive statistics- Spatial association: global and local spatialautocorrelation statistics

Spatial regression:- Basic OLS model- Spatial lag model- Spatial error model



STARSSTARS:http://regionalanalysislab.org/index.php/Main/STARS

Created by Serge ReySerge Rey, Arizona State University.


STARS (II)STARS (II):http://regionalanalysislab.org/index.php/Main/STARS


STARS (III)STARS (III):http://regionalanalysislab.org/index.php/Main/STARS


spdepspdep forfor R: R: http://cran.r-project.org

Created by Roger Roger BivandBivand, Norwegian School ofEconomics and Business Administration.


Future Luc Luc AnselinAnselin,s project: combination ofGEODAGEODA-- STARSSTARS--SPDEPSPDEPopensource software.

PYSALPYSAL:http://geodacenter.asu.edu/pysal


PYSAL (II)PYSAL (II)


SpatialSpatial EconometricsEconometrics ToolboxToolbox forfor MatlabMatlab:http://www.spatial-econometrics.com

Created by James James LeSageLeSage, University of Toledo.

Main contents:

2 Spatial autoregressive models2.1 The rst-order spatial AR model2.2 The mixed autoregressive-regressive model2.3 The spatial errors model2.4 The general spatial model

3 Bayesian Spatial autoregressive models

4 Locally linear spatial models4.1 Spatial expansion4.2 DARP models4.3 GWR4.4 A Bayesian Approach to GWR

5 Limited dependent variable models5.2 The Gibbs sampler5.3 Heteroscedastic models

6 VAR and Error Correction Models6.1 VAR models6.2 Error correction models6.3 Bayesian variants6.4 Forecasting the models


Created by Luc Luc AnselinAnselin

Main contents:

1 Data management and algebra2 Spatial weight matrices

2.1 Creation & characteristics2.2 Spatial correlogram2.3 Spatial lags

3 ESDA3.1 Basic descriptive statistics3.2 Joint count, Morans I & Gearys c3.3 G statistics & QAP measures

4 SPATIAL REGRESSION4.1 Basic OLS regression4.2 Spatial lag & spatial error models4.3 Instrumental Variables estimation4.4 Heteroskedastic model4.5 Trend surface model4.6 Spatial regimes & S-ANOVA4.7 Spatial expansion

SpaceStatSpaceStat:http://www.terraseer.com


1.4. Some applications in spatialeconometrics (I)

Cancer mortality rate model Homicide rate Spatial -convergence regional model Household per capita income

Session 1


1.3. Some applications... (II)

Session 1

. HAINING, R. (1995), Data problems in spatial econometric modeling. In L. Anselin and R. Florax (ed.), New directions in spatial econometrics. Springer-Verlag, Berlin; pp. 156-171.

y: cancer mortality ratei: one of the 87 Glasgow community medicine areasx: deprivation indexW: spatial weight matrix0, 1, : parameters to be estimatedu, : stochastic error terms

Haining: Cancer mortality rate model

(spatial-error model)


1.3. Some applications... (III)

Session 1

. BALLER, R., L. ANSELIN, S. MESSNER and D. HAWKINS (2001), Structural covariates of U.S. county homicide rates: incorporating spatial effects. Criminology (prxima publicacin).

H: homicide ratei: U.S. countyD: resource deprivation indexP: population structureV: percent divorcedU: unemployment rateE: median age

Baller, Anselin, Messner, Deane and Hawkings: Homicide rate

(spatial-lag model)

W: spatial weight matrix: spatial autoregressive parameter0, 1, 2, 3, 5, 6: exogenous vars. Parameters: i.i.d. stochastic error term


1.3. Some applications... (IV)

Session 1

. REY, S. and B. MONTOURI (1999), US regional income convergence: a spatial econometric perspective. Regional Studies, vol. 33.2; pp. 143-156.

yi,t: real per capita income in state i year tk: year periodW: spatial weight matrix, , : parameters to be estimatedu: i.i.d. stochastic error term

Rey & Montouri: Spatial -convergence regional model(spatial cross-regressive model)


1.3. Some applications... (V)Session 1

. CHASCO, C. (2003), Econometra espacialaplicada a la prediccin-extrapolacin de datos microterritoriales. Consejera de

Economa e Innovacin Tecnolgica de la Comunidad de Madrid.

Chasco: Household per capita income

(spatial-lag model with two spatial regimes)

Spatial lag

Documents

Sesion1_Introduccion Geoespecial Econometria