Econometría espacial con aplicaciones

Econometría espacial con
aplicaciones
Profesora: Coro Chasco Yrigoyen
Univeridad Autónoma de Madrid
Lugar: Universidad Politécnica de Barcelona
12-13, 18-20 de junio, 2007
©2007, Coro Chasco Yrigoyen
All Rights Reserved
Overview and Goals
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Overview: 21 hours Intensive Course
lectures + PC training sessions
Goals:
Sound understanding of basic and more advanced
principles of spatial econometrics
Offer tools for practical application of the methodology
Commonly available software products used in the GIS
framework (SpaceStat and GeoDa) will be introduced
and practised in the PC training sessions.
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Course Index
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S1: Introduction to spatial econometrics
S2: Spatial effects, spatial dependence
S3: Spatial autocorrelation tests
S4: Exploratory Spatial Data Analysis (ESDA)
S5: Specification of spatial dependence models
S6: Spatial regression models: OLS estimation and testing
PS1: GeoDa: introduction and ESDA
S7: Spatial dependence models: estimation and testing
S8: Modelling strategies in spatial regression models
PS2: SpaceStat: confirmatory spatial data analysis
S9: Specification of spatial heterogeneity models
S10: Spatial heterogeneity models: estimation and testing
PS3: Practical exercise and evaluation
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2007, Coro Chasco Yrigoyen
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Session 1: Introduction to
Spatial Econometrics
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Fundamentals of spatial econometrics
Spatial econometrics history
Spatial data problems
Some applications in spatial econometrics
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Session 1
1.1. Fundamentals of spatial
econometrics (I)
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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
Regional & urban
economics
Physical phenomena:
biology & geology
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Session 1
1.1. Fundamentals of spatial
econometrics (II)
Spatial
autocorrelation
Spatial
heterogeneity
Core
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Session 1
1.2. Spatial econometrics history
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Early 70s: Paelink coins the term “spatial econometrics”
1979: Paelinck & Klaasen book - “Spatial econometrics”
1975/1981: Cliff and Ord’s books
1988: Anselin’s book- “Spatial econometrics: Methods and
models”
1991/1995/1998/2001: Anselin – SpaceStat versions
1995: Anselin & Florax (eds) – “New directions in spatial
econometrics”
First 2000s : LeSage’s Spatial Econometrics Toolbox
(Matlab), Bivand’s spdep (R) y Rey’s STARS (Python)
2004: Anselin, Florax & Rey (eds) – “Advances in spatial
econometrics”
2003: Anselin’s GeoDa and PySAL
2006: Arbia – “Spatial econometrics”
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Session 1
1.3. Spatial data
Spatial data nature
„ Spatial data problems
„ Spatial data empirical
applications
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Session 1
1.3.1. Spatial data nature
Time:
Time continous
and unidimensional
Past (t-1)
Space:
Space continuous and
bidimensional
Northwest
West
Southwest
North
i
South
Northeast
Present (t)
East
Future (t+1)
Southeast
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HAINING, R. (1995), “Data problems in spatial
econometric modeling”. In L. Anselin and R. Florax
Session 1
(ed.), “New directions in spatial econometrics”.
Springer-Verlag, Berlin; pp. 156-171.
1.3.1. Spatial data
nature (II)
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How discretize space?
GIS: Raster & vector data
Raster data or “field view”:
considers de world as a field, a
continuous variation
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
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Session 1
1.3.1. Spatial data nature (III)
FRECUENCIES
Trim.
Time series:
Month
Spatial data:
Year
SCALES
Province
Country
Year
Region
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Session 1
1.3.1. Spatial data nature (IV)
Type of spatial data:
Polygons
Points
Lines
(e.g. roads)
Points
(e.g. outlets)
(e.g. districts)
M-30
CONCEPCION
CONCEPCION
CONCEPCION
A
GUINDALERA
GUINDALERA
GUINDALERA
LISTA
LISTA
LISTA
VENTAS
VENTAS
VENTAS
GOYA
GOYA
GOYA
FUENTE
FUENTE
DEL
BERRO
FUENTEDEL
DELBERRO
BERRO
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Type of time
series data:
12
(e.g.months)
Session 1
1.3.1. Spatial data nature (V)
1 temporal
reference:
2 spatial references:
Spain:
coordinates
B.C.
Greenwich:
longitude 0
(-300,4200)
(0,0)
Year 0
Equator:
Axis X:
latitude 0
Longitude
A.C.
Axis Y:
Latitude
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Session 1
1.3.2. Spatial data problems
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Aggregation and spatial arrangement
Changes of supports
Identification
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Micro-macro aggregation problem – Econometrics
Modifiable Areal Unit Problem (MAUP) - Geography
Ecological fallacy - Sociology
Change of Support Problem (COSP) - Geostatistics
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ANSELIN, L (1988), “Spatial econometrics: methods
and models”, Kluwer Academic Publishers
Session 1
1.3.2. Spatial data problems (II)
Modifiable Areal Unit Problem (MAUP)
The statistical measures for cross-sectional data are sensitive to the
way in which the spatial units are organised. The level of
aggregation and the spatial arrangement in zones (i.e.,
combinations of contiguous units) affects the magnitude of various
measures of association, such as spatial autocorrelation coefficients
and parameters in a regression model.
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Spatial data aggregation only lead to sensical conclusions when the
underlying phenomenon is homogeneous.
If not, the inherent spatial
heterogeneiy and structural
instability should be
accounted for in the various
aggregation schemes.
a1
a2
A
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b1
B
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b2
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 (III)
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The different types of
spatial data (point, line,
area, surface), occurring
naturally or as a result of
the measurement process,
potentially allow many ways
of integrating these data.
Changing the support of
a spatial variable (volume,
geometrical size, shape &
spatial orientation) -typically
by aggregation/averagingcreates a new variable.
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Session 1
1.3.2. Spatial data problems (IV)
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From an econometric standpoint, MAUP is also an identification
problem,
problem since there is insufficient information in the data to allow
for 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.
SYSTEM OF SIMULTANEOUS
LINEAR EQUATIONS
LINEAR SPATIAL
AUTOREGRESSIVE MODEL
N
N
yi = ρ ∑ wij yi
yi = ∑ ρi wij yi
i =1
i =1
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Session 1
1.3.3. Spatial data empirical
applications
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Empirical applications with spatial
data imply the use of:
„ Statistical
data
„ GIS & digital maps
„ Spatial econometrics software
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1.3.3. Spatial data empirical
applications (II)
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Statistical data:
data
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Primary data: from private or public surveys...
Secondary data. E.g. in Spain:
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Regional data: INE, IVIE-BBVA, “la Caixa”...
Municipal data: INE, “la Caixa”-LR Klein Institute...
Districts, census tracts: INE, Regional Statistics
Offices
Others: Expérian, Mosaic, Data Segmento, Sitesa...
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1.3.3. Spatial data empirical
applications (III)
¾ GIS: Managment, analysis and visualization of spatial data. It is
estructures in interactive maps, spatial data, geoprocessing
models, data models and metadata”
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1.3.3. Spatial data empirical
applications (IV)
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Digital maps:
maps
„ Instituto Nacional de Estadística:
regions, provinces, municipalities,
districts, census tracts, streets...
„ ESRI: Muniview, Censalview, Arcópolis
„ MapInfo
„ Others: Maptel...
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1.3.3. Spatial data empirical
applications (V)
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Spatial econometrics
software:
Focused on ESDA:
GEODA:
GEODA https://www.geoda.uiuc.edu/downloadin.php
STARS:
STARS http://regal.sdsu.edu/index.php
Focused on confirmatory analysis:
SpaceStat:
SpaceStat http://www.terraseer.com
Spatial Econometrics Toolbox (Matlab):
http://www.spatial-econometrics.com
spdep (R): http://cran.r-project.org
PySAL (Python): http://sal.uiuc.edu
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GEODA:
GEODA
https://www.geoda.uiuc.edu/downloadin.php
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Created by Luc Anselin,
Anselin University of
Illinois in Urbana-Champaign
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GEODA:
GEODA
https://www.geoda.uiuc.edu/downloadin.php
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GIS + ESDA + Spatial regression
Exploratory Spatial Data Analysis (AEDE):
- Data managment
- Mapping and descriptive statistics
- Spatial association: global and local spatial
autocorrelation statistics
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Spatial regression:
- Basic OLS model
- Spatial lag model
- Spatial error model
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GEODA:
GEODA
https://www.geoda.uiuc.edu/downloadin.php
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STARS:
STARS
http://regal.sdsu.edu/index.php
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Created by Serge Rey,
Rey San Diego State
University.
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STARS (II):
(II)
http://regal.sdsu.edu/index.php
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STARS (III):
(III)
http://regal.sdsu.edu/index.php
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spdep for R: http://cran.r-project.org
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Created by Roger Bivand,
Bivand Norwegian School of
Economics and Business Administration,.
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PYSAL:
PYSAL
http://sal.uiuc.edu
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Future Luc Anselin,’s
Anselin
project: combination of
GEODA- STARS-SPDEP
opensource
30 software.
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PYSAL (II)
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Spatial Econometrics Toolbox for Matlab:
Matlab
http://www.spatial-econometrics.com
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Created by James LeSage,
LeSage
University of Toledo.
Main contents:
2 Spatial autoregressive models
2.1 The rst-order spatial AR model
2.2 The mixed autoregressiveregressive model
2.3 The spatial errors model
2.4 The general spatial model
3 Bayesian Spatial autoregressive
models
4 Locally linear spatial models
4.1 Spatial expansion
4.2 DARP models
4.3 GWR
4.4 A Bayesian Approach to GWR
5 Limited dependent variable models
5.2 The Gibbs sampler
5.3 Heteroscedastic models
6 VAR and Error Correction Models
6.1 VAR models
6.2 Error correction models
6.3 Bayesian variants
6.4 Forecasting the models
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Main contents:
SpaceStat:
SpaceStat
1 Data management and algebra
2 Spatial weight matrices
http://www.terraseer.com
2.1 Creation & characteristics
2.2 Spatial correlogram
2.3 Spatial lags
„ Created by Luc Anselin
3 ESDA
3.1 Basic descriptive statistics
3.2 Joint count, Moran’s I & Geary’s c
3.3 G statistics & QAP measures
4 SPATIAL REGRESSION
4.1 Basic OLS regression
4.2 Spatial lag & spatial error models
4.3 Instrumental Variables estimation
4.4 Heteroskedastic model
4.5 Trend surface model
4.6 Spatial regimes & S-ANOVA
4.7 Spatial expansion
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Session 1
1.4. Some applications in spatial
econometrics (I)
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Cancer mortality rate model
Homicide rate
Spatial β-convergence regional model
Household per capita income
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Session 1
1.3. Some applications... (II)
Haining: Cancer mortality rate model
(spatial-error model)
y: cancer mortality rate
i:
one of the 87 Glasgow community medicine areas
x: deprivation index
W: spatial weight matrix
β0, β1, λ: parameters to be estimated
u, ε:
stochastic error terms
. 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.
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Session 1
1.3. Some applications... (III)
Baller, Anselin, Messner, Deane and Hawkings: Homicide rate
(spatial-lag model)
H:
i:
D:
P:
V:
U:
E:
homicide rate
U.S. county
resource deprivation index
population structure
percent divorced
unemployment rate
median age
W: spatial weight matrix
ρ: spatial autoregressive parameter
β0, β1, β2, β3, β5, β6: exogenous vars. Parameters
ε: i.i.d. stochastic error term
. BALLER, R., L. ANSELIN, S. MESSNER and D. HAWKINS (2001), “Structural covariates of U.S. county
homicide rates: incorporating spatial effects”. Criminology (próxima publicación).
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Session 1
1.3. Some applications... (IV)
Rey & Montouri: Spatial β-convergence regional model
(spatial cross-regressive model)
yi,t:
real per capita income in state i year t
k:
year period
W:
spatial weight matrix
α, β, γ : parameters to be estimated
u:
i.i.d. stochastic error term
. REY, S. and B. MONTOURI (1999), “US regional income convergence: a spatial
econometric perspective”. Regional Studies, vol. 33.2; pp. 143-156.
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Session 1
1.3. Some applications... (V)
Chasco: Household per capita income
(spatial-lag model with two spatial regimes)
Spatial lag
. CHASCO, C. (2003), “Econometría espacial
aplicada a la predicción-extrapolación de
datos microterritoriales”. Consejería de
Economía e Innovación Tecnológica de la
Comunidad de Madrid.
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