Spatial Econometrics Models using Matlab Shawn Bucholtz GIS Team, ERS

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Spatial Econometrics Models using MatlabShawn
BucholtzGIS Team, ERS
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• Topics for Discussion
• Overview of Matlab
• Comparing Matlab to other programs
• Econometrics in Matlab
• Spatial Econometrics in Matlab
• Useful Toolboxes in Matlab

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• Overview of Matlab

• MATLAB is a high-level language and interactive
  environment that enables you to perform
  computationally intensive tasks faster than with
  traditional programming languages such as C, C,
  and Fortran.
• http//www.mathworks.com/products/pfo/
• Object oriented language
• Data structure vectors, matrices,
  multidimensional arrays, structured arrays,
  sparse matrices, Sparse Arrays

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• Key Features of Matlab
• Developing Algorithms and Applications
• Analyzing and Accessing Data
• Visualizing Data
• Performing Numeric Computation
• Publishing Results and Deploying Applications

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How Does Matlab Compare to Other Common Programs?
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• Econometrics using Matlab
• Matlab toolboxes for statistics, optimization
• Econometrics Toolbox by Jim LeSage
• least-squares, simultaneous systems (2SLS,3SLS,
  SUR)
• limited dependent variable (logit, probit, tobit)
  and Bayesian variants
• time-series (VAR, BVAR, ECM) estimation and
  accompanying forecasting functions
• ridge, Theil-goldberger, switching regimes,
  robust regression
• regression diagnostics, e.g. Belsley, Kuh Welsch,
  Cook-Weisberg
• cointegration testing
• statistical distributions (CDF, PDF and random
  deviate generation)
• Bayesian Gibbs sampling estimation and MCMC
  convergence diagnostics
• maximum likelihood and Bayesian spatial
  econometrics functions
• lots of other stuff, over 350 functions

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• Spatial Econometrics Models
• Spatial econometrics is a blanket term for
  statistical tests and models used to address
  potential issues introduced by the presence of
  spatial effects in regression analysis.
• Three spatial effects
• spatial lag dependence spatial error
  dependence spatial heterogeneity

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A Hedonic Example
What are the determinants of the price of a house?
Price Sq. ft. Age Median Income Dist. to
Metro error error captures all the
determinants that you cant think of, cant model
or measure correctly, or dont have data to
measure.
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Spatial Autoregressive Model
Price W Price Sq. ft. Age Median
Income Dist. to Metro error Where W is a
spatial weight matrix
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Spatial Error Model Recall that the regression
model contains an error term Spatial dependence
can occur when 1) Spatially correlated omitted
variables 2) Spatially correlated aggregate
variables 3) Spatially correlated errors in
variable measurement
It can be accounted for by the spatial error
model Price Sq. ft. Age Median Income
Dist. to Metro error error Werror µ
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• Spatial Weight Matrix
• Provides the structure of assumed spatial
  relationships.
• Recall from before that the price of a house was
  hypothesized to be a function of a weight average
  of the prices of the surrounding houses, among
  other things.

• Weight Matrix contains a d term for every
  combination of observations in the data set
• d may be the inverse distance between
  observations or 0,1 if they share a border and/or
  vertex.

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Spatial Econometrics in Matlab

• Opinion Probably the best software for spatial
  econometric models
• Matlabs routines for sparse matrices
  significantly increase computational speed
• Extensively supported via Spatial Econometrics
  Library from Jim LeSage.
• Easy integration with Matlab Mapping Toolbox

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Spatial Econometrics in Matlab Available
models Spatial Autoregressive Model (SAR)-- ML
and GMM estimators Spatial Error Model (SEM)-- ML
and GMM estimators General Spatial Model (SAC)--
ML and GMM estimators Spatial Durbin Models
(SDM) Spatial Error Probit Models (SEMP) SAR
model with Fixed Effects (Panel Data) SEM model
with Fixed Effects (Panel Data) Bayesian
Geographically Weighted Regressions
(BGWR) Casettis Spatial Expansion Model
(DARP)
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Spatial Econometrics in Matlab
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Other Useful Toolboxes for Matlab
MATLAB Compiler 4.3 -- Convert MATLAB programs
into stand-alone applications and software
components MATLAB Builder for COM 1.1.5
Convert your Matlab programs into COM
objects MATLAB Web Server 1.2.4 -- Deploy MATLAB
and Simulink applications over the Internet via
HTML Distributed Computing Toolbox 1.0.2 -- Run
MATLAB and Simulink applications on a computer
cluster