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PEP 0007 Spatial Econometrics
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========  ======================================
Author    Luc Anselin <luc.anselin@asu.edu>
          Serge Rey <sjsrey@gmail.com>,David Folch <dfolch@asu.edu>,Daniel Arribas-Bel <daniel.arribas.bel@gmail.com>,Pedro Amaral <pvmda2@cam.ac.uk>,Nicholas Malizia <nmalizia@gmail.com>,Ran Wei <rwei5@asu.edu>,Jing Yao <jyao13@asu.edu>,Elizabeth Mack <Elizabeth.A.Mack@asu.edu>
Status    Approved 1.1
Created   12-Oct-2010
Updated   12-Oct-2010
========  ======================================

Abstract
========

The spatial econometrics module will provide a uniform interface to the
spatial econometric functionality contained in the former PySpace and
current GeoDaSpace efforts. This module would centralize all specification,
estimation, diagnostic testing and prediction/simulation for spatial
econometric models.


Motivation
==========

Spatial econometric methodology is at the core of GeoDa and 
GeoDaSpace. This module would allow access to state of the art
methods at the source code level.


Reference Implementation
========================

We suggest adding the module ``pysal.spreg``. As development
progresses, there may be a need for submodules dealing with
pure cross sectional regression, spatial panel models and spatial probit.

Core methods to be implemented include:

   * OLS estimation with diagnostics for spatial effects
   * 2SLS estimation with diagnostics for spatial effects
   * spatial 2SLS for spatial lag model (with endogeneity)
   * GM and GMM estimation for spatial error model
   * GMM spatial error with heteroskedasticity
   * spatial HAC estimation

A significant component of the effort for this PEP would consist of
implementing methods with good performance on very large data
sets, exploiting sparse matrix operations in scipy.

References
==========

[1] Anselin, L. (1988). Spatial Econometrics, Methods and Models. Kluwer, Dordrecht.

[2] Anselin, L. (2006). Spatial econometrics. In Mills, T. and Patterson, K., editors,
     Palgrave Handbook of Econometrics, Volume I, Econometric Theory, pp. 901-969.
     Palgrave Macmillan, Basingstoke.
     
[3] Arraiz, I., Drukker, D., Kelejian H.H., and Prucha, I.R. (2010). A spatial Cliff-Ord-type
     model with heteroskedastic innovations: small and large sample results.
     Journal of Regional Science 50: 592-614.
     
[4] Kelejian, H.H. and Prucha, I.R. (1998). A generalized spatial two stage least squares
     procedure for estimationg a spatial autoregressive model with autoregressive
     disturbances. Journal of Real Estate Finance and Economics 17: 99-121.
     
[5] Kelejian, H.H. and Prucha, I.R. (1999). A generalized moments estimator  for the
     autoregressive parameter in a spatial model. International Economic Review 40: 509-533.
     
[6] Kelejian, H.H. and Prucha, I.R. (2007). HAC estimation in a spatial framework.
     Journal of Econometrics 140: 131-154.
     
[7] Kelejian, H.H. and Prucha, I.R. (2010). Specification and estimation of spatial autoregressive
     models with autoregressive and heteroskedastic disturbances. Journal of Econometrics
     (forthcoming).
