Rossi, Francesca
(2011)
Improved tests for spatial autoregressions.
PhD thesis, London School of Economics and Political Science.
Abstract
Econometric modelling and statistical inference are considerably complicated by the
possibility of correlation across data data recorded at different locations in space. A
major branch of the spatial econometrics literature has focused on testing the null
hypothesis of spatial independence in Spatial Autoregressions (SAR) and the asymptotic
properties of standard test statistics have been widely considered. However, finite
sample properties of such tests have received relatively little consideration. Indeed,
spatial datasets are likely to be small or moderately-sized and thus the derivation of
finite sample corrections appears to be a crucially important task in order to obtain
reliable tests. In this project we consider finite sample corrections based on formal
Edgeworth expansions for the cumulative distribution function of some relevant test
statistics.
In Chapter 1 we provide the background for the results derived in this thesis.
Specifically, we describe SAR models together with some established results in first
order asymptotic theory for tests for independence in such models and give a brief
account on Edgeworth expansions. In Chapters 2 and 3 we present refined procedures
for testing nullity of the spatial parameter in pure SAR based on ordinary
least squares and Gaussian maximum likelihood, respectively. In both cases, the
Edgeworth-corrected tests are compared with those obtained by a bootstrap procedure,
which is supposed to have similar properties. The practical performance of new
tests is assessed with Monte Carlo simulations and two empirical examples. In Chapter
4 we propose finite sample corrections for Lagrange Multiplier statistics, which are
computationally particularly convenient as the estimation of the spatial parameter is
not required. Monte Carlo simulations and the numerical implementation of Imhof's
procedure confirm that the corrected tests outperform standard ones. In Chapter 5 the
slightly more general model known as \mixed" SAR is considered. We derive suitable
finite sample corrections for standard tests when the parameters are estimated by ordinary
least squares and instrumental variables. A Monte Carlo study again confirms
that the new tests outperform ones based on the central limit theorem approximation
in small and moderately-sized samples.
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