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Improved tests for spatial autoregressions

Rossi, Francesca (2011) Improved tests for spatial autoregressions. PhD thesis, London School of Economics and Political Science.

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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.

Item Type: Thesis (PhD)
Additional Information: © 2011 Francesca Rossi
Library of Congress subject classification: H Social Sciences > HB Economic Theory
Sets: Departments > Economics
Supervisor: Robinson, Peter

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