Essays on spatial econometrics

Resumo

This dissertation focus on spatial stochastic process on a lattice (Cliff & Ord--type of models). My contribution consists of using Edgeworth and saddlepoint series to investigate small sample size and power properties of tests for detecting spatial dependence in spatial autoregressive (SAR) stochastic processes, and proposing a new class of spatial econometric models where the spatial dependence parameters that enter the mean structure are different from the ones in the covariance structure. This allows a clearer interpretation of models' parameters and generalizes the set of local and global models suggested by Anselin (2003) as an alternative to the traditional Cliff & Ord models. I propose an estimation procedure for the model's parameters and derive the asymptotic distribution of the parameters' estimators. The suggested model provides some insights on the structure of the commonly used mixed regressive, spatial autoregressive model with spatial autoregressive disturbances (SARAR). The study of the small sample properties of tests to detect spatial dependence expands on the existing literature by allowing the neighborhood structure to be a nonlinear function of the spatial dependence parameter. The use of series approximations instead of the often used Monte Carlo simulation allows a simple way to compare test properties across different neighborhood structures and to correct for size when comparing power. I obtain the power envelope for testing the presence of spatial dependence in the SAR process using the optimal invariant test statistic, which is also locally uniformly most powerful invariant (LUMPI). I have found that the LUMPI test is virtually UMP since its power is very close to the power envelope. I suggest a practical procedure to build a test that, while not UMP, retain good power properties in a wider range for the spatial parameter when compared to the LUMPI test. I find that power increases with sample size and with the spatial dependence parameter -- which agrees with the literature. However, I call into question the consensus view that power decreases as the spatial weight matrix becomes more densely connected. This finding in the literature reflects an error of measure because the hypothesis being compared are at very different statistical distance from the null. After adjusting for this, the power is larger for alternative hypothesis further away from the null -- as one would expect.

Ficha do documento

Tipo

Tese

Ano

2012

Instituição

Fundação Getulio Vargas

Fonte

Repositório da FGV

Idioma

Inglês

Acesso

Acesso aberto

Identificador

oai:repositorio.fgv.br:10438/11268

Temas

Economia

Palavras-chave

Spatial econometricsSpatial autoregressive and moving average modelsTwo-stage least squaresSmall sampleSaddlepointInvariant testsUniuformly most poweful testsGeneralized moments estimationHeteroskedascityAsymptoticsCliff & Ord modelEdgeworth seriesHypothesis testingEconometria espacialMínimos quadrados em dois estágiosMétodo generalizado dos momentosAmostras finitasHeteroscedasticidadeAssintóticaCliff & OrdEdgeworthTeste de hipótesesTestes invariantesTestes UMPEconometriaEspaço em economiaEconomiaEspaço em economia - Modelos matemáticos