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Estimation of a Weights Matrix for Determining Spatial Effects

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  • Elcyon Caiado Rocha Lima
  • Paulo Brígido Rocha Macedo

Abstract

Spatial dependence results from the existence of spillover effects such as the impact of the price of one housing unit on the price of its adjacent neighbors. One way to account for spatial dependence is to specify spatial lag models in which a spatially lagged variable is assumed to play a role in explaining the variation of the original dependent variable. Most studies use a priori non-sample information in the construction of the spatial weights matrix which serves as a spatial lag operator. In contrast, this study assumes no a priori value for the spatial weights matrix in the estimation of spillover effects. We adopt a classical maximum likelihood approach and also a Bayesian Sampling-Importance-Resampling (SIR) procedure to estimate the weights matrix and the significance of spatial dependence. We apply the two estimation procedures to data on housing prices in the city of Belo Horizonte, Brazil, and compare the results obtained with these two techniques with the one derived by a priori fixing the weights. The analysis shows that the likelihood function of the weights matrix parameters has a well-defined peak, and the estimated distance-decay parameter is quite different from the standard a priori assumptions such as the “all-or-nothing” decay within the cut-off distance or the “inverse distance” adopted in the empirical literature. A existência de efeitos de “transbordamento”, como o impacto do preço de uma unidade residencial no preço de seus vizinhos adjacentes, caracteriza a chamada “dependência espacial”. Uma forma de se levar em conta a dependência espacial é especificar modelos de defasagem espacial nos quais se supõe que uma variável espacialmente defasada explica, pelo menos parcialmente, a variação da variável dependente original. A maioria dos estudos fixa a priori os parâmetros utilizados na construção da matriz de pesos espaciais que serve de operador da defasagem espacial. Em contraste, este trabalho não pressupõe qualquer valor a priori para os parâmetros da matriz de pesos espaciais na estimação de efeitos de transbordamento. Nós adotamos uma abordagem de máxima verossimilhança clássica e um procedimento bayesiano, Sampling–Importance–Resampling (SIR), para estimar os pesos da matriz e a significância da dependência espacial. Utilizamos dados de unidades residenciais da cidade de Belo Horizonte, e comparamos os resultados obtidos com o procedimento desenvolvido com aqueles derivados a partir da fixação a priori dos pesos espaciais. A análise mostra que a função de verossimilhança tem um pico bem definido, e o parâmetro de decaimento estimado é bastante diverso dos valores prefixados usualmente adotados na literatura empírica, como o decaimento “tudo-ou-nada” dentro da distância crítica ou o uso do “inverso da distância”.

Suggested Citation

  • Elcyon Caiado Rocha Lima & Paulo Brígido Rocha Macedo, 2015. "Estimation of a Weights Matrix for Determining Spatial Effects," Discussion Papers 0087, Instituto de Pesquisa Econômica Aplicada - IPEA.
  • Handle: RePEc:ipe:ipetds:0087
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