IDEAS home Printed from
   My bibliography  Save this paper

Estimation of a Weights Matrix for Determining Spatial Effects


  • Elcyon Caiado Rocha Lima
  • Paulo Brígido Rocha Macedo


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

    Download full text from publisher

    File URL:
    Download Restriction: no

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ipe:ipetds:0087. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Fabio Schiavinatto). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.