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Dealing with spatial data pooled over time in statistical models

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Abstract

Recent developments in spatial econometrics have been devoted to spatio-temporal data and how spatial panel data structure should be modeled. Little effort has been devoted to the way one must deal with spatial data pooled over time. This paper presents the characteristics of spatial data pooled over time and proposes a simple way to take into account unidirectional temporal effect as well as multidirectional spatial effect in the estimation process. An empirical example, using data on 25,357 single family homes sold in Lucas County, OH (USA), between 1993 and 1998 (available in the MatLab library), is used to illustrate the potential of the approach proposed.

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Notes

  1. Two observations having the same geographical coordinates.

  2. Except if the panel is unbalanced.

  3. Of course, it can also account for potential anticipation by considering that the first period after may exert influence on the actual observations, as noted by Dubé et al. (2011a).

  4. Of course, the determination of the optimal kernel size remains an important topic that is not explicitly treated in the paper.

  5. Of course, this definition can be extended to include more details such as days \(dd\). The general form of the function can be approximated by \(v_{i} = 365 \times (yyyy_{i}-yyyy_{min}) + 31 \times (mm_{i}-1) + dd_{i}\), assuming that a difference of a few days does not affect the structure of the matrix since the months do not have the same number of days.

  6. The definition of the temporal weights matrix generalizes the specification of Pace et al. (1998, 2000) and Smith and Wu (2009).

  7. As is the case for the definition of the spatial relation, \(s_{ij}\), in Eq. (2), \(\gamma \) usually takes a value 0, 1 or 2.

  8. The definition uses absolute values to ensure that the matrix \(T\) has non-negative values since the difference in date of observation gives non-symmetric measures. Such specification ensures that the temporal weights matrix is also symmetric.

  9. Defining a term by term multiplication of matrices and noted \(\odot \).

  10. \(w_{ij} = s_{ij} \times t_{ij}\).

  11. The optimal impact of the age on house prices can be obtained by: \(\beta _{log(age)} \times (-1/\beta _{age})\).

  12. The general form of the matrix is \(W_{0} = S_{0} \odot T_{0}\). The matrix \(W_{0}\) is used to detect spatial autocorrelation pattern among residuals using the Moran’s \(I\) index.

  13. The estimation routines developed in MatLab by Lesage (1999), based on maximum likelihood is used to estimate the model using the spatio-temporal weights matrix instead of the spatial weights matrix. The SEM specification is used since the dynamic time lagged variables represent a special case of spatial autoregressive (SAR) model and fail to control adequately for spatial autocorrelation.

  14. The spatio-temporal weights matrix used is the same that previously served to calculate the Moran’s \(I\) index: \(W_{0}= S_{0}\odot T_{0}\).

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Authors and Affiliations

  1. Univeristé du Québec À Rimouski, 300 allée des Ursulines, Rimouski, QC, G5L 3A1, Canada

    Jean Dubé

  2. Laboratoire d’Économie et de Gestion, 2 boulevard Gabriel, BP 26611, 21066 , Dijon Cedex, France

    Diègo Legros

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  1. Jean Dubé
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  2. Diègo Legros
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Correspondence to Jean Dubé.

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Dubé, J., Legros, D. Dealing with spatial data pooled over time in statistical models. Lett Spat Resour Sci 6, 1–18 (2013). https://doi.org/10.1007/s12076-012-0082-3

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