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Spatial Panel Data Model with error dependence: a Bayesian Separable Covariance Approach

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Abstract

A hierarchical Bayesian model for spatial panel data is proposed. The idea behind the proposed method is to analyze spatially dependent panel data by means of a separable covariance matrix. Let us indicate the observations as yit, i = 1,...,N regions and t = 1,...,T time, var(y), the covariance matrix of y is written as a Kronecker product of a purely spatial and a purely temporal covariance. On the one hand, the structure of separable covariances dramatically reduces the number of parameters, while on the other, the lack of a structured pattern for spatial and temporal covariances permits to capture possible unknown dependencies (both in time and space). The use of the Bayesian approach allows to overcome some of the difficulties of the classical (MLE or GMM based) approach. We present two illustrative examples: the estimation of cigarette price elasticity and of the determinants of the house price in 120 municipalities in the Province of Rome.

Suggested Citation

  • Samantha Leorato & Maura Mezzetti, 2015. "Spatial Panel Data Model with error dependence: a Bayesian Separable Covariance Approach," CEIS Research Paper 338, Tor Vergata University, CEIS, revised 09 Apr 2015.
  • Handle: RePEc:rtv:ceisrp:338
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    References listed on IDEAS

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    1. Pesaran, M. Hashem & Tosetti, Elisa, 2011. "Large panels with common factors and spatial correlation," Journal of Econometrics, Elsevier, vol. 161(2), pages 182-202, April.
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    3. Alexander Chudik & M. Hashem Pesaran & Elisa Tosetti, 2011. "Weak and strong cross‐section dependence and estimation of large panels," Econometrics Journal, Royal Economic Society, vol. 14(1), pages 45-90, February.
    4. LeSage, James P. & Kelley Pace, R., 2007. "A matrix exponential spatial specification," Journal of Econometrics, Elsevier, vol. 140(1), pages 190-214, September.
    5. Baltagi, Badi H. & Heun Song, Seuck & Cheol Jung, Byoung & Koh, Won, 2007. "Testing for serial correlation, spatial autocorrelation and random effects using panel data," Journal of Econometrics, Elsevier, vol. 140(1), pages 5-51, September.
    6. Tiziana Caliman & Enrico di Bella, 2011. "Spatial Autoregressive Models for House Price Dynamics in Italy," Economics Bulletin, AccessEcon, vol. 31(2), pages 1837-1855.
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    More about this item

    Keywords

    Bayesian Inference; Kronecker Product; Separable Covariance Matrix; Inverted Wishart Distribution; Spatial-Temporal Dependence;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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