IDEAS home Printed from https://ideas.repec.org/p/rtv/ceisrp/338.html
   My bibliography  Save this paper

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

Author

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
    as

    Download full text from publisher

    File URL: https://ceistorvergata.it/RePEc/rpaper/RP338.pdf
    File Function: Main text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kelejian, Harry H. & Prucha, Ingmar R., 2010. "Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Econometrics, Elsevier, vol. 157(1), pages 53-67, July.
    2. Manfred M. Fischer & Arthur Getis (ed.), 2010. "Handbook of Applied Spatial Analysis," Springer Books, Springer, number 978-3-642-03647-7, April.
    3. 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.
    4. 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.
    5. Vasilis Sarafidis & Tom Wansbeek, 2012. "Cross-Sectional Dependence in Panel Data Analysis," Econometric Reviews, Taylor & Francis Journals, vol. 31(5), pages 483-531, September.
    6. 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.
    7. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    8. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    9. Mitchell, Matthew W. & Genton, Marc G. & Gumpertz, Marcia L., 2006. "A likelihood ratio test for separability of covariances," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1025-1043, May.
    10. Baltagi, Badi H. & Song, Seuck Heun & Koh, Won, 2003. "Testing panel data regression models with spatial error correlation," Journal of Econometrics, Elsevier, vol. 117(1), pages 123-150, November.
    11. LeSage, James P. & Kelley Pace, R., 2007. "A matrix exponential spatial specification," Journal of Econometrics, Elsevier, vol. 140(1), pages 190-214, September.
    12. Tiziana Caliman & Enrico di Bella, 2011. "Spatial Autoregressive Models for House Price Dynamics in Italy," Economics Bulletin, AccessEcon, vol. 31(2), pages 1837-1855.
    13. László Mátyás & Patrick Sevestre (ed.), 2008. "The Econometrics of Panel Data," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-540-75892-1.
    14. Baltagi, Badi H & Levin, Dan, 1986. "Estimating Dynamic Demand for Cigarettes Using Panel Data: The Effects of Bootlegging, Taxation and Advertising Reconsidered," The Review of Economics and Statistics, MIT Press, vol. 68(1), pages 148-155, February.
    15. Kapoor, Mudit & Kelejian, Harry H. & Prucha, Ingmar R., 2007. "Panel data models with spatially correlated error components," Journal of Econometrics, Elsevier, vol. 140(1), pages 97-130, September.
    16. Baltagi, Badi H. & Kelejian, Harry H. & Prucha, Ingmar R., 2007. "Analysis of spatially dependent data," Journal of Econometrics, Elsevier, vol. 140(1), pages 1-4, September.
    17. repec:hal:journl:peer-00796743 is not listed on IDEAS
    18. Lee, Lung-fei & Yu, Jihai, 2010. "Some recent developments in spatial panel data models," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 255-271, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Debarsy, Nicolas & Ertur, Cem, 2010. "Testing for spatial autocorrelation in a fixed effects panel data model," Regional Science and Urban Economics, Elsevier, vol. 40(6), pages 453-470, November.
    2. Su, Liangjun & Yang, Zhenlin, 2015. "QML estimation of dynamic panel data models with spatial errors," Journal of Econometrics, Elsevier, vol. 185(1), pages 230-258.
    3. repec:rri:wpaper:201303 is not listed on IDEAS
    4. Harry H. Kelejian & Gianfranco Piras, 2013. "A J-Test for Panel Models with Fixed Effects, Spatial and Time," Working Papers Working Paper 2013-03, Regional Research Institute, West Virginia University.
    5. Michele Aquaro & Natalia Bailey & M. Hashem Pesaran, 2021. "Estimation and inference for spatial models with heterogeneous coefficients: An application to US house prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(1), pages 18-44, January.
    6. Badi H. Baltagi & Peter Egger & Michael Pfaffermayr, 2013. "A Generalized Spatial Panel Data Model with Random Effects," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 650-685, August.
    7. Roger Bivand & Giovanni Millo & Gianfranco Piras, 2021. "A Review of Software for Spatial Econometrics in R," Mathematics, MDPI, vol. 9(11), pages 1-40, June.
    8. Giuseppe Arbia, 2011. "A Lustrum of SEA: Recent Research Trends Following the Creation of the Spatial Econometrics Association (2007--2011)," Spatial Economic Analysis, Taylor & Francis Journals, vol. 6(4), pages 377-395, July.
    9. Gianfranco Piras, 2013. "Efficient GMM Estimation of a Cliff and Ord Panel Data Model with Random Effects," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(3), pages 370-388, September.
    10. Lee, Lung-fei & Yu, Jihai, 2010. "Some recent developments in spatial panel data models," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 255-271, September.
    11. Vasilis Sarafidis & Tom Wansbeek, 2012. "Cross-Sectional Dependence in Panel Data Analysis," Econometric Reviews, Taylor & Francis Journals, vol. 31(5), pages 483-531, September.
    12. Alexander Chudik & M. Hashem Pesaran, 2013. "Large panel data models with cross-sectional dependence: a survey," Globalization Institute Working Papers 153, Federal Reserve Bank of Dallas.
    13. repec:asg:wpaper:1013 is not listed on IDEAS
    14. Luc Anselin, 2010. "Thirty years of spatial econometrics," Papers in Regional Science, Wiley Blackwell, vol. 89(1), pages 3-25, March.
    15. Bai, Jushan & Li, Kunpeng, 2013. "Spatial panel data models with common shocks," MPRA Paper 52786, University Library of Munich, Germany, revised 09 Mar 2014.
    16. Harry H. Kelejian & Gianfranco Piras, 2016. "A J test for dynamic panel model with fixed effects, and nonparametric spatial and time dependence," Empirical Economics, Springer, vol. 51(4), pages 1581-1605, December.
    17. Millo, Giovanni, 2014. "Maximum likelihood estimation of spatially and serially correlated panels with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 914-933.
    18. Cem Ertur & Antonio Musolesi, 2017. "Weak and Strong Cross‐Sectional Dependence: A Panel Data Analysis of International Technology Diffusion," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(3), pages 477-503, April.
    19. Michele Aquaro & Natalia Bailey & M. Hashem Pesaran, 2015. "Quasi Maximum Likelihood Estimation of Spatial Models with Heterogeneous Coefficients," CESifo Working Paper Series 5428, CESifo.
    20. Michele Aquaro & Natalia Bailey & M. Hashem Pesaran, 2015. "Quasi Maximum Likelihood Estimation of Spatial Models with Heterogeneous Coefficients," Working Papers 749, Queen Mary University of London, School of Economics and Finance.
    21. Burridge, Peter & Iacone, Fabrizio & Lazarová, Štěpána, 2015. "Spatial effects in a common trend model of US city-level CPI," Regional Science and Urban Economics, Elsevier, vol. 54(C), pages 87-98.
    22. Cynthia Fan Yang, 2021. "Common factors and spatial dependence: an application to US house prices," Econometric Reviews, Taylor & Francis Journals, vol. 40(1), pages 14-50, January.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    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:rtv:ceisrp:338. See general information about how to correct material in RePEc.

    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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Barbara Piazzi (email available below). General contact details of provider: https://edirc.repec.org/data/csrotit.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.