IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v188y2015i1p1-21.html
   My bibliography  Save this article

Large sample properties of the matrix exponential spatial specification with an application to FDI

Author

Listed:
  • Debarsy, Nicolas
  • Jin, Fei
  • Lee, Lung-fei

Abstract

This paper studies large sample properties of the matrix exponential spatial specification (MESS). We find that the quasi-maximum likelihood estimator (QMLE) for the MESS is consistent under heteroskedasticity, a property not shared by the QMLE of the SAR model. For the general model that has MESS in both the dependent variable and disturbances, labeled MESS(1,1), the QMLE can be consistent under unknown heteroskedasticity when the spatial weights matrices in the two MESS processes are commutative. We also consider the generalized method of moments estimator (GMME). In the homoskedastic case, we derive a best GMME that is as efficient as the maximum likelihood estimator under normality and can be asymptotically more efficient than the QMLE under non-normality. In the heteroskedastic case, an optimal GMME can be more efficient than the QMLE asymptotically. The QML approach for the MESS has the computational advantage over that of a SAR model. The computational simplicity carries over to MESS models with any finite order of spatial matrices. No parameter range needs to be imposed in order for the model to be stable. Results of Monte Carlo experiments for finite sample properties of the estimators are reported. Finally, the MESS(1,1) is applied to Belgium’s outward FDI data and we observe that the dominant motivation of Belgium’s outward FDI lies in finding cheaper factor inputs.

Suggested Citation

  • Debarsy, Nicolas & Jin, Fei & Lee, Lung-fei, 2015. "Large sample properties of the matrix exponential spatial specification with an application to FDI," Journal of Econometrics, Elsevier, vol. 188(1), pages 1-21.
    • Handle: RePEc:eee:econom:v:188:y:2015:i:1:p:1-21
    DOI: 10.1016/j.jeconom.2015.02.046
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407615001219
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2015.02.046?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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. Bruce A. Blonigen & Ronald B. Davies & Glen R. Waddell & Helen T. Naughton, 2019. "FDI in Space: Spatial Autoregressive Relationships in Foreign Direct Investment," World Scientific Book Chapters, in: Foreign Direct Investment, chapter 2, pages 55-88, World Scientific Publishing Co. Pte. Ltd..
    3. Lee, Lung-fei & Yu, Jihai, 2010. "Estimation of spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 154(2), pages 165-185, February.
    4. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
    5. 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.
    6. Lee, Lung-fei, 2007. "The method of elimination and substitution in the GMM estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 140(1), pages 155-189, September.
    7. LeSage, James P. & Kelley Pace, R., 2007. "A matrix exponential spatial specification," Journal of Econometrics, Elsevier, vol. 140(1), pages 190-214, September.
    8. Baltagi, Badi H. & Egger, Peter & Pfaffermayr, Michael, 2007. "Estimating models of complex FDI: Are there third-country effects?," Journal of Econometrics, Elsevier, vol. 140(1), pages 260-281, September.
    9. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
    10. Harry Garretsen & Jolanda Peeters, 2009. "FDI and the relevance of spatial linkages: do third-country effects matter for Dutch FDI?," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 145(2), pages 319-338, July.
    11. Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
    12. Davies, Ronald B., 2005. "Fragmentation of headquarter services and FDI," The North American Journal of Economics and Finance, Elsevier, vol. 16(1), pages 61-79, March.
    13. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July.
    14. Baltagi, Badi H. & Egger, Peter & Pfaffermayr, Michael, 2008. "Estimating regional trade agreement effects on FDI in an interdependent world," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 194-208, July.
    15. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    16. Han, Xiaoyi & Lee, Lung-fei, 2013. "Model selection using J-test for the spatial autoregressive model vs. the matrix exponential spatial model," Regional Science and Urban Economics, Elsevier, vol. 43(2), pages 250-271.
    17. Cletus C. Coughlin & Eran Segev, 2000. "Foreign Direct Investment in China: A Spatial Econometric Study," The World Economy, Wiley Blackwell, vol. 23(1), pages 1-23, January.
    18. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
    19. Elhorst, J. Paul & Lacombe, Donald J. & Piras, Gianfranco, 2012. "On model specification and parameter space definitions in higher order spatial econometric models," Regional Science and Urban Economics, Elsevier, vol. 42(1-2), pages 211-220.
    20. J. Elhorst, 2010. "Applied Spatial Econometrics: Raising the Bar," Spatial Economic Analysis, Taylor & Francis Journals, vol. 5(1), pages 9-28.
    21. Liu, Xiaodong & Lee, Lung-fei & Bollinger, Christopher R., 2010. "An efficient GMM estimator of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 159(2), pages 303-319, December.
    22. Lee, Lung-fei, 2007. "GMM and 2SLS estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 137(2), pages 489-514, April.
    23. Lee, Lung-fei & Liu, Xiaodong, 2010. "Efficient Gmm Estimation Of High Order Spatial Autoregressive Models With Autoregressive Disturbances," Econometric Theory, Cambridge University Press, vol. 26(1), pages 187-230, February.
    24. Lung-fei Lee, 2003. "Best Spatial Two-Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 307-335.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhenlin Yang, 2018. "Bootstrap LM tests for higher-order spatial effects in spatial linear regression models," Empirical Economics, Springer, vol. 55(1), pages 35-68, August.
    2. Yong Bao & Xiaotian Liu & Lihong Yang, 2020. "Indirect Inference Estimation of Spatial Autoregressions," Econometrics, MDPI, vol. 8(3), pages 1-26, September.
    3. Baltagi, Badi H. & Pirotte, Alain & Yang, Zhenlin, 2021. "Diagnostic tests for homoskedasticity in spatial cross-sectional or panel models," Journal of Econometrics, Elsevier, vol. 224(2), pages 245-270.
    4. R. Kelley Pace & Raffaella Calabrese, 2022. "Ignoring Spatial and Spatiotemporal Dependence in the Disturbances Can Make Black Swans Appear Grey," The Journal of Real Estate Finance and Economics, Springer, vol. 65(1), pages 1-21, July.
    5. Abhimanyu Gupta & Xi Qu, 2021. "Consistent specification testing under spatial dependence," Papers 2101.10255, arXiv.org, revised Aug 2022.
    6. Philipp Otto & Osman Dou{g}an & Suleyman Tac{s}p{i}nar & Wolfgang Schmid & Anil K. Bera, 2023. "Spatial and Spatiotemporal Volatility Models: A Review," Papers 2308.13061, arXiv.org.
    7. Ye Yang & Osman Doğan & Süleyman Taşpınar, 2021. "Fast estimation of matrix exponential spatial models," Journal of Spatial Econometrics, Springer, vol. 2(1), pages 1-50, December.
    8. Zhang, Yuanqing & Feng, Shuhui & Jin, Fei, 2019. "QML estimation of the matrix exponential spatial specification panel data model with fixed effects and heteroskedasticity," Economics Letters, Elsevier, vol. 180(C), pages 1-5.
    9. Jin, Fei & Lee, Lung-fei, 2018. "Irregular N2SLS and LASSO estimation of the matrix exponential spatial specification model," Journal of Econometrics, Elsevier, vol. 206(2), pages 336-358.
    10. Bing Su & Fukang Zhu & Ke Zhu, 2023. "Statistical inference for the logarithmic spatial heteroskedasticity model with exogenous variables," Papers 2301.06658, arXiv.org.
    11. Ye Yang & Osman Dogan & Suleyman Taspinar & Fei Jin, 2023. "A Review of Cross-Sectional Matrix Exponential Spatial Models," Papers 2311.14813, arXiv.org.
    12. Jin, Fei & Lee, Lung-fei, 2019. "GEL estimation and tests of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 208(2), pages 585-612.
    13. Kong, Wei & Yang, Kai, 2021. "Efficient GMM estimation of a spatial autoregressive model with an endogenous spatial weights matrix," Economics Letters, Elsevier, vol. 208(C).
    14. Liu, Tuo & Lee, Lung-fei, 2019. "A likelihood ratio test for spatial model selection," Journal of Econometrics, Elsevier, vol. 213(2), pages 434-458.
    15. Michael Pfarrhofer & Philipp Piribauer, 2018. "Flexible shrinkage in high-dimensional Bayesian spatial autoregressive models," Papers 1805.10822, arXiv.org.
    16. Bo Pieter Johannes Andree & Francisco Blasques & Eric Koomen, 2017. "Smooth Transition Spatial Autoregressive Models," Tinbergen Institute Discussion Papers 17-050/III, Tinbergen Institute.

    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. Doğan, Osman & Taşpınar, Süleyman, 2013. "GMM estimation of spatial autoregressive models with moving average disturbances," Regional Science and Urban Economics, Elsevier, vol. 43(6), pages 903-926.
    2. David M. Drukker & Peter Egger & Ingmar R. Prucha, 2013. "On Two-Step Estimation of a Spatial Autoregressive Model with Autoregressive Disturbances and Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 686-733, August.
    3. Doğan, Osman & Taşpınar, Süleyman, 2014. "Spatial autoregressive models with unknown heteroskedasticity: A comparison of Bayesian and robust GMM approach," Regional Science and Urban Economics, Elsevier, vol. 45(C), pages 1-21.
    4. Zhang, Xinyu & Yu, Jihai, 2018. "Spatial weights matrix selection and model averaging for spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 203(1), pages 1-18.
    5. Badi H. Baltagi & Peter H. Egger & Michaela Kesina, 2022. "Bayesian estimation of multivariate panel probits with higher‐order network interdependence and an application to firms' global market participation in Guangdong," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(7), pages 1356-1378, November.
    6. Liu, Shew Fan & Yang, Zhenlin, 2015. "Modified QML estimation of spatial autoregressive models with unknown heteroskedasticity and nonnormality," Regional Science and Urban Economics, Elsevier, vol. 52(C), pages 50-70.
    7. Debarsy, Nicolas & Ertur, Cem, 2019. "Interaction matrix selection in spatial autoregressive models with an application to growth theory," Regional Science and Urban Economics, Elsevier, vol. 75(C), pages 49-69.
    8. Wang, Wei & Lee, Lung-Fei & Bao, Yan, 2018. "GMM estimation of the spatial autoregressive model in a system of interrelated networks," Regional Science and Urban Economics, Elsevier, vol. 69(C), pages 167-198.
    9. Liu, Xiaodong & Saraiva, Paulo, 2015. "GMM estimation of SAR models with endogenous regressors," Regional Science and Urban Economics, Elsevier, vol. 55(C), pages 68-79.
    10. Jin, Fei & Lee, Lung-fei, 2019. "GEL estimation and tests of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 208(2), pages 585-612.
    11. Liangjun Su & Xi Qu, 2017. "Specification Test for Spatial Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 572-584, October.
    12. William C. Horrace & Hyunseok Jung & Shane Sanders, 2022. "Network Competition and Team Chemistry in the NBA," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 35-49, January.
    13. Nicolas DEBARSY & Cem ERTUR, 2016. "Interaction matrix selection in spatial econometrics with an application to growth theory," LEO Working Papers / DR LEO 2172, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    14. Pesaran, M. Hashem & Yang, Cynthia Fan, 2021. "Estimation and inference in spatial models with dominant units," Journal of Econometrics, Elsevier, vol. 221(2), pages 591-615.
    15. Shew Fan Liu & Zhenlin Yang, 2015. "Asymptotic Distribution and Finite Sample Bias Correction of QML Estimators for Spatial Error Dependence Model," Econometrics, MDPI, vol. 3(2), pages 1-36, May.
    16. 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.
    17. Jin, Fei & Lee, Lung-fei, 2012. "Approximated likelihood and root estimators for spatial interaction in spatial autoregressive models," Regional Science and Urban Economics, Elsevier, vol. 42(3), pages 446-458.
    18. Jin, Fei & Lee, Lung-fei, 2020. "Asymptotically efficient root estimators for spatial autoregressive models with spatial autoregressive disturbances," Economics Letters, Elsevier, vol. 194(C).
    19. Lee, Lung-fei & Yu, Jihai, 2014. "Efficient GMM estimation of spatial dynamic panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 180(2), pages 174-197.

    More about this item

    Keywords

    Spatial autocorrelation; MESS; QML; GMM; Heteroskedasticity; Delta method; FDI;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • F14 - International Economics - - Trade - - - Empirical Studies of Trade
    • F21 - International Economics - - International Factor Movements and International Business - - - International Investment; Long-Term Capital Movements

    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:eee:econom:v:188:y:2015:i:1:p:1-21. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.