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Large Sample Properties of the Matrix Exponential Spatial Specification with an Application to FDI

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  • Nicolas DEBARSY
  • Fei JIN
  • Lung-fei LEE

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 model 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.
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Suggested Citation

  • Nicolas DEBARSY & Fei JIN & Lung-fei LEE, 2014. "Large Sample Properties of the Matrix Exponential Spatial Specification with an Application to FDI," LEO Working Papers / DR LEO 2244, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    • Handle: RePEc:leo:wpaper:2244
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    Citations

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    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.

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    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

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