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Indirect inference in spatial autoregression

Author

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  • Maria Kyriacou
  • Peter C. B. Phillips
  • Francesca Rossi

Abstract

Ordinary least‐squares (OLS) is well known to produce an inconsistent estimator of the spatial parameter in pure spatial autoregression (SAR). In this paper, we explore the potential of indirect inference to correct the inconsistency of OLS. Under broad conditions, it is shown that indirect inference (II) based on OLS produces consistent and asymptotically normal estimates in pure SAR regression. The II estimator used here is robust to departures from normal disturbances and is computationally straightforward compared with quasi‐maximum likelihood (QML). Monte Carlo experiments based on various specifications of the weight matrix show that: (a) the II estimator displays little bias even in very small samples and gives overall performance that is comparable to the QML while raising variance in some cases; (b) II applied to QML also enjoys good finite sample properties; and (c) II shows robust performance in the presence of heavy‐tailed error distributions.

Suggested Citation

  • Maria Kyriacou & Peter C. B. Phillips & Francesca Rossi, 2017. "Indirect inference in spatial autoregression," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 168-189, June.
    • Handle: RePEc:wly:emjrnl:v:20:y:2017:i:2:p:168-189
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    File URL: http://hdl.handle.net/10.1111/ectj.12084
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    Citations

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    Cited by:

    1. Vicky Fasen‐Hartmann & Sebastian Kimmig, 2020. "Robust estimation of stationary continuous‐time arma models via indirect inference," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 620-651, September.
    2. Kyriacou, Maria & Phillips, Peter C.B. & Rossi, Francesca, 2023. "Continuously Updated Indirect Inference In Heteroskedastic Spatial Models," Econometric Theory, Cambridge University Press, vol. 39(1), pages 107-145, February.
    3. Yong Bao & Xiaotian Liu & Lihong Yang, 2020. "Indirect Inference Estimation of Spatial Autoregressions," Econometrics, MDPI, vol. 8(3), pages 1-26, September.
    4. Francesca Rossi & Peter M. Robinson, 2020. "Higher-Order Least Squares Inference for Spatial Autoregressions," Working Papers 04/2020, University of Verona, Department of Economics.
    5. Bonev, Petyo & Matthieu Glachant & Magnus Söderberg, 2020. "Implicit Yardstick Competition," Economics Working Paper Series 2009, University of St. Gallen, School of Economics and Political Science.
    6. Rossi, Francesca & Robinson, Peter M., 2023. "Higher-order least squares inference for spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 244-269.
    7. Lee, Jungyoon & Robinson, Peter M., 2020. "Adaptive inference on pure spatial models," Journal of Econometrics, Elsevier, vol. 216(2), pages 375-393.
    8. Bao, Yong, 2024. "Estimating spatial autoregressions under heteroskedasticity without searching for instruments," Regional Science and Urban Economics, Elsevier, vol. 106(C).
    9. Carlo Grillenzoni, 2024. "Forecasting Lattice and Point Spatial Data: Comparison of Unilateral and Multilateral SAR Models," Forecasting, MDPI, vol. 6(3), pages 1-18, August.
    10. Marcus J. Chambers & Maria Kyriacou, 2018. "Jackknife Bias Reduction in the Presence of a Near-Unit Root," Econometrics, MDPI, vol. 6(1), pages 1-28, March.
    11. Bonev, Petyo & Glachant, Matthieu & Söderberg, Magnus, 2018. "A Mechanism for Institutionalised Threat of Regulation: Evidence from the Swedish District Heating Market," Economics Working Paper Series 1805, University of St. Gallen, School of Economics and Political Science.
    12. Bonev, Petyo & Glachant, Matthieu & Söderberg, Magnus, 2022. "Implicit yardstick competition between heating monopolies in urban areas: Theory and evidence from Sweden," Energy Economics, Elsevier, vol. 109(C).
    13. Federico Martellosio & Grant Hillier, 2019. "Adjusted QMLE for the spatial autoregressive parameter," Papers 1909.08141, arXiv.org.
    14. Yong Bao, 2021. "Indirect Inference Estimation of a First-Order Dynamic Panel Data Model," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 79-98, December.
    15. Jungyoon Lee & Peter M Robinson, 2018. "Adaptive Inference on Pure Spatial Models," STICERD - Econometrics Paper Series 596, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    16. J. Paul Elhorst, 2022. "The dynamic general nesting spatial econometric model for spatial panels with common factors: Further raising the bar," Review of Regional Research: Jahrbuch für Regionalwissenschaft, Springer;Gesellschaft für Regionalforschung (GfR), vol. 42(3), pages 249-267, December.
    17. Martellosio, Federico & Hillier, Grant, 2020. "Adjusted QMLE for the spatial autoregressive parameter," Journal of Econometrics, Elsevier, vol. 219(2), pages 488-506.

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