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Inference on higher-order spatial autoregressive models with increasingly many parameters

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  • Gupta, Abhimanyu
  • Robinson, Peter M.

Abstract

This paper develops consistency and asymptotic normality of parameter estimates for a higher-order spatial autoregressive model whose order, and number of regressors, are allowed to approach infinity slowly with sample size. Both least squares and instrumental variables estimates are examined, and the permissible rate of growth of the dimension of the parameter space relative to sample size is studied. Besides allowing the number of parameters to increase with the data, this has the advantage of accommodating some asymptotic regimes that are suggested by certain spatial settings, several of which are discussed. A small empirical example is also included, and a Monte Carlo study analyses various implications of the theory in finite samples.

Suggested Citation

  • Gupta, Abhimanyu & Robinson, Peter M., 2015. "Inference on higher-order spatial autoregressive models with increasingly many parameters," Journal of Econometrics, Elsevier, vol. 186(1), pages 19-31.
  • Handle: RePEc:eee:econom:v:186:y:2015:i:1:p:19-31
    DOI: 10.1016/j.jeconom.2014.12.008
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    Cited by:

    1. Gupta, Abhimanyu & Robinson, Peter M., 2018. "Pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension," Journal of Econometrics, Elsevier, vol. 202(1), pages 92-107.
    2. Badi H. Baltagi & Sophia Ding & Peter H. Egger, 2020. "A Panel Data Model with Generalized Higher-Order Networks Effects," CESifo Working Paper Series 8653, CESifo.
    3. FUJII Daisuke, 2016. "Shock Propagations in Granular Networks," Discussion papers 16057, Research Institute of Economy, Trade and Industry (RIETI).
    4. Gopal K. Basak & Arnab Bhattacharjee & Samarjit Das, 2018. "Causal ordering and inference on acyclic networks," Empirical Economics, Springer, vol. 55(1), pages 213-232, August.
    5. Ayden Higgins & Federico Martellosio, 2019. "Shrinkage Estimation of Network Spillovers with Factor Structured Errors," Papers 1909.02823, arXiv.org, revised Jul 2021.
    6. Jakub Olejnik & Alicja Olejnik, 2020. "QML estimation with non-summable weight matrices," Journal of Geographical Systems, Springer, vol. 22(4), pages 469-495, October.
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    8. Arnab Bhattacharjee & Sudipto Roy, 2019. "Abnormal Returns or Mismeasured Risk? Network Effects and Risk Spillover in Stock Returns," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 12(2), pages 1-13, March.
    9. Abhimanyu Gupta, 2020. "Efficient closed-form estimation of large spatial autoregressions," Papers 2008.12395, arXiv.org, revised May 2021.
    10. Gupta, Abhimanyu & Robinson, Peter M., 2018. "Pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension," Journal of Econometrics, Elsevier, vol. 202(1), pages 92-107.
    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. Li, Kunpeng, 2017. "Fixed-effects dynamic spatial panel data models and impulse response analysis," Journal of Econometrics, Elsevier, vol. 198(1), pages 102-121.
    13. Kwok, Hon Ho, 2019. "Identification and estimation of linear social interaction models," Journal of Econometrics, Elsevier, vol. 210(2), pages 434-458.
    14. Abhimanyu Gupta & Xi Qu, 2021. "Consistent specification testing under spatial dependence," Papers 2101.10255, arXiv.org, revised Aug 2021.
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    16. Gupta, Abhimanyu & Kokas, Sotirios & Michaelides, Alexander, 2017. "Credit Market Spillovers: Evidence from a Syndicated Loan Market Network," CEPR Discussion Papers 12424, C.E.P.R. Discussion Papers.
    17. Gupta, Abhimanyu, 2019. "Estimation Of Spatial Autoregressions With Stochastic Weight Matrices," Econometric Theory, Cambridge University Press, vol. 35(2), pages 417-463, April.
    18. Ma, Yingying & Lan, Wei & Zhou, Fanying & Wang, Hansheng, 2020. "Approximate least squares estimation for spatial autoregressive models with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    19. Kelejian, Harry H. & Piras, Gianfranco, 2014. "Estimation of spatial models with endogenous weighting matrices, and an application to a demand model for cigarettes," Regional Science and Urban Economics, Elsevier, vol. 46(C), pages 140-149.
    20. Gupta, Abhimanyu, 2018. "Nonparametric specification testing via the trinity of tests," Journal of Econometrics, Elsevier, vol. 203(1), pages 169-185.
    21. Han, Xiaoyi & Hsieh, Chih-Sheng & Lee, Lung-fei, 2017. "Estimation and model selection of higher-order spatial autoregressive model: An efficient Bayesian approach," Regional Science and Urban Economics, Elsevier, vol. 63(C), pages 97-120.
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    More about this item

    Keywords

    Spatial autoregression; Increasingly many parameters; Central limit theorem; Rate of convergence; Spatial panel data;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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