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Semiparametric Estimation and Testing of Smooth Coefficient Spatial Autoregressive Models

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  • Malikov, Emir
  • Sun, Yiguo

Abstract

This paper considers a flexible semiparametric spatial autoregressive (mixed-regressive) model in which unknown coefficients are permitted to be nonparametric functions of some contextual variables to allow for potential nonlinearities and parameter heterogeneity in the spatial relationship. Unlike other semiparametric spatial dependence models, ours permits the spatial autoregressive parameter to meaningfully vary across units and thus allows the identification of a neighborhood-specific spatial dependence measure conditional on the vector of contextual variables. We propose several (locally) nonparametric GMM estimators for our model. The developed two-stage estimators incorporate both the linear and quadratic orthogonality conditions and are capable of accommodating a variety of data generating processes, including the instance of a pure spatially autoregressive semiparametric model with no relevant regressors as well as multiple partially linear specifications. All proposed estimators are shown to be consistent and asymptotically normal. We also contribute to the literature by putting forward two test statistics to test for parameter constancy in our model. Both tests are consistent.

Suggested Citation

  • Malikov, Emir & Sun, Yiguo, 2017. "Semiparametric Estimation and Testing of Smooth Coefficient Spatial Autoregressive Models," MPRA Paper 77253, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:77253
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    Cited by:

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    2. Alberto Gude & Inmaculada Álvarez & Luis Orea, 2018. "Heterogeneous spillovers among Spanish provinces: a generalized spatial stochastic frontier model," Journal of Productivity Analysis, Springer, vol. 50(3), pages 155-173, December.
    3. Xuan Liang & Jiti Gao & Xiaodong Gong, 2021. "Semiparametric Spatial Autoregressive Panel Data Model with Fixed Effects and Time-Varying Coefficients," Monash Econometrics and Business Statistics Working Papers 5/21, Monash University, Department of Econometrics and Business Statistics.
    4. Huang, Danyang & Wang, Feifei & Zhu, Xuening & Wang, Hansheng, 2020. "Two-mode network autoregressive model for large-scale networks," Journal of Econometrics, Elsevier, vol. 216(1), pages 203-219.
    5. Orea, Luis & Álvarez, Inmaculada C., 2019. "Spatial Production Economics," Efficiency Series Papers 2019/06, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    6. Shunan Zhao & Man Jin & Subal C. Kumbhakar, 2021. "Estimation of firm productivity in the presence of spillovers and common shocks," Empirical Economics, Springer, vol. 60(6), pages 3135-3170, June.
    7. Sun, Yiguo & Malikov, Emir, 2018. "Estimation and inference in functional-coefficient spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 203(2), pages 359-378.
    8. Xuan Liang & Jiti Gao & Xiaodong Gong, 2019. "Time-Varying Coefficient Spatial Autoregressive Panel Data Model with Fixed Effects," Monash Econometrics and Business Statistics Working Papers 26/19, Monash University, Department of Econometrics and Business Statistics.

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    More about this item

    Keywords

    Consistent Test; Constrained Estimation; Local Linear Fitting; Nonparametric GMM; Partially Linear; Quadratic Moments; SAR; Spatial Lag;
    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
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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