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Bayesian Estimation of the Semiparametric Spatial Lag Model

Author

Listed:
  • Kunming Li

    (College of Economics and Management, Fujian Agriculture and Forestry University, Fuzhou 350002, China)

  • Liting Fang

    (School of Economics and Management, Fuzhou University, Fuzhou 350108, China)

Abstract

This paper proposes a semiparametric spatial lag model and develops a Bayesian estimation method for this model. In the estimation of the model, the paper combines Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm, random walk Metropolis sampler, and Gibbs sampling techniques to sample all the parameters. The paper conducts numerical simulations to validate the proposed Bayesian estimation theory using a numerical example. The simulation results demonstrate satisfactory estimation performance of the parameter part and the fitting performance of the nonparametric function under different spatial weight matrix settings. Furthermore, the paper applies the constructed model and its estimation method to an empirical study on the relationship between economic growth and carbon emissions in China, illustrating the practical application value of the theoretical results.

Suggested Citation

  • Kunming Li & Liting Fang, 2024. "Bayesian Estimation of the Semiparametric Spatial Lag Model," Mathematics, MDPI, vol. 12(14), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2289-:d:1440307
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    References listed on IDEAS

    as
    1. Kang, Emily L. & Cressie, Noel, 2011. "Bayesian Inference for the Spatial Random Effects Model," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 972-983.
    2. Malikov, Emir & Sun, Yiguo, 2017. "Semiparametric estimation and testing of smooth coefficient spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 199(1), pages 12-34.
    3. York, Richard & Rosa, Eugene A. & Dietz, Thomas, 2003. "STIRPAT, IPAT and ImPACT: analytic tools for unpacking the driving forces of environmental impacts," Ecological Economics, Elsevier, vol. 46(3), pages 351-365, October.
    4. Gelfand, Alan E. & Kottas, Athanasios & MacEachern, Steven N., 2005. "Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1021-1035, September.
    5. Su, Liangjun & Jin, Sainan, 2010. "Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 157(1), pages 18-33, July.
    6. Emir Malikov & Yiguo Sun & Diane Hite, 2019. "(Under)Mining local residential property values: A semiparametric spatial quantile autoregression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(1), pages 82-109, January.
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