<p>Deep learning technology has been successfully applied in multiple fields, especially in the area of statistical inference. The stochastic frontier model, as a main method for measuring technical efficiency, has always received extensive attention. This paper creatively combines the two. We propose a nonparametric spatial autoregressive stochastic frontier model that takes into account both nonparametric endogenous spatial spillover effects and nonparametric additive frontier functions. We adopt deep neural networks to capture endogenous nonparametric spatial effects and fit the model, construct instrumental variables to obtain consistent estimators of nonparametric spatial spillover effect terms, and apply moment estimation methods to estimate model parameters. This method not only enhances the capacity to identify spatial effects, but also enables accurate estimation of model parameters and technical efficiency. Through simulation experiments and the application of actual data, we prove the efficacy and practicality of the proposed method.</p>

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Deep Learning for Spatial Additive Stochastic Frontier Model with Nonparametric Spatial Effects

  • Jianxin Lv,
  • Yunquan Song,
  • Zhijian Wang

摘要

Deep learning technology has been successfully applied in multiple fields, especially in the area of statistical inference. The stochastic frontier model, as a main method for measuring technical efficiency, has always received extensive attention. This paper creatively combines the two. We propose a nonparametric spatial autoregressive stochastic frontier model that takes into account both nonparametric endogenous spatial spillover effects and nonparametric additive frontier functions. We adopt deep neural networks to capture endogenous nonparametric spatial effects and fit the model, construct instrumental variables to obtain consistent estimators of nonparametric spatial spillover effect terms, and apply moment estimation methods to estimate model parameters. This method not only enhances the capacity to identify spatial effects, but also enables accurate estimation of model parameters and technical efficiency. Through simulation experiments and the application of actual data, we prove the efficacy and practicality of the proposed method.