Deep Learning Based Estimation in Higher-Order Semiparametric Additive Stochastic Frontier Model

Wanqing Wu, Yunquan Song () and Zhijian Wang
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Wanqing Wu: China University of Petroleum
Yunquan Song: China University of Petroleum
Zhijian Wang: Xiamen University

Networks and Spatial Economics, 2025, vol. 25, issue 3, No 9, 793-845

Abstract: Abstract In this paper, we propose a higher-order semiparametric additive spatial stochastic frontier model that is linear in the spatial lag on the dependent variable, while the functional form of the frontier is nonparametric. The application of deep neural networks to this model is investigated and an effective two-step estimation process is proposed. In the first step, we introduce a Higher-order spatial stochastic frontier neural network (HSSFNN) to fit the model, making full use of the powerful generalisation ability of artificial neural network models. And in the second step, we use the maximum likelihood estimation to estimate the remaining model parameters. In the Monte Carlo simulation experiments, by comparing with the B-spline-based GMM method, the multilayer perceptron (MLP) method, and the maximum likelihood estimation (MLE) method, it was demonstrated that the proposed method has superior performance in estimation and prediction, partly addressing the black box issue in deep learning models. The results of empirical analysis reveal that the proposed method is effective in the practice of chemical enterprises in China.

Keywords: Higher-order semiparametric additive spatial stochastic frontier models; Technical efficiency; Maximum likelihood estimation; Deep learning; Neural networks (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11067-025-09682-2

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