基於神經網路的隨機前沿分析方法

Abstract

不管是在經濟學還是在業界中，效率與產能之間的關係一直都是大家想洞悉的主題之一，而其中一個方式就是隨機前沿分析（stochastic frontier analysis）。然而，這種傳統方法存在著本質上的限制，因為它們是線性模型而無法捕捉在資料中潛在的非線性關係。相比之下，基於神經網路（neural network）的方法為提高前沿分析的準確性和適應性提供了一個有潛力的途徑。然而，為了符合生產前沿的定義，仍然需要對模型施加一些限制，例如生產函數應該要是擬凸函數(quasi-concave function)。在本論文中，我們引入一種新的方法來彌合這一差距：通過對損失函數施加凹性正則化，訓練基於神經網絡的隨機生產前沿模型。為了評估我們的方法，我們在一個模擬數據集上進行了實驗，該數據集包括效率和統計噪音。實驗結果顯示，使用凹性正則化在測試情境下始終改善了估計邊界的凹性。在複雜的測試情境中，我們的方法表現超越了其他模型。然而，在簡單的情境下，像Stata這樣的傳統工具仍然具有競爭力。

The pursuit of efficiency and productivity improvement has been a fundamental goal in various fields, ranging from economics to industrial engineering. One of the approaches to capture and analyze the production processes is stochastic frontier analysis (Aigner et al., 1977). However, conventional methods exhibit limitations, primarily due to their inability to capture complex nonlinearities. In contrast, neural network-based approaches present a promising avenue for elevating the accuracy of frontier estimation. However, to conform the production frontier's definition, some constraints still need to be imposed on the model, such as the concavity of inputs. In this thesis, we bridge this gap by introducing a novel approach: training a neural network-based stochastic production frontier model by imposing the concavity regularization to loss function. To evaluate our approach, we conduct an experiment on a simulated dataset adopted technical inefficiency and statistical noise. Our approach shows that the imposition of concavity regularization consistently improves the concavity of estimated frontiers across tested scenarios. In more complex scenarios, our approach demonstrates remarkable performance surpassing other models. However, in simpler scenarios, traditional tools like Stata remain competitive.