六成分追蹤隨機邊界模型

Six-Component Panel Stochastic Frontier Model

王邦瑜(Pang-Yu Wang)

指導教授 ： 王泓仁 ； 陳南光

國立臺灣大學/社會科學院/經濟學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201702234

摘要

本文在以下兩方面拓展了 Polacheck and Yoon (1996) 的架構，並建構一個六成分追蹤隨機邊界模型 (以下簡稱本模型)：一、本模型多包含了具隨機效果 (random effect) 的個人異質性 (individual heterogeneity)，二、本模型揭示如何將雙層架構下不隨時間變動的不效率效果 (time-invariant inefficiency effects) 判別 (identify) 出來。Polacheck and Yoon (1996) 雖有包括不隨時間變動的不效率效果，但在估計上卻無法判別出來。
我們採用 Kumbhakar et al. (2014) 的兩階段估計法來估計模型。該法的優點在於易於估計，而且不需要六個隨機變數的卷積 (convoluted) 機率密度函數的封閉解 (closed form)。對於不效率項 (inefficiency terms)，我們考慮三種分配假設：截斷常態分佈 (truncated-normal distribution)、半常態分佈 (half-normal distribution)，與指數分佈 (exponential distribution)。當分配假設為截斷常態分佈時，本文在文獻中是第一篇推導出關鍵的機率密度函數，並在第二階段的估計中使用；我們也推導了 Jondrow et al. (1982) 的不效率指標 (inefficiency index) 與 Battese and Coelli (1988) 的效率指標 (efficiency index)。
在本模型的架構下，許多其他的隨機邊界模型是本模型的特例。這代表本模型在文獻上可以被看作是較為一般化的情形。
最後，在假設所有的不效率項服從指數分配的形下，我們提供了蒙地卡羅模擬以觀察本模型估計值的誤差與均方差 (mean squared error)。

關鍵字

雙層隨機邊界模型 ； 截斷常態分佈 ； 最大概似估計法 ； 隨機效果 ； 一般最小平方估計法 ； 追蹤資料

並列摘要

In this thesis, we propose a six-component panel stochastic frontier (SF) model that extends the two-tier panel SF model of Polacheck and Yoon (1996) in two major ways: (1) It includes individual heterogeneity which is treated as a random effect. (2) It shows how the time-invariant inefficiency effects in both of the tiers can be identified. The model of Polacheck and Yoon (1996) includes the time-invariant inefficiency effects, but they are not identified in the estimation.
We use the two-step estimation approach of Kumbhakar et al. (2014) to estimate the model. The approach is easy to conduct and does not require a closed form of the convoluted density of all the model's six random components. We consider three distributional assumptions on the inefficiency terms: truncated-normal, half-normal, and exponential. For the case of the truncated-normal, we are the first in the literature to derive key density functions which are used in the second step of the estimation; we also derive the (in)efficiency indexes of Jondrow et al. (1982) and Battese and Coelli (1988) for such a model.
Our model nests many of the existing SF models as special cases. This indicates that our model is one of the more general models in the literature.
Finally, we present Monte Carlo simulations to observe biases and mean squared errors of the estimates in our model with two-tier normal-exponential specifications.

並列關鍵字

Two-Tier Stochastic Frontier Model ； Truncated-Normal Distribution ； Maximum Likelihood Estimation ； Random Effect ； Generalized Least Square (GLS) Estimation ； Panel Data

參考文獻

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