EM Algorithm for the Stochastic Frontier Model

EM演算法在隨機邊界模型之應用

張曉芬(Hsiao-Fen Chang)

《真理財經學報》 15期 (2006/12) Pp. 109-122

https://doi.org/10.29963/TOJEB.200612.0005

摘要

一個隨機邊界模型定義如下：
y(下标 it)=β0+x(下标 it)β+v(下标 it)-µ(下标 i) i=1,...N；t=1,...,T ε≡v(下标 it)-U(下标 i)
y(下标 it)是第i公司，第t個時間點的生產值取對數值(logarithm)。x(下标 it)是投入變數的向量。效率這個要素(efficiency component µ(下标 i)≥0)是一個非負的常態慨。無效率是只公司的產出在邊界以下。v(下标 it)是一個不可觀測的隨機變數。模型的假設是：
v(下标 it)~N(0,σ^2) µ(下标 i)~N(上标 +)(0,σ(上标 2 下标 µ))在建造各別生產效率µ(下标 i)的信賴區間有幾種估計過程：
1)JLMS和MC方法
2)MCB方法
本論文將應用EM演算法來求σ(上标 2 下标 *)和µ(上标 * 下标 it)的最大概似估計值。

關鍵字

隨機邊界模型 ； EM演算法 ； 單調遞減＼遞增函數

並列摘要

A stochastic frontier model in a panel data is written as
y(subscript it) =β0+x(subscript it)β+v(subscript it)-µ(subscript t) i=1,...N; t = 1,...,T ε(subscript it)≡v(subscript it)-µ(subscript t)
Where y(subscript it) is the logarithm of the output of the ith firm and tth time periods, x(subscript it) is a vector of input. The efficiency component (µ(subscript i)≥0) is a one-sided, non-negative error, derived from a half-normal distribution. Technical inefficiency exists to the extent that a firm's output lies beneath the frontier. The stochastic component v(subscript it) is an unobservable random variable (a statistical noise). The model assume the following:
v(subscript it)~N(0,σ^2) µ1~N(superscript +)(0,σ(superscript 2 subscript µ)
There are several estimation techniques procedures about construction of confidence intervals of the individual producer's inefficiency µ(subscript i)
1) JLMS and MC method
2) MCB method
In this paper, we consider the application of the EM algorithm for ML estimation of the parameters and µ(superscript * subscript it) and σ(superscript 2 subscript *).

並列關鍵字

A stochastic frontier model ； EM algorithm ； confidence intervals ； monotone decreasing\increasing function

參考文獻

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