應用Beta迴歸模型於第二階段DEA效率分析：以臺灣電信服務公司為例

Beta Regression Models for Second Stage DEA Efficiency Analyses: Evidence from Taiwan Telecommunication Companies

吳光耀(Kuang-Yao Wu) ； 謝志光(Chih-Kuang Hsieh)

《管理研究學報》 14卷1期 (2014/06) Pp. 65-94

https://doi.org/10.6626/MR.2014.14(1).03

摘要

資料包絡分析（DEA）法一般用於評估相似組織間的相對效率，隨後的第二階段分析中，通常採用迴歸方法來探討可能影響效率值的情境獨立變數。典型DEA模型所得的效率值界定在（0,1］半封閉區間，且其分配可能呈現不對稱與機率值集結於1的現象。但既有常用的一些迴歸方法（例如線性、Tobit設限模式）則忽視這些特徵，以致於容易產生偏誤或不一致的估計量。其實，Beta分配最適合表達介於0到1區間的應變數，並可呈現多樣的偏峰型態及包容變異數不齊一，惟其應用於第二階段DEA效率分析的研究似乎闕如。本研究目的為實證Beta系列模型在分析影響效率因素的可應用性，並以臺灣電信服務公司為數值案例，在R軟體的gamlss平台下比較各種模型的適用性，包括線性、設限、截斷、Beta及InflatedBeta迴歸。案例實證結果指出InflatedBeta模型最為適用，其迴歸結果也合理地解釋產業經濟學理論：產業外部環境、產業市場結構及企業管理行為對於營運效率的表現具影響性。此外，案例也顯示了線性、設限與截斷等三種迴歸之適配值的出界問題。

關鍵字

Beta分配 ； 兩階段資料包絡分析 ； 電信服務產業 ； 0到1區間應變數 ； 具位置尺度形狀參數的廣義加法模型

並列摘要

Data envelopment analysis (DEA) is commonly used to evaluate the relative efficiency of a number of similar organizational units. Often, in the second stage, a regression methodology is used to analyze a set of contextual independent variables which may impact the performance. Typically, the DEA efficiency scores are measured in the half-closed interval (0,1], and the normalization of its distribution is likely to be asymmetrical with the probability mass at 1. However, these features are ignored in regression methods commonly used (such as linear or Tobit censored models), thereby resulting in a biased or inconsistent estimator. One of the most suitable candidates for modeling dependent variables valued from 0 to 1 is the class of beta distributions, which naturally incorporates features such as skewness and heteroskedasticity. Nevertheless, the Beta models seem to be rarely used in the second stage DEA. This study aims to demonstrate the applicability of the Beta regressions to examine exogenous factors affecting efficiency. Taiwan telecommunication companies are employed as a numerical example, where a variety of regression techniques, including linear, censored, truncated, Beta and inflated Beta, developed in gamlss package of R software are used for comparison. Empirical results indicate that inflated Beta is the most suitable regression model. It is shown by inflated Beta that the factors of external environment, market structure and market conduct have a significant impact on operating efficiency. It is also found in linear, censored or truncated model that some fitted values are out of bound.

並列關鍵字

Beta Distribution ； Two-Stage Data Envelopment Analysis (DEA) ； Telecommunication Industry ； Proportion Dependent Variables ； Generalized Additive Models for Location ； Scale and Shape (GAMLSS)