隨機邊界模型中個體特定技術效率的預測：兩個預測量的比較

Prediction of Individual-Specific Technical Efficiencies in the Stochastic Frontier Model: A Comparison of Two Predictors

張曦(Hsi Chang)

指導教授 ： 王泓仁

國立臺灣大學/社會科學院/經濟學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201902493

摘要

在隨機邊界模型的文獻中，如何對於每一個觀察樣本的效率進行估計是一項很重要的挑戰。目前文獻中廣泛使用的方法由Jondrow 等人（1982）提出（以下稱為JLMS），透過給定個體的組合誤差觀察值，計算模型當中效率項的條件期望值（E(ui|ϵi)）來估計其個體的不效率程度（ui）。較早期的隨機邊界模型中，由於假設效率項的機率分配為同質性，需要透過此方法才能得到個體的效率估計。然而，當隨機前沿模型擴展為具有異質性的效率機率分配時，效率項之無條件期望值（E(ui)）即可做為個體的效率估計量，簡易好用，不一定需要使用複雜的條件期望值。目前文獻中，採用貝氏估計方法的文章多採用無條件期望值估計量，而使用最大概似估計方法的文章則多採用條件期望值估計量，然而文獻中對於爲什麼採用特定估計量，並沒有提出具體的理由。
在本文中，我們首先對上述兩種期望值的名稱、符號做釐清，提出了不同於既有文獻的主張。然後我們探討其統計特性，包括一致性、偏誤性、及平均方差（mean square error；MSE）。我們發現，若不考慮估計效果（estimation effect），JLMS 估計值一定有較小的MSE；我們從訊息–雜訊比的角度，提出了據理論根據的解釋。若考慮了估計效果，則理論上兩者的MSE 大小不易比較。因此，我們再以模擬的方式探討數值差異。
在另一方面，若考慮樣本外預期，則只有無條件期望值估計量能被應用，而這也影響了我們對無效率邊際效果計算的選擇：對於Wang（2002）與Kumbhakar 和Sun（2013）提出的兩種邊際效應估計方法，我們認爲前者的方法更為合理。

關鍵字

隨機邊界模型 ； 截斷常態分佈 ； 生產效率 ； 個體技術效率 ； 最大概似估計法 ； 橫斷資料

並列摘要

In a typical stochastic frontier study, one of the important goals is to estimate the observation-specific technical inefficiency. A widely used predictor is the mean of the inefficiency term conditional on the composed error, E(ui|ϵi), proposed by Jondrow, et al. (1982). With the homoscedastic inefficiency, it is necessary to use the JLMS predictor since the mean of the inefficiency term is constant. However, when the stochastic frontier model expands to accommodate heteroscedasticity in the inefficiency term, the unconditional (E(ui)) is able to produce individual-specific predictor for inefficiency, and the computation of this predictor is much more easy. The choice of the predictors seems to be arbitrary in the literature. For instance, the unconditional mean predictor is preferred with the Bayesian method while the JLMS predictor is always adopted with the MLE estimation.
In this thesis, we aim at examining and comparing the statistical properties of the two predictors when the inefficiency term of the model is heteroscedastic. We start by advocating the proper notations for the predictors, which is an issue that has been neglected in the literature. We then discuss their statistical properties, including the consistency, unbiasedness, and the size of the mean square error (MSE). We find that, without the estimation effect, the JLMS predictor has a smaller MSE compared to the unconditional predictor. We provide a theoretical explanation of the result based on the signal-to-noise ratio of the predictors. If the estimation effect is taken into account, however, the relative size of the MSEs is difficult to tell analytically. We use simulations to show the numerical results.
We also discuss the predictors’ application in the context of out-of-sample prediction. We show that only the unconditional predictor is appropriate in this context. By the same token, we find that the marginal effect estimator proposed by Wang (2002) is more reasonable than that proposed by Kumbhakar and Sun (2013).

並列關鍵字

Stochastic Frontier Model ； Truncated-Normal-Distribution ； Production Efficiency ； Individual-Specific Technical Efficiencies ； MLE ； Cross- Sectional Data

參考文獻

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