Estimating the Fixed-Effect Stochastic Frontier Models with Error in Variables: A GMM Method

自Greene (2005) 引入了固定效果的隨機邊界模型（TFESF Models）後，由於在微觀計量分析中常見的附帶參數問題（incidental parameters problem），其估計方法的改進一直受到關注。因為複雜的概似函數，傳統的最大概似法（MLE）在估計具固定效果的隨機邊界模型中遇到了問題。而當該模型出現變數衡量誤差時，參數的估計會產生偏誤。 本文擴展了Chen and Wang (2015) 提出的對於TFESF模型的動差估計法，在考慮了變數衡量問題後，提出了一個一般動差估計法來解決如何估計TFESF模型。在第一步的估計策略中，我們主要采用Hong and Tamer (2003)關於非線性變數測量誤差的模型。據此模型，我們可以得到關於模型變數系數和測量誤差變異數的估計式。此估計式具有一致性和常態的極限分配。在第二步的估計策略中，我們擴展Chen and Wang (2015)的方法，在考慮當一個變數存在測量誤差時，如何得到具有一致性和常態極限分配的估計式，如隨機邊界模型關注的無效率系數（inefficiency index）。最後，模擬的結果顯示，當樣本數充分大時，本文的估計方法能有效地降低估計偏誤（bias）和均方差（Mean Squared Error）。Since Greene (2005) introduced the true-fixed effect stochastic frontier (TFESF) model, its estimation method has been gaining attention due to the complication from the heterogeneous effects (incidental parameters problem) in the microeconometric analysis. Traditional MLE methods have trouble dealing with it because of its inherently complex likelihood functions. The estimation also deteriorates into serious bias when measurement error problem arises for fixed effect panel data models. This paper proposes a two-step estimation strategy to address the two aforementioned problems. In the first step, we extend Hong and Tamer(2003) to obtain a consistent estimator of interest and the measurement error''s variance needed to estimate ineffciency parameters in stochastic frontier analysis in the second step. Then, we show how to extend Chen and Wang(2015) and derive the MoM estimator for TFESF models when its composite error varies in distribution. We derive closed-form estimators for two-parameter models (normal-half nor-mal or normal-exponential). Finally, simulation results indicate that our MoM estimators have good performance for finite sample sizes