斷點隨機前緣迴歸分析

Abstract

在本文中，我們提出了一個新的斷點迴歸 (regression discontinuity) 下的隨機前緣模型 (stochastic frontier model)，來衡量處理效果 (treatment effect) 如何影響前緣函數和效率水平。我們假設在運行變數 (running variable) 的斷點處 (cutoff) 將潛在結果變數 (potential outcome variables)中的前緣函數和非負的效率變數參數化。給定適當的條件，我們呈現對應參數的可辨認性 (identification) 和條件平均處理效果 (conditional average treatment effect)。然後，與非參數最大概似法的方法不同，我們在斷點處提出了一種半參數形式的局部非線性最小平方估計法 (local nonlinear least square method) 來估計。我們也將呈現參數估計的一致性和漸近常態分佈以及斷點處條件平均處置效應估計量的漸近常態分佈。

In this paper, we propose a new stochastic frontier model under a sharp regression discontinuity design to measure how treatment affects both the frontier function and the level of inefficiency at the cutoff. We assume that the frontier function and the conditional expectation of nonnegative inefficiency of the potential outome variable are parametrically specified at the cutoff of the running variable. Under suitable conditions, we show the identification of the corresponding parameters and the conditional average treatment effect. Then we propose a local nonlinear least square estimator with the semiparameter form with respect to the running variable at the cutoff that is different from nonparametric maximum likelihood methods. We show the consistency and asymptotics normal distribution of the estimator of parameters and asymptotics normal distribution of the estimator of the conditional average treatment effect at the cutoff.