多維模糊斷點迴歸設計下的新估計方法

Abstract

當政策、療程之施行與否取決於受試者是否通過某些特定標準時，研究者可以使用斷點迴歸(Regression discontinuity design；RDD)對局部平均處理效應(LATE)做不偏估計。在本篇論文中，我們將會回顧多維模糊斷點迴歸(Multidimensional RDD)之概念與假設，在其中處置(Treatment)施行與否取決於多個標準，而受試者也不盡然都遵從指示接受或不接受處置。本文第一個貢獻為推廣Lo (2017)及Hsu、Kuan與Lo (2018)文中概念，並指出傳統的估計方法未考慮資料中潛在的異質性，從而可能導致估計偏誤。此外，我們指出兩個異質性的潛在來源：指標變數(Assignment variable、Running variable)邊際效果不同，以及接受處置的機率不同。由此我們針對多維模糊斷點迴歸提出平均法(Average Method)以及交點法(Intersection Method)，成功克服資料中的異質性。在模擬中，我們發現我們提出的方法相較於傳統估計法確實能更準確地估計出處置效果，顯示我們的方法能夠在更普遍的環境下進行估計。

Regression discontinuity design (RDD) is an easy, yet rigorous setting allowing researchers to unbiasedly estimate local average treatment effect, particularly when the treatment is determined by whether subjects pass certain pre-specified thresholds or not. In this thesis, we shall review basic concepts and assumptions of multidimensional fuzzy RDD, in which there are multiple thresholds, and we do not require all subjects to follow the assignment rule. As the first contribution, we generalize the idea in Lo (2017) and Hsu, Kuan, Lo (2018), pointing out traditional estimation methods fail to take potential heterogeneity in the dataset into account and hence induce biased estimates. In addition, we identify the two potential sources of heterogeneity: different marginal effect of running variables and different treatment probabilities. With this in mind, we propose average method and intersection method for multidimensional fuzzy RDD, overcoming potential heterogeneity in the dataset. In the simulation study, we find out that our methods do produce a more accruate estimate than traditional methods, showing that our methods can accomodate much more general settings than traditional ones can do.