有效廣義動差估計在相關動差條件的選擇

Abstract

廣義動差估計在許多領域都是普遍的參數估計方法。從原始動差一致估計的初始參數可能不是有效率的。假設存在一些合格的動差，這些動差的線性組合能夠提升參數估計的有效性。本篇文章提出一個從合格動差集合當中，系統性地篩選相關動差條件的方法。此流程透過正交轉換移除多餘的動差，也使用懲罰項的概念，識別候選相關動差條件所提供額外的參數訊息。在工具變數模型的模擬中，正確選擇相關動差條件以提供最大參數訊息的比例，隨著樣本數增加而上升。此外，透過本文提出的方法得到的廣義動差估計式，隨著樣本數增加，估計式會靠近模擬設計下最有效率的參數估計。

The generalized method of moment (GMM) is a prevalent estimation methodology in various fields of study. A preliminary estimator obtained from a set of conservative moments can consistently identify the parameters but may not be efficient. Suppose there exists some valid moments whose linear combinations are relevant to improve estimation efficiency. This paper proposes a method to select relevant moment conditions from a valid set systematically. The procedure removes redundant moments through orthogonal transformations and recognizes extra information provided by candidate relevant moments based on the BIC-type penalty concept. In the simulation study of an instrumental variable model, the proportion to select ideal relevant moments providing the most information of parameters rises as the sample size increases. Furthermore, a GMM estimator obtained from the proposed method is close to the efficient parameter estimator under this simulation setting when the sample size becomes large.