COVARIANCE MATRIX ESTIMATION AND THE LIMITING BEHAVIOR OF THE OVERIDENTIFYING RESTRICTIONS TEST IN THE PRESENCE OF NEGLECTED STRUCTURAL INSTABILITY
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遗漏结构不稳定时协方差估计与过度识别检验的极限行为
- 研究问题
- 当矩条件存在被忽略的单一结构突变时，过度识别限制检验能否发现误设，其发散速度如何受 HAC 协方差估计影响？
- 方法与思路
- 作者比较基于中心化与未中心化自协方差的 HAC 估计，推导检验统计量在结构不稳定下的极限行为，并研究矩条件选择。
- 材料陈述的贡献
- 摘要称检验未必一致；一致时，未中心化方案以 T/bT 发散，中心化方案可为 T/bT 或 T，并据此给出矩选择一致性的条件。
- 阅读关注点
- 应核对导致检验不一致的突变形式、中心化方式与带宽条件，以及不同发散速度如何影响候选矩条件的选择规则。
- 阅读边界
- 仅据所给出版社摘要，无法判断哪些结构突变可被检验识别或各速率成立的完整条件，也不能将结果推广至多个突变点。
原文摘要
We consider the limiting behavior of the overidentifying restrictions test in the presence of neglected structural instability at a single “break point.” It is shown that the test need not be consistent against this type of misspecification. If it is consistent then it emerges that the limiting behavior of this test statistic depends on the covariance matrix estimator employed. In this paper we consider the case in which a heteroskedasticity autocorrelation covariance (HAC) is used. It is shown that (i) if the HAC estimator is based on uncentered autocovariances then the overidentifying restrictions test diverges at rate T/bT where T is the sample size and bT is the bandwidth; (ii) if the HAC estimator is based on centered autocovariances then the rate of increase of the overidentifying restrictions test is either T/bT or T depending on the form of the instability. These results are used to provide conditions for the consistency of the method of moment selection of Andrews (1999, Econometrica 67, 543–564) when certain elements of the candidate set of moments are misspecified as a result of neglected structural instability.This work was begun while Hall was a Senior Research Fellow and Peixe was a graduate student at the Department of Economics, University of Birmingham, UK, and this support is gratefully acknowledged. Peixe also gratefully acknowledges financial support from FCT under Grant PRAXIS XXI/BD/13453/97. We are very grateful for the very useful comments of Don Andrews and two anonymous referees.