Inference When a Parameter Is Not Identified Under the Null

对结构变化和参数不稳定性的检验在计量经济学和统计学中有着悠久的历史。参数往往是不可察觉的简化形式，如品味、技术和制度。尽管我们有理由相信这些不可观测的东西在样本期间大致是恒定的，但它很少是先验明显的，因此应该接受规格测试。尽管对这一问题的研究历史悠久，但大多数研究人员采用简单的样本分割检验或预测误差检验，这两种检验都不是最优的。本项目的目的是开发一种即使在非线性情况下也易于计算的、在恒定参数零假设下计算的参数不稳定性的强有力的检验方法。所采用的方法是使用近似拉格朗日乘数检验，以检验参数为鞅的选择。这包括简单的结构性中断以及随机行走。渐近分布是非标准的，但如果回归变量是非趋势的，则渐近分布不随干扰参数而变化。利用随机过程理论的一些最新发展，发展了适当的渐近理论。

Testing for structural change and parameter instability has a long history in econometrics and statistics. Parameters are frequently reduced forms of unobservables, such as taste, technology and institutions. Although it may be reasonable to believe that these unobservables have been roughly constant over the sample period, it is rarely a priori obvious and should therefore be subject to a specification test. Despite the long history of study of this problem, most researchers apply simple sample split tests or forecast error tests, neither of which are optimal. The purpose of this project is to develop a powerful test for parameter instability calculated under the null hypothesis of constant parameters which is easy to calculate, even in non-linear contexts. The approach taken is to use an approximate Lagrange Multiplier test against the alternative that the parameter is martingale. This includes simple structural breaks as well as random walks. The asymptotic distribution is non-standard, but invariant to nuisance parameters if the regressors are non-trended. Appropriate asymptotic theory is developed, which makes use of some recent developments in stochastic process theory.