Inference When a Parameter Is Not Identified Under the Null

结构变化和参数不稳定性的测试在计量经济学和统计学中有着悠久的历史。参数通常是不可观察的简化形式，例如品味、技术和制度。尽管可以合理地相信这些不可观察量在样本期间大致恒定，但它很少是先验明显的，因此应该接受规范测试。尽管对该问题的研究历史悠久，但大多数研究人员都采用简单的样本分割测试或预测误差测试，但这两种方法都不是最佳的。该项目的目的是开发一种强大的测试方法，用于在常数参数的零假设下计算参数不稳定性，即使在非线性环境中，该方法也易于计算。 所采取的方法是使用近似拉格朗日乘数检验来对抗参数为鞅的替代方案。这包括简单的结构断裂以及随机游走。渐近分布是非标准的，但如果回归量是非趋势的，则对有害参数具有不变性。适当的渐近理论得到了发展，它利用了随机过程理论的一些最新发展。

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.