This article studies the problem of testing partial parameter stability in cointegrated regression models. The existing literature considers a variety of models depending on whether all regression coefficients are allowed to change (pure structural change) or a subset of the coefficients is held fixed (partial structural change). We first show that the limit distributions of the test statistics in the latter case are not invariant to changes in the coefficients not being tested; in fact, they diverge as the sample size increases. To address this issue, we propose a simple two-step procedure to test for partial parameter stability. The first entails the application of a joint test of stability for all coefficients. Upon a rejection, the second conducts a stability test on the subset of coefficients of interest while allowing the other coefficients to change at the estimated breakpoints. Its limit distribution is standard chi-square. The relevant asymptotic theory is provided along with simulations that illustrate the usefulness of the procedure in finite samples. In an application to US money demand, we show how the proposed approach can be fruitfully employed to estimate the welfare cost of inflation.

中文翻译：

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在协整回归模型中测试部分参数稳定性的两步程序

本文研究协整回归模型中检验部分参数稳定性的问题。现有文献考虑了多种模型，这取决于是否允许所有回归系数发生变化（纯结构变化）或系数的子集保持固定（部分结构变化）。我们首先表明，在后一种情况下，检验统计量的极限分布对于未检验的系数的变化不是不变的；事实上，它们随着样本量的增加而发散。为了解决这个问题，我们提出了一个简单的两步程序来测试部分参数的稳定性。第一个需要对所有系数进行稳定性联合检验。一经拒绝，第二个对感兴趣的系数子集进行稳定性测试，同时允许其他系数在估计的断点处发生变化。它的极限分布是标准卡方。提供了相关的渐近理论以及说明该过程在有限样本中的有用性的模拟。在对美国货币需求的应用中，我们展示了如何有效地使用所提出的方法来估计通货膨胀的福利成本。