Abstract
In this article, we introduce a monitoring scheme to (sequentially) detect structural changes in linear models with endogenous explanatory variables and develop asymptotic theories for them. The method is based on cumulative sums (CUSUM) of weighted residuals, in which the unknown in-control parameters have been replaced by its GMM estimate from the training sample. We characterize the limit distributions of the CUSUM process and the corresponding test statistic and results show that these tests are consistent. Moreover, We also obtain and tabulate the asymptotic critical values of the tests when p = 2. We also investigate our distribution theory with a Monte Carlo simulation which indicates the applicability of the methods.
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