“Data-driven GMM test for parameter instability” by Stepana Lazarova
Queen Mary University of London
We propose a test against general parameter instability in parametric models. The test is carried out using moment conditions so that the parameters only need to be estimated once, under the null hypothesis of stability. Moreover, any consistent estimator of parameter under the null can be used. The test is minimax rate optimal, that is, the test has uniform power against a large class of alternatives which can converge to the null with the best possible rate. The test is adaptive to unknown smoothness and to unknown sparsity properties of the alternatives. The test is computationally simple and the critical values are quantiles of a chi-squared distribution. An important feature of our test is that it can be used to construct a test whose power is better than power of another given test. A small Monte Carlo simulation study shows that the test has good size and power in small and moderate samples and that it has better power than other tests against some alternatives. We also demonstrate the power improvement when our test is combined with another test to improve on the power of that test.