Test for partial parameter instability in regressions with I(1) processes

This paper derives the limiting distribution of LM-type tests for possible departure from constancy in ‘subsets’ of cointegrating coefficients. In particular, models with nonconstancy on intercept or stochastic trend coefficients are considered. It is found that the limiting representations of these subset tests can be characterized as functions of continuous-time martingales depending on the asymptotics of both the whole regressor vector and the regressors whose coefficients are under tests. Critical values are computed using large-sample approximation. Monte Carlo experiments are conducted to investigate the finite sample size and power. The subset tests are found to dominate the joint test when there is partial coefficient variation.