  We propose a new framework for assessing Granger causality in quantiles in
unstable environments, for a fixed quantile or over a continuum of quantile
levels. Our proposed test statistics are consistent against fixed alternatives,
they have nontrivial power against local alternatives, and they are pivotal in
certain important special cases. In addition, we show the validity of a
bootstrap procedure when asymptotic distributions depend on nuisance
parameters. Monte Carlo simulations reveal that the proposed test statistics
have correct empirical size and high power, even in absence of structural
breaks. Finally, two empirical applications in energy economics and
macroeconomics highlight the applicability of our method as the new tests
provide stronger evidence of Granger causality.
