Tests for causality between integrated variables using asymptotic and bootstrap distributions: theory and application

Causality tests in the Granger's sense are increasingly applied in empirical research. Since the unit root revolution in time-series analysis, several modifications of tests for causality have been introduced in the literature. One of the recent developments is the Toda–Yamamoto modified Wald (MWALD) test, which is attractive due to its simple application, its absence of pre-testing distortions, and its basis on a standard asymptotical distribution irrespective of the number of unit roots and the cointegrating properties of the data. This study investigates the size properties of the MWALD test and finds that in small sample sizes this test performs poorly on those properties when using its asymptotical…