A prominent test of long‐run monetary neutrality (LRMN) involves regressing long‐horizon output growth on long‐horizon money growth. We obtain limited support for LRMN with this test in long‐annual Australian, Canadian, UK and US samples. Although empirical confidence intervals yield evidence in favour of LRMN, Monte Carlo experiments reveal the power of this test is near its size. Thus, this test is unlikely to detect important deviations from LRMN. These problems arise because the long‐horizon regression test of LRMN relies on estimates of the covariance of long‐horizon output growth and long‐horizon money growth. Copyright © 2004 John Wiley & Sons, Ltd.