Money does Granger-cause output in the bivariate output-money relation

A bivariate Granger-causality test on money and output finds statistically significant causality when data are measured in log levels, but not when they are measured in first differences of the logs. Which of these results is right? The answer to that question matters because a finding of no Granger-causality from money to output would substantially embarrass existing business cycle models in which money plays an important role [Eichenbaum and Singleton (1986)]. Monte Carlo simulation experiments indicate that, most probably, the first difference results reflect lack of power, whereas the level results reflect Granger-causality that is actually in the data.