We provide empirical support for an analytical DSGE model with nominal wage stickiness where growth is driven by learning-by-doing and money shocks and their variance are allowed to impact on long-run output growth. In our theoretical model the variance of monetary shocks has a negative effect on growth, while output volatility is good for growth as a positive relationship exists. Using a bivariate GARCH-M model we test the empirical conditional mean and variance relationships of nominal money and production growth rates in the G7 countries. We corroborate the theoretical model predictions with evidence from Bonferroni multiple tests across the G7.