Velocity of money, equilibrium (in)determinacy and endogenous growth

We show that in a canonical one-sector AK model of endogenous growth with a generalized cash-in-advance constraint, the growth and velocity effects of money are closely related to the local stability properties of the economy's balanced growth paths. When a positive fraction (excluding 100%) of gross investment is subject to the liquidity constraint, the economy displays saddle-path stability and negative effects of money on output growth and velocity due to a dominating portfolio substitution effect. By contrast, when the opposing intertemporal substitution effect dominates, the economy exhibits indeterminacy and sunspots, as well as a positive correlation between money, output growth and velocity. Finally, when real balances are required only for the household's consumption purchases, money becomes superneutral in the growth-rate and also in the velocity sense because the equilibrium real rate of return on capital remains constant.