Endogenous rates of time preference in monetary growth models: stability and comparative dynamics

Two optimal monetary growth models are analyzed. In the first (Model C), the rate of time preference is assumed constant; and in the other (Model V) the rate of time preference is endogenous;In Model C, the constancy of the rate of time preference is found to drive the long-run super-neutrality of money in the model. Changes in (theta), the growth rate of money supply, have no long-run effects on the real sector. The long-run capital-labor ratio is such that its marginal product is the sum of the rate of time preference, the growth rate of the population, and the rate of capital depreciation. A change in (theta) does not affect these parameters, leaving the long-run capital-labor ratio unchanged;In Model V, changes in (theta) are not neutral in the long-run. The endogeneity of the rate of time preference allows changes in (theta) to affect the optimality condition for the long-run capital-labor ratio. An increase in (theta) increases the long-run (steady state) values of the capital-labor ratio and consumption;In both models, the increase in (theta) increases the long-run inflation rate, reducing the real rate of return on holding real money balances; this induces agents to hold less money at the new steady state. In Model C, the reduction in holdings of money is all that happens in the long-run. However, in Model V the rate of time preference provides a link between the monetary and real sectors of the economy; agents are induced, through adjustments in the rate of time preference, to shift from the asset with the relatively lower real rate of return (money) to that with the relatively higher real rate of return (capital);Also, in both models the increase in (theta) lowers the long-run achievable utility level. However, the reduction in utility is smaller in Model V. Stability analysis shows that both models display saddle point behavior.