Inflation, Endogenous Growth, Transaction Costs, and Varying Discount Rates

This paper explores the relation between inflation and economic growth using the transaction costs model with a socially determined discount rate and a linear production technology. Even when the labor decision is inelastic, this paper demonstrates that inflation affects the endogenous growth with nonconstant time preferences. In particular, if the degree of impatience is decreasing in the economy-wide average ratio of assets (the sum of capital and money holdings) to consumption, then the relation between inflation and economic growth is hump-shaped, which supports other empirical evidences. A zero rate of growth of the money supply achieves the maximized endogenous growth.

The intuition is as follows. The higher the rates of money supply the lower are real balances and the higher are the transaction costs, and this discourages consumption or increases the ratio of capital to consumption. At the same time, higher cost of money holdings decreases money supply or the ratio of money to consumption. When an economic agent is less patient as the ratio of assets to consumption increases, the agent becomes either less patient if the capital effect is stronger or more patient if the money effect is stronger. When the cost of holding money is sufficiently high, the capital effect is dominant, lowering the economic growth.

In addition, we discuss local stability, conduct several numerical exercises, and compare our model with the discount rates determined internally by the individual. We claim that stability analysis does not matter in endogenous monetary models. Our numerical exercises confirm that the hump-shaped relation between inflation and the rate of economic growth is established with a set of plausible parameters. Our comparison proves that if the discount rate depends on relative individual consumption, then the results of the comparative statics on the balanced growth path (BGP) are observationally equivalent in both models.

Our paper has three contributions. First, this model gives a solution to the puzzle posed by Gomme (1993) and Bullard and Keating (1995) that there exists a positive link between inflation and the growth rate in low-inflation countries. Our solution sheds new light on monetary policy. Second, we consider the monetary model with varying discount rate in an endogenous growth framework, whereas Palivos et al. (1997) and Meng (2006) focused their attention on a real economy. Third, we find that in some types of models, the comparative statics on the BGP has the same results whether the discount rate is determined externally and internally.

References:

• Bullard, J., and J. Keating (1995) “The long-run relationship between inflation and output in postwar economies.” Journal of Monetary Economics, 51, 477—496.
• Gomme, P. (1993) “Money and economic growth revised: Measuring the costs of inflation in an endogenous growth model.” Journal of Monetary Economics, 32, 51—77.
• Meng, Q. (2006) “Impatience and equilibrium indeterminacy.” Journal of Economic Dynamics and Control, 30, 2671—2692.
• Palivos, T., P. Wang, and J. Zhang (1997) “On the existence of the balanced growth equilibrium.” International Economic Review, 38, 205—224.