Interest rates and monetary policy

Abstract

This article conducts a thorough intertemporal analysis of nominal interest rate based monetary policy. Its main contribution is to show how such a policy can have different effects depending on the assumptions made about the saving and borrowing behaviour of firms. We consider two cases: (i) consumers are savers and firms are borrowers and (ii) both consumers and firms are borrowers (the nation as a whole is borrowing from abroad). In one case we confirm conventional wisdom, but in the other case we find there may be unexpected and surprising results. Moreover, our analysis has important implications for both inflation and nominal exchange rate targeting policies.

Notes

¹ In order to build a two-country model we require there to be product differentiation, some varieties of which are produced domestically and some in the foreign country, hence the assumption of monopolistic competition rather than perfect competition is appropriate and standard in this type of literature, see for example Obstfeld and Rogoff (1995, 1996).

² A full symbols list is provided in Appendix.

³ This also implies the zero long run profit condition .

⁴ Given the CES-consumption index employed the demand function for good i of individual j can be shown to be: . Thus and hence marginal revenue is . Equating with marginal costs (right hand side of Equation 2 gives and using the definition of price in Equation 3 yields a solution for output as . This follows Helpman and Krugman (1985).

⁵ We assume that the government runs a balanced budget. Since the government deficit is always zero it therefore does not need to appear in the national income identity. The Ricardian Equivalence Proposition, which holds in this model, implies that we do not need to analyse issues surrounding the effects of tax vs. bond finance, as in Obstfeld and Rogoff (1995, 1996).

⁶ Note that usually the marginal rate of intertemporal substitution refers to the substitution between goods over time, whereas here it is between goods consumed today and money held today (that is saving today held as money balance for future consumption).

⁷ Domestic inflation is defined as: where P^d is the price index

where E is the domestic nominal exchange rate (domestic price of foreign currency). Since we have assumed that the domestic country is large, this implies n is closer to one than zero. Similarly, foreign inflation is defined as: where p^f is the price index

Notice that this implies that and since , (prices equal to marginal products) from Equation 4, noting that , (growth of real wages must equal the growth of real money), hence a la Quantity Theory, but not in one for one proportion.

⁸ This is similar to the Keynesian transactions demand for money.

⁹ Due to an intertemporal effect, rather than a Keynesian speculative effect.

¹⁰ A rise in inflation causes agents to substitute present consumption in place of future consumption, increasing the real demand for money (life-cycle theory of consumption).

¹¹ That is, the production function has the normal properties (importantly, diminishing marginal productivity).

¹² From the definition of the real exchange rate, , then . Since and are moving in opposite directions, the effect on is ambiguous.

¹³ To avoid undue repetition of analysis, we don’t consider the case where both consumers and firms are savers (in this scenario, there is a similar ambiguity concerning the effects on the trade balance and hence the exchange rate that are detailed above in Case I). Likewise we don’t repeat the standard textbook (Obstfeld and Rogoff, 1996) case where firms are savers and consumers are borrowers (here the trade balance unambiguously improves and hence is identically opposite to the analysis provided in Case II below).