Monetary Factorsin a Perfectly Competitive Model

To examine the impact of monetary factors in this new classical model, let us assume the existence of a money demand function by households and firms, which in logarithms, takes the form

where η is the semi-elasticity of money demand with respect to the nominal interest rate.³

From the definition of the real interest rate through the Fisher equation (14.19), the nominal interest rate is equal to

where the real interest rate r is determined by (14.23) and is independent of monetary factors.

We will see that, as in the case of the models analyzed in chapter 12, when the central bank follows a rule for the money supply, then the model determines the price level, inflation, and nominal interest rates. If the central bank pegs the nominal interest rate, the price level and the nominal money supply cannot be determined, unless the nominal interest rate reacts sufficiently strongly to changes in the price level.

14.2.1 An Exogenous Path for the Money Supply

If the central bank determines an exogenous path for the money supply, then from (14.24) and (14.25), it follows that

Under the assumption that η > 0, the rational expectations solution of (14.26) implies that

From (14.27), the price level and inflation are determined as functions of the exogenous path of the money supply and the paths of real output and the real interest rate, which, as we have seen, are independent of monetary factors in this new classical model.

14.2.2 An Exogenous Path for the Nominal Interest Rate

If we assume that the central bank follows an exogenous path for the nominal interest rate, then from the Fisher equation (14.25), it follows that

Equation (14.28) determines expected inflation, not actual inflation, given the exogenous path of nominal interest rates. This equation is consistent with any price level path that satisfies

where ξ is any shock that satisfies E_t (ξ_t+1) = 0. Equation (14.29) suggests that there are multiple equilibria for the price level and inflation, depending on ξ. This price level indeterminacy when the central bank follows an exogenous path for the nominal interest rate is also transferred to the money supply, through the money demand function (14.24). Consequently, neither the money supply nor the price level can be determined uniquely when the central bank follows an exogenous path for the nominal interest rate.

14.2.3 An Inflation-Based Nominal Interest Rate Rule

Central banks predominantly use the nominal interest rate as their preferred monetary instrument. However, they follow policies according to which the path of nominal interest rates is not exogenous but depends on past, current, and expected future economic developments, mainly inflation. For example, if inflation rises, central banks usually raise nominal interest rates to reduce it, and vice versa. After all, this is the essence of the interest rate rule proposed more than a century ago by Wicksell [1898]. Let us therefore assume the following rule for determining nominal interest rates:

where ϕ > 0 is the reaction of the central bank nominal interest rate to inflation, and π^* is the inflation target of the central bank (presumably the optimal steady state inflation rate).⁴

From (14.25) and (14.30), we therefore have that

where = π − π* is the deviation of the current inflation rate from the target of the central bank.

Solving (14.31) under rational expectations yields

if ϕ > 1, and

if ϕ ≤ 1. Here ξ is any shock that satisfies E_t (ξ_t+1) = 0.

Thus, if the reaction of the central bank nominal interest rates to inflation is sufficiently pronounced (ϕ > 1), there is no indeterminacy problem for inflation. The fundamental solution is given by (14.32). If the reaction of the nominal interest rates to inflation is not sufficiently pronounced (ϕ ≤ 1), then the problem of inflation indeterminacy and the possibility of price bubbles remains.

14.2.4 Optimal Monetary Policy

Equation (14.32) can be used to determine the optimal ϕ if the objective of the central bank is to stabilize inflation around its steady state target. After all, in this model, real variables are always equal to their equilibrium level, so monetary policy cannot have any other objective.

The optimal monetary policy rule is clearly to let ϕ tend to infinity (i.e., an interest rate policy that, by (14.32), completely stabilizes inflation around the steady state target of the central bank). Thus, optimal monetary policy in a new classical model implies complete stabilization of inflation at the optimal steady state inflation rate π^*.⁵

In any case, as we have already seen, in new classical models of aggregate fluctuations, only real factors affect fluctuations in real variables. Monetary factors and monetary policy only affect real money balances and nominal variables, such as the price level, inflation, nominal interest rates, and the nominal money stock.

14.3