# RDP 8905: Monetary Policy Instruments: A Theoretical Analysis 5. Price Targets or Nominal Income Targets?

The analysis to this point has used a very simple model in which output is fixed at the natural rate. This has sufficed to illustrate a number of basic principles concerning the potential role of interest rate rules, but it has been necessary to assume that the sole objective of policy is stabilisation of the price level. The remainder of the paper introduces a more general model with variable output, in order to consider two kinds of policy rule of thumb which seem of particular relevance, and which could not be analysed in the simpler framework: these are nominal income targets (to be looked at in this section), and targets with base drift (section 6).

The generalised model is expressed as

The demand equation has thus been supplemented by a standard supply function in which output responds to unanticipated inflation. The model is closed using one of two alternative interest rate rules:

## (a) A price level target

The full model under a price level target is given by equations (1), (2') and (8). The model can be solved by conjecturing a reduced form solution of the form

which implies yt = β(π1ut2vt) + λγt−1 + vt.

A solution is obtained by applying the method of undetermined coefficients, from which it can be shown that

The model solution can thus be written as

Conditional variances of pt and yt are then

It is assumed that the objective of policy is to minimise a weighted sum of the output and price variances given by

where h is the relative weight given to price stabilisation in the policy objective. Optimising this function with respect to the response parameter γ gives the solution

The optimal size of response to a deviation of the price level from target is thus an increasing function of the relative weight given to prices in the objective function, and of the relative variance of aggregate demand shocks as compared with supply shocks. The reason for this latter conclusion is that when shocks originate on the demand side, the interest rate policy response given by the rule of thumb will tend to stabilise both prices and output; for example, a positive demand shock will tend to push up both prices and output, and the positive interest rate response will tend to dampen both. On the other hand, if a shock originates on the supply side, the interest response will tend to dampen the effect on one variable while amplifying the effect on the other. As a result of this structural feature, the optimal degree of policy responsiveness to a price shock is higher when shocks come primarily from the demand side; less stabilisation is achieved when supply side shocks are predominant.

## (b) A nominal income target

In this case the rule of thumb for policy is defined in terms of a deviation from target in nominal income. The policy rule is defined by equation (9) above. Repeating the solution method used in the case of the price level target, it can be shown that the following solution to the model is obtained:

The interesting question is to compare the objective function under this solution, with that obtained for the case of a price level target. It turns out that unambiguous comparisons cannot be made unless values of the model parameters are known. However, a comparison of the solutions given by (14) and (15) with those given in (10) and (11) makes clear the following two conclusions.

1. A nominal income target always gives a lower output variance than does a price level target. It follows that when sufficient weight is given to output stabilisation in the objective function, the nominal income target is superior.
2. Nominal income targeting gives a lower price level variance than price targeting when the relative variance of demand-side shocks, as compared with supply shocks, is sufficiently large. The intuitive reason for this is that supply shocks tend to push output and prices in opposite directions, whereas demand shocks push the two variables in the same direction. A nominal income target will therefore tend to be relatively good at responding to demand shocks, whereas the rule with a price target has a comparative advantage in responding to supply shocks.

As an implication of the above two points, any case for use of a price target in preference to targeting nominal income would require both that a low weight is given to real output stabilisation, and an assumption that supply-side shocks are relatively large.