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An earlier version of this paper was presented at a workshop on “Asset Prices and the Conduct of Monetary Policy,” held at the Board of Governors of the Federal Reserve System (Washington, D.C., December 1989). We are grateful to participants in the workshop, especially Michael Gavin, for valuable comments. We would also like to thank Matthew Canzoneri, Pablo Guidotti, Mohsin Khan, David Papell, and Carmen Reinhart for helpful comments and discussions.
Notice that, by the law of large numbers, η is non-stochastic.
We feel comfortable with this “ad-hoc” specification because the same results would obtain if demands for assets and goods were derived from optimizing consumers, as follows from Calvo and Végh (1990b). Therefore, this paper’s specification enables us to convey the same message with a much more tractable model.
In what follows, the interest rate I will be referred to as the pure nominal interest rate to distinguish it from i, which will be referred to simply as the nominal interest rate.
Throughout the paper, superscripts “h” and “ℓ” refer to “high” and “low” values of policy parameters, respectively.
In what follows—and unless otherwise specified—this assumption will be maintained when referring to I.
For the sake of brevity, and since it is not the main focus of the paper, specific reference will not be made to the responses of real cash balances, h, and real demand-deposits, z, whose steady-state values follow from (18) and (19) and dynamic paths from (6) and (7).
The term “transition” will be used to refer to the period [0,T).
This is not necessarily the case. As may be inferred from Figure 1, output may rise during all of the transition.
As Calvo (1983) shows, the indeterminacy of the inflation rate also arises if demands for money and goods are derived from optimizing consumers. Hence, since the lack of microfoundations on the demand side is not the source of the problem, it is meaningful to tackle this issue in a non-optimizing model, which allows for a simple analytical framework. Moreover, the basic results would not change if demands were derived from optimizing consumers subject to “liquidity-in-advance” constraints, as shown in Calvo and Végh (1990b).
We certainly do not wish to claim that this way of getting around the indeterminacy problem is better than specifying policy rules. The usefulness of each approach probably depends on the purposes at hand. The advantage of the approach taken in this paper is that interest rate policy can be studied independently of money supply policy.
Note that, unlike the case of a temporary increase in the rate of growth of the money supply, the length of time during which i is higher makes no qualitative difference for the paths of m and π. The reason is that since μ is given, the fall in the inflation rate on impact always implies that real money balances increase at the beginning of the transition no matter what the magnitude of T is.
In the context of a small open economy with flexible exchange rates and prices, the (measured) inflation rate also falls on impact and rises afterwards overshooting its steady-state value, as shown in Calvo and Végh (1990c). The only difference is that at t=T, the inflation rate falls precipitously to μ, while in the present context it thus so steadily over time.
The overshooting of the inflation rate could induce policymakers to further raise interest rates. Policy rules that tie interest rate increases to the inflation rate could be easily incorporated into the present framework.
By definition, T=0 corresponds to the case in which the change in the nominal interest rate is permanent.
Strictly speaking, the price level falls on impact while the inflation rate increases on impact. However, since price data is collected at discrete intervals, the initial fall in the price level will show as an initial fall in the rate of inflation.