A. Basic Model
Substituting into equation (5) using (7), (8), (9), and (A.1) gives
Substituting into equation (6) using (1), (7), (8), (9), and (A.1) gives
Substituting into equation (4) using (1), (7), (8), (9), and (A.1) gives
The method of undetermined coefficients derives expressions for the coefficients in terms of the structural parameters by noting that in each equation (A.2), (A.3), and (A.4) the left- and right-hand side expressions must be identical irrespective of particular time-series values of the predetermined variables and the disturbance terms. Using this method the coefficients on the disturbance terms and π30, π31, and π32 can be determined easily. Using equations (A.3) and (A.4) it can be determined that
With the positive root π12 is equal to 1 and with the negative root π12 is equal to 1-d3c1 which is greater than one which from equation (7) would imply explosive price behavior. If such explosive price behavior is excluded then π12=1 is the unique solution which allows the other coefficients to be solved as given in (10) by straightforward substitution. The coefficients for the disturbance terms are as follows
where Φ = (d1+d3c2a1).
B. An alternative rule
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The author would like to thank C. Adams, S.T. Beza, G. Calvo, L. Ebrill, K. Gerhaeusser, I. Guajardo, J. Guzman and T. Reichmann for many valuable comments and suggestions. All remaining errors are the responsibility of the author.
Similar policies were used during other periods but it was during this period that the targeting procedure was most explicit.
Many alternative definitions of indeterminacy exist in the literature. Adams and Gros (1986), for example, define price indeterminacy as existing when an economic model fails to reveal the long-term price level. Under this definition the price level is indeterminate in the model examined in this paper.
Since the IPC was computed on a calendar month basis it was centered on the 15th day of the month and thus it was approximately measuring inflation from the middle of the previous month to the middle of the current month, assuming inflation is linearly distributed. The interest rate target, however, was targeting the cumulative daily interest rate from the 15th of the current month to the 14th of the following month. Thus the nominal interest rate of any given month was made to match the inflation of the previous month.
The authorities also changed the calculation of the price index and established that the IPC would measure the average price level from the 15th day of one month until the 14th day of the second month. The interest rate targeting period was also moved back by two weeks at that time. Thus the same comparison can be made between the IPC and the cumulative overnight interest rate as before with the period shifted two weeks earlier. Developments associated with these changes distort the calculation of the real interest rate in June and July 1987.
As indicated in various issues of the Brazilian business daily newspaper, the Gazeta Mercantil, during this period.
From November 1986 to June 1987 the overnight interest rate in Chart 1 is measured from the 15th of one month to the 14th of the next month. From July 1987 to December 1988 the overnight interest rate is measured on a calendar month basis.
There is some controversy as to whether such a formulation of a monetary policy is completely specified. McCallum (1986) contends that a “pure (nominal) interest rate peg,” which he defines as a policy of standing ready to buy or sell any quantity of securities at a given interest rate, does not constitute a well-formulated monetary policy since it does not indicate if the monetary authorities will permit base drift of the money supply. Benavie and Froyen (1988) argue that if the monetary authorities are not going to permit base drift this is another element of the policy which would not be feasible because if they simultaneously sought to eliminate base drift they could not peg the interest rate completely. Walsh (1986) and Goodfriend (1987) have also pointed out that base drift is necessary for price level stationarity. In this paper it is assumed that the authorities are not concerned about base drift.
Strictly ut and vt in equation (6) should have (1/b1) as coefficients but since it does not affect the analysis these coefficients will be dropped for notational simplicity.
The real balance term could take a different form such as mt-1-pt. McCallum (1986) argues that the more appropriate form of the real balance term would be mt-1-pt given the budget constraint. In the present model if the real balance term in equation (3) were mt-1-pt it would complicate the procedure for arriving at a solution because mt-1 would be added to the system as a predetermined variable; however, the expected price level would still be determined.
Note that if under rule (2) the real balance effect were included in the is curve as mt-1 then mt-1 would be a predetermined variable and the price level would be determined since once again the structural model would indicate the variable to be used as the basis of the formation of expectations.