The object here is to find the limiting values, as λ → −∞ and λ1 → −∞, of the expressions in (26) and (27), where
As a preliminary matter, note that as λ → −∞ we have Ψ → 1−b3λ1 and Θ → b3λ1(1+α) − α. Also note that the derivatives with respect to λ1 of these last two expressions are −b3 and b3(1+α), respectively. Accordingly, we see from l’Hopital’s rule that the limiting value (as λ1 and λ → − ∞) of Ψ/Θ is −1/(1+α). Separately, we have Ψ → ∞ and Θ → −∞.
From those results we readily see that the coefficients in (26) both approach zero in the limit as λ and λ1 → −∞. The result is also obvious for the coefficient on
Bryant, Ralph C., Dale W. Henderson, Gerald Holtham, Peter Hooper, and Steven Symansky (eds.), Empirical Macroeconomics for Interdependent Economies (Washington: Brookings Institution, 1988).
Bryant, Ralph C., David A. Currie, Jacob A. Frenkel, Paul R. Masson, and Richard Portes (eds.), Macroeconomic Policies in an Interdependent World (Washington: International Monetary Fund, 1989).
Boughton, James M., “Policy Assignment Strategies with Somewhat Flexible Exchange rates,” in B. Eichengreen, M.H. Miller, and R. Portes (eds.), Blueprints for Exchange Rate Management (New York: Academic Press, 1989).
Currie, David A., and Simon Wren-Lewis, “An Appraisal of Alternative Blueprints for International Policy Coordination,” European Economic Review, Vol. 33 (1989), pp. 1769-1785.
Currie, David A., and Simon Wren-Lewis, “Evaluating the Extended Target Zone Proposal for the G3,” Economic Journal, Vol. 100 (March 1990), pp. 105-123.
Edison, Hali J., Marcus H. Miller, and John Williamson, “On Evaluating and Extending the Target Zone Proposal,” Journal of Policy Modeling, Vol. 9 (1987), pp. 199-224.
Flood, Robert P., “Explanations of Exchange-Rate Volatility and Other Empirical Regularities in Some Popular Models of the Foreign Exchange Market,” Carnegie Rochester Conference Series on Economic Policy, Vol. 15 (Autumn 1981), pp. 219-249.
Frenkel, Jacob A., Morris Goldstein, and Paul R. Masson, “Simulating the Effects of Some Simple Coordinated Versus Uncoordinated Policy Rules,” in Bryant et al. (1989).
Genberg, Hans, and Alexander Swoboda, “The Current Account and the Policy Mix Under Flexible Exchange Rates,” IMF Working Paper No. 87/70 (October 1987).
McCallum, Bennett T., “Rational Expectations and Macroeconomic Stabilization Policy: An Overview,” Journal of Money, Credit, and Banking, Vol. 12 (November 1980, Part 2), pp. 716-746.
McCallum, Bennett T., “Targets, Indicators, and Instruments of Monetary Policy,” in W.S. Haraf and P. Cagan (eds.), Monetary Policy in a Changing Financial Environment (Washington: American Enterprise Institute, 1990).
Warwick J., and Jeffrey D. Sachs, “Comparing the Global Performance of Alternative Exchange Arrangements,” Journal of International Money and Finance, Vol. 7 (December 1988), pp. 387-410.
Williamson, John, and Marcus H. Miller, Targets and Indicators: A Blueprint for the International Coordination of Economic Policy, (Washington: Institute for International Economics, 1987).
This paper was prepared while the author was spending an Instructive period as a Visiting Scholar at the International Monetary Fund. He is indebted to James Boughton, Hans Genberg, Paul Masson, and IMF Seminar participants for helpful comments and criticism.
At a March 1990 conference held at the Brookings Institution, for example, groups (or individuals) presented simulation studies generated with the following multi-country models: GEM, INTERMOD, MSG, MX3, MULTIMOD, MPS, LIVERPOOL, and TAYLOR.
Resulting conference volumes include Bryant, Henderson, Holtham, Hooper, and Symansky (1988) and Bryant, Currie, Frenkel, Masson, and Portes (1989).
More generally, instrument settings may reflect responses to deviations of several variables from their baseline paths, with different weights for the different variables.
Also the open market desk may make significant adjustments between FOMC meetings.
That there are certain advantages to the use of annual models is not being disputed. The argument is only that one cannot escape the policy response problem by recourse to annual data.
That contemporaneous observation of some variables is not plausible but that expectations can nevertheless be incorporated is recognized, and applied in some of the simulation experiments, by McKibbon and Sachs (1988).
In most studies, mean values over a large number of simulation experiments would be reported for these measures.
For an extensive discussion of this proposition, which attracted much attention during the 1970s but little in recent years, see McCallum (1980, pp. 724–738).
It is not being claimed that all models including “surprise” supply functions possess the policy ineffectiveness property; that they do not is demonstrated explicitly in McCallum (1980, p. 736). The point being made here simply begins with a case in which, by assumption, this property holds.
Similar conclusions would clearly hold for root-mean-square or mean-absolute measures of
It is well known from Fischer (1977) that the effectiveness proposition will not hold when this modification is adopted.
To do so, first eliminate yt between (2′) and (9). Then take the difference between the resulting equation evaluated at simulated and baseline values and insert (10) to eliminate
For simplicity of exposition, expression (12) assumes—unnecessarily—that ut and vt are uncorrelated.
Expression (12) is misleading, however, in its apparent suggestion that
Williamson (1988, p. 114) summarizes the rules as follows: “Each participating country would have an endogenous target rate of growth of nominal Income… This would provide one intermediate target for each country. The other would be a target for the (real effective) exchange rate…. This set of (2n - 1) intermediate targets would be pursued by the following set of assignment rules: (1) the average level of world interest rates [is dedicated to average nominal income growth]; (2) differences in interest rates among countries would be revised when necessary to prevent exchange rates from deviating from their target levels by more than, say, 10 percent; (3) national fiscal policies would be revised with a view to achieving national target rates of growth of nominal income.”
According to Edison, Miller, and Williamson (1987, p. 201), this suggestion was made by John Taylor at a Brookings conference in March 1986.
Also see Currie and Wren-Lewis (1990). The earlier study of Edison, Miller, and Williamson (1987) was concerned with evaluation of the ETZ proposal but not its comparison with the alternative scheme. The points developed in the present paper are nevertheless germane to the Edison, Miller, and Williamson analysis.
I do not mean to suggest that Frenkel, Goldstein, and Masson (1989) are persuaded by their own findings. On the contrary, they express some skepticism regarding the merits of the ETZ proposal (pp. 229–230). From a substantive (rather than methodological) perspective, therefore, I would view the arguments of the present paper as generally supportive of the views of Frenkel, Goldstein, and Masson.
In fact, Currie and Wren-Lewis (1989) (1990) describe their monetary instrument as a real interest rate. But the latter is implemented as a nominal rate less an expected inflation rate, so the rule can be rewritten with the latter variable on the right-hand side. That makes their rule fall into form (1) less clearly, but it does not alter the aspects of rule (1) that are relevant for the issues of concern in the present paper.
Thus the ETZ scheme actually assigns monetary policy partly to a real target and partly to a nominal target.
McKibbin and Sachs (1989) have found that, in simulations with the MSG model, the ETZ proposal has “a long-run stability problem” and have suggested that “the apparent contradiction” in comparison with Currie and Wren-Lewis (1990) and Edison, Miller, and Williamson (1987) stems from the MSG model’s “strict adherence to all intertemporal budget constraints” (1989, p. 191). Another difference is the treatment of expectations, which are rational in the MSG model. Although representing no contrast with the just-mentioned models, it should be noted that the MSG model’s policy rules do not rely in the standard way upon baseline values.
In this step we take Etubt+1 and Etvbt+1 to equal zero, not ubt+1 and vbt+1, since we are assuming that expectations are rational but not omniscient in the baseline simulation.
Here use is made of the fact that and V(vt-vbt = V(vt) = σ2v since the paths ubt and vbt are “given” from the perspective of the variance calculations.
The example of this section, like the two of Section III, is clearly one in which there are no dynamics—no effects on current endogenous variables of their own lagged values. Thus the problems generated by inappropriate instrument choice are not ones that manifest themselves necessarily in terms of dynamic instability. But the absence of dynamics does not imply that the problems are in any sense unrealistic; clearly, they would continue to exist if the models were elaborated so as to bring in adjustment costs, lagged responses, etc. Such features have been excluded from the examples only to keep the analysis simple and uncluttered.
A few analysts, for example, might contend that the monetary base is not fully controllable within each day and so should not be regarded as a legitimate instrument.
An important feature of this rule is that the policymaker can use it for arbitrary values of the target growth rate of nominal GNP by simply changing the 0.00739 values in (28) and (29) to the desired magnitude. If a five percent annual inflation rate were desired for instance, then nominal GNP should be made to grow at eight percent per year and the 0.00739 figures should be changed to 0.01924.