Poole - 1970 - Optimal Choice of Monetary Policy Instruments in a.pdf

Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model Author(s): William Poole Source: The Quarterly Journal of Economics , May, 1970, Vol. 84, No. 2 (May, 1970), pp. 197-216 Published by: Oxford University Press Stable URL: https://www.jstor.org/stable/1883009 REFERENCES...

Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model Author(s): William Poole Source: The Quarterly Journal of Economics , May, 1970, Vol. 84, No. 2 (May, 1970), pp. 197-216 Published by: Oxford University Press Stable URL: https://www.jstor.org/stable/1883009 REFERENCES Linked references are available on JSTOR for this article: https://www.jstor.org/stable/1883009?seq=1&cid=pdfreference#references_tab_contents You may need to log in to JSTOR to access the linked references. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at https://about.jstor.org/terms Oxford University Press is collaborating with JSTOR to digitize, preserve and extend access to The Quarterly Journal of Economics This content downloaded from 92.202.12.4 on Thu, 02 May 2024 06:28:59 +00:00 All use subject to https://about.jstor.org/terms OPTIMAL CHOICE OF MONETARY POLICY INSTRUMENTS IN A SIMPLE STOCHASTIC MACRO MODEL * WILLIAM POOLE I. Introduction, 197.- II. The instrument problem, 199.-III. A static stochastic model, 203.- IV. The combination policy, 208.-V. A dynamic model, 209.- VI. Concluding observations, 214.- Appendix, 215. I. INTRODUCTION In this paper a solution to the "instrument problem"-more commonly known as the "target problem"-is determined within the context of the Hicksian IS-LM model. Baldly stated, the problem arises as a result of the fact that the monetary authorities may operate through either interest rate changes or money stock changes, but not through both independently, and therefore must decide whether to use the interest rate or the money stock as the policy instrument. The analysis produces two major findings. First, for some values of the parameters an interest rate policy is superior to a money stock policy while for other values of the parameters the reverse is true. Second, it is possible to define a combination policy in which the interest rate and money stock are maintained in a certain relationship to each other -the nature of the relation- ship depending on the values of the parameters - and to show that the optimal combination policy is as good as or superior to either the interest rate or money stock policies no matter what the values of the parameters. The remainder of this section will be spent in clarifying some terminological questions connected with the words "instrument" and "target." Then in Section II the nature of the instrument problem will be discussed more carefully and an intuitive solution to the problem will be presented. In Section III the intuitive solution is made precise by applying the theory of optimal decision making under uncertainty to a formal model. In Section IV it is shown that the "either-or" solution to the instrument problem can be improved * An earlier version of this paper was presented at the December 1967 meetings of the Econometric Society, and I am indebted to my discussant at the meetings, Donald P. Tucker, for many useful comments. I am also indebted to Carl F. Christ, Jurg Niehans, William H. Oakland, and the referees of this journal for their valuable comments. Unfortunately, I am unable to pass off responsibility for any remaining errors to the above-named individuals. This content downloaded from 92.202.12.4 on Thu, 02 May 2024 06:28:59 +00:00 All use subject to https://about.jstor.org/terms 198 QUARTERLY JOURNAL OF ECONOMICS upon by adopting a combination policy in which the interest rate and money stock are maintained in a constant relationship to each other. The analysis is extended in Section V to a dynamic model. Finally, in Section VI appear concluding remarks and suggestions for further research. Before analyzing the nature of the instrument problem it may be helpful to comment on terminology. A considerable literature exists in which economic policy is discussed in terms of the adjustment of policy instruments in order to influence variables termed "target" or "goal" variables. However, recent monetary policy literature has sometimes departed from this framework by introducing the concept of "proximate" or "intermediate" targets which lie between the instruments (or "tools") of monetary policy (e.g., open market operations, discount rate, and so on) and goals of policy. The rationale for introducing the proximate target concept would seem to be the notion that a close and systematic relationship exists between proximate targets and goals, the relationship holding over time and space, while the relationship between the tools of monetary policy and the proximate targets depends heavily on institutional factors which are stable neither over time nor over space. However, if as assumed throughout this paper the money stock can be set at exactly the desired level, then the money stock may as well be called an instrument of monetary policy rather than a proximate target. The definition of an instrument as a policy-controlled variable which can be set exactly for all practical purposes is, of course, not very precise since people may disagree as to what "practical purposes" are. Nevertheless, such an approach promotes a fruitful evolution of research since at a given state of knowledge failures to reach desired levels of goal variables may be largely due to factors other than errors in reaching desired values of instruments. With advances in knowledge it becomes increasingly important to ac- count for errors in reaching desired values of instruments, and the analysis can then shift the definition of "instruments" to more pre- cisely controllable variables. It is, for example, a straightforward matter to use the approach of this paper to treat the monetary base as an instrument and the money stock as a stochastic function of the monetary base. In the analysis of this paper policy variables assumed to be controlled without error will be called instruments, and no use will be made of the proximate target concept. It is to the nature of the instrument problem that we now turn. This content downloaded from 92.202.12.4 on Thu, 02 May 2024 06:28:59 +00:00 All use subject to https://about.jstor.org/terms OPTIMAL CHOICE OF MONETARY POLICY 199 II. THE INSTRUMENT PROBLEM The proper choice of monetary policy instruments is a topic which has been hotly debated in recent years. Three major positions in the debate may be identified. First, there are those who argue that monetary policy should set the money stock while letting the interest rate fluctuate as it will. In one variant of this position the authorities should simply achieve a constant rate of growth of the money stock; in another variant the authorities should adjust the growth in the money stock in response to the current state of the economy, causing the money stock to grow more rapidly in recession and less rapidly in boom. The second major position in the debate is held by those who favor using money market conditions as the monetary policy instrument. The more precise proponents of this general position would argue that the authorities should push interest rates up in times of boom and down in times of recession, while the money supply is allowed to fluctuate as it will. Others, while conceding the impor- tance of interest rates, would also tend to think in terms of the level of free reserves in the banking system, the rate of growth of bank credit with one or more components of bank credit being specially emphasized, or the overall "tone" of the money markets. Most proponents of this position would probably agree that the short-term interest rate is the best single variable to represent money market conditions if a single variable must be selected for analytical purposes. The third major position is taken by the fence-sitters who argue that the monetary authorities should use both the money stock and the interest rate as instruments. It is, of course, recognized that the money stock and the interest rate cannot be set independently, but the idea seems to be to maintain some sort of relationship between the two instruments. The trouble with this position is that it usually amounts to nothing more than a plea for wise behavior by the authorities since it is never explained how the instruments should be adjusted according to economic conditions. However, as shown in Section IV, this position can be made precise within the context of a well-defined model. The very existence of the instrument problem may puzzle those who are used to thinking of policy formulation in terms of a deterministic macro model. In such a model, assuming that it is possible to reach full employment through monetary policy, the policy prescription may be in terms of either the interest rate or the money This content downloaded from 92.202.12.4 on Thu, 02 May 2024 06:28:59 +00:00 All use subject to https://about.jstor.org/terms 200 QUARTERLY JOURNAL OF ECONOMICS stock; it makes no difference which instrument is selected. This point may be demonstrated within the context of a Hicksian IS-LM type model. r LM : is ~~~~~i Yf Y FIGURE I Figure I shows level is assumed as setting the money stock at the level such that the LM function will cut the IS function at the full employment level of income, YfAlternatively, the policy problem could be viewed as in Figure II with the monetary authorities setting the interest rate at r*,' thereby making the LM function horizontal.2 In the deterministic model it obviously makes no difference whatsoever whether the policy prescription is in terms of setting the interest rate at r* or in terms of setting the money stock at the level, say M*, that makes the LM function cut the IS function at Yf. But now consider Figure III, in which the IS function is ran1. The interest rate could be set through a bond-pegging program such as practiced by the United States during World War II. Of course, the level of the peg could be altered from time to time. 2. The LM function is ordinarily defined in terms of a constant money stock. However, a logical extension is to treat the money supply as interests elastic as a result of the activities of the commercial banking system or, in the present context, of the monetary authorities. A pegged interest rate, of course, is a polar case in terms of interest elasticity of supply. This content downloaded from 92.202.12.4 on Thu, 02 May 2024 06:28:59 +00:00 All use subject to https://about.jstor.org/terms t c OPTIMAL CHOICE OF MONETARY POLICY 201 LM I\ Is Yf Y FIGURE II LMl LM2 ISI Is YO Y. Yf Y2 Y3 Y FIGmn MI This content downloaded from 92.202.12.4 on Thu, 02 May 2024 06:28:59 +00:00 All use subject to https://about.jstor.org/terms 202 QUARTERLY JOURNAL OF ECONOMICS domly shocked and may lie anywhere between IS1 and IS2. On the assumption that the money demand function is stable, if the money stock is set at M* the LM function will be LM1 and income may end up anywhere between Y1 and Y2. However, if the interest rate is set at r*, the LM function will be LM2, and income may end up anywhere between Yo and Y3, a much wider range than Yj to Y2. In Figure III it is clear that there is a problem of the proper choice of the instrument, and that the problem should be resolved by setting the money stock at M* while letting the interest rate end up where it will rather than by setting the interest rate at r* and letting the money stock end up at whatever level is necessary to obtain r*. LM1 LM3 LM Y1 Yf Y2 Y FIGURE IV In Figure IV the situation is analyzed in which the IS function is stable but the money demand function is randomly shocked. Setting the money stock at M* will lead to an LM function between LM1 and LM2, and income between Y1 and Y2, while setting the interest rate at r* will lead to LM3 and Yf. The interest rate is th proper instrument in this case. In general there will be stochastic disturbances in both the real and the monetary sectors of the economy. In examining the situaThis content downloaded from 92.202.12.4 on Thu, 02 May 2024 06:28:59 +00:00 All use subject to https://about.jstor.org/terms OPTIMAL CHOICE OF MONETARY POLICY 203 tions represented by Figures III and IV, it appears that in the general case the solution of the instrument problem depends on the rela- tive importance of the random disturbances and on the slopes of the IS and LM functions, i.e., on the structural parameters of the system. With these general ideas in mind, it is now possible to proceed to a formal model. III. A STATIC STOCHASTIC MODEL Let us begin by presenting a nonstochastic linear version of the Hicksian IS-LM model depicted in Figure I. The model has the two equations (la) Y=a,+alr, al O. b2 L when b2 < 0.9 What this means is that the higher is the interest sensitivity of the demand for money (the lower b2 is algebraically), the lower is the minimum expected loss from a money stock policy. The intuitive explanation for this result (which may on first thought seem peculiar) is as follows: first, note that this result requires puv