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Kerr, William; Robert King,. "Limits on interest rate rules in the IS model." Economic Quarterly. Federal Reserve Bank of Richmond. 1996. HighBeam Research. 20 Aug. 2018 <https://www.highbeam.com>.
Kerr, William; Robert King,. "Limits on interest rate rules in the IS model." Economic Quarterly. 1996. HighBeam Research. (August 20, 2018). https://www.highbeam.com/doc/1G1-18754997.html
Kerr, William; Robert King,. "Limits on interest rate rules in the IS model." Economic Quarterly. Federal Reserve Bank of Richmond. 1996. Retrieved August 20, 2018 from HighBeam Research: https://www.highbeam.com/doc/1G1-18754997.html
Many central banks have long used a short-term nominal interest rate as the main instrument through which monetary policy actions are implemented. Some monetary authorities have even viewed their main job as managing nominal interest rates, by using an interest rate rule for monetary policy. It is therefore important to understand the consequences of such monetary policies for the behavior of aggregate economic activity.
Over the past several decades, accordingly, there has been a substantial amount of research on interest rate rules.(1) This literature finds that the feasibility and desirability of interest rate rules depends on the structure of the model used to approximate macroeconomic reality. In the standard textbook Keynesian macroeconomic model, there are few limits: almost any interest rate policy can be used, including some that make the interest rate exogenously determined by the monetary authority. In fully articulated macroeconomic models in which agents have dynamic choice problems and rational expectations, there are much more stringent limits on interest rate rules. Most basically, if it is assumed that the monetary policy authority attempts to set the nominal interest rate without reference to the state of the economy, then it may be impossible for a researcher to determine a unique macroeconomic equilibrium within his model.
Why are such sharply different answers about the limits to interest rate rules given by these two model-building approaches? It is hard to reach an answer to this question in part because the modeling strategies are themselves so sharply different. The standard textbook model contains a small number of behavioral relations - an IS schedule, an LM schedule, a Phillips curve or aggregate supply schedule, etc. - that are directly specified. The standard fully articulated model contains a much larger number of relations - efficiency conditions of firms and households, resource constraints, etc. - that implicitly restrict the economy's equilibrium. Thus, for example, in a fully articulated model, the IS schedule is not directly specified. Rather, it is an outcome of the consumption-savings decisions of households, the investment decisions of firms, and the aggregate constraint on sources and uses of output.
Accordingly, in this article, we employ a series of macroeconomic models to shed light on how aspects of model structure influence the limits on interest rate rules. In particular, we show that a simple respecification of the IS schedule, which we call the expectational IS schedule, makes the textbook model generate the same limits on interest rate rules as the fully articulated models. We then use this simple model to study the design of interest rate rules with nominal anchors.(2) If the monetary authority adjusts the interest rate in response to deviations of the price level from a target path, then there is a unique equilibrium under a wide range of parameter choices: all that is required is that the authority raise the nominal rate when the price level is above the target path and lower it when the price level is below the target path. By contrast, if the monetary authority responds to deviations of the inflation rate from a target path, then a much more aggressive pattern is needed: the monetary authority must make the nominal rate rise by more than one-for-one with the inflation rate.(3) Our results on interest rate rules with nominal anchors are preserved when we further extend the model to include the influence of expectations on aggregate supply.
1. INTEREST RATE RULES IN THE TEXTBOOK MODEL
In the textbook IS-LM model with a fixed price level, it is easy to implement monetary policy by use of an interest rate instrument and, indeed, with a pure interest rate rule which specifies the actions of the monetary authority entirely in terms of the interest rate. Under such a rule, the monetary sector simply serves to determine the quantity of nominal money, given the interest rate determined by the monetary authority and the level of output determined by macroeconomic equilibrium. Accordingly, as in the title of this article, one may describe the analysis as being conducted within the "IS model" rather than in the "IS-LM model."
In this section, we first study the fixed-price IS model's operation under a simple interest rate rule and rederive the familiar result discussed above. We then extend the IS model to consider sustained inflation by adding a Phillips curve and a Fisher equation. Our main finding carries over to the extended model: in versions of the textbook model, pure interest rate rules are admissible descriptions of monetary policy.
Specification of a Pure Interest Rate Rule
We assume that the "pure interest rate rule" for monetary policy takes the form
[Mathematical Expression Omitted],
where the nominal interest rate [R.sub.t] contains a constant average level [Mathematical Expression Omitted]. (Throughout the article, we use a subscript t to denote the level of the variable at date t of our discrete time analysis and an underbar to denote the level of the variable in the initial stationary position). There are also exogenous stochastic components to interest rate policy, [x.sub.t], that evolve according to
[x.sub.t] = [Rho][x.sub.t-1] + [[Epsilon].sub.t], (2)
with [[Epsilon].sub.t] being a series of independently and identically distributed random variables and [Rho] being a parameter that governs the persistence of the stochastic components of monetary policy. Such pure interest rate rules contrast with alternative interest rate rules in which the level of the nominal interest rate depends on the current state of the economy, as considered, for example, by Poole (1970) and McCallum (1981).
The Standard IS Curve and the Determination of Output
In many discussions concerning the influence of monetary disturbances on real activity, particularly over short periods, it is conventional to view output as determined by aggregate demand and the price level as predetermined. In such discussions, aggregate demand is governed by specifications closely related to the standard IS function used in this article,
[Mathematical Expression Omitted],
where y denotes the log-level of output and r denotes the real rate of interest. The parameter s governs the slope of the IS schedule as conventionally drawn in (y, r) space: the slope is [s.sup.-1] so that a larger value of s corresponds to a flatter IS curve. It is conventional to view the IS curve as fairly steep (small s), so that large changes in real interest rates are necessary to produce relatively small changes in real output.
With fixed prices, as in the famous model of Hicks (1937), nominal and real interest rates are the same ([R.sub.t] = [r.sub.t]). Thus, one can use the interest rate role and the IS curve to determine real activity. Algebraically, the result is
[Mathematical Expression Omitted].
A higher rate of interest leads to a decline in the level of output with an "interest rate multiplier" of s.(4)
Poole (1970) studies the optimal choice of the monetary policy instrument in an IS-LM framework with a fixed price level; he finds that it is optimal for the monetary authority to use an interest rate instrument if there are predominant shocks to money demand. Given that many central bankers perceive great instability in money demand, Poole's analytical result is frequently used to buttress arguments for casting monetary policy in terms of pure interest rate rules. From this standpoint it is notable that in the model of this section - which we view as an abstraction of a way in which monetary policy is frequently discussed - the monetary sector is an afterthought to monetary policy analysis. The familiar "LM" schedule, which we have not as yet specified, serves only to determine the quantity of money given the price level, real income, and the nominal interest rate.
Inflation and Inflationary Expectations
During the 1950s and 1960s, the simple IS model proved inappropriate for thinking about sustained inflation, so the modern textbook presentation now includes additional features. First, a Phillips curve (or aggregate supply schedule) is introduced that makes inflation depend on the gap between actual and capacity output. We write this specification as
[Mathematical Expression Omitted],
where the inflation rate [Pi] is defined as the change in log price level, [[Pi].sub.t] [equivalent to] [P.sub.t] - [Pt.sub.-1]. The parameter [Psi] governs the amount of inflation ([Pi]) that arises from a given level of excess demand. Second, the Fisher equation is used to describe the relationship between the real interest rate ([r.sub.t]) and the nominal interest rate ([R.sub.t]),
[R.sub.t] = [r.sub.t] + [E.sub.t][[Pi].sub.t+1], (6)
where the expected rate of inflation is [E.sub.t][[Pi].sub.t+1]. Throughout the article, we use the notation [E.sub.t][z.sub.t+s] to denote the date t expectation of any variable z at date t + s.
To study the effects of these two modifications for the determination of output, we must solve for a reduced form (general equilibrium) equation that describes the links between output, expected future output, and the nominal interest rate. Closely related to the standard IS schedule, this specification is
[Mathematical Expression Omitted].
This general equilibrium locus implies that there is a difference between temporary and permanent variations in interest rates. Holding [E.sub.t][y.sub.t+1] constant at [Mathematical Expression Omitted], as is appropriate for temporary variations, we have the standard IS curve determination of output as above. With [E.sub.t][y.sub.t+1] = [y.sub.t], which is appropriate for permanent disturbances, an alternative general equilibrium schedule arises which is "flatter" in (y, R) space than the conventional specification. This "flattening" reflects the following chain of effects. When variations in output are expected to occur in the future, they will be accompanied by inflation because of the positive Phillips curve link between inflation and output. With the consequent higher expected inflation at date t, the real interest rate will be lower and aggregate demand will be higher at a particular nominal interest rate.
Thus, "policy multipliers" depend on what one assumes about the adjustment of inflation expectations. If expectations do not adjust, the effects of increasing the nominal interest rate are given by [Delta]y/[Delta]R = -s and [Delta][Pi]/[Delta]R = s[Psi], whereas the effects if expectations do adjust are [Delta]y/[Delta]R = -s/[1 - s[Psi]] and [Delta][Pi]/[Delta]R = -s[Psi][1 - s[Psi]]. At the short-run horizons that the IS model is usually thought of as describing best, the conventional view is that there is a steep IS curve (small s) and a flat Phillips curve (small [Psi]) so that the denominator of the preceding expressions is positive. Notably, then, the output and inflation effects of a change in the interest rate are of larger magnitude if there is an adjustment of expectations than if there is not. For example, a rise in the nominal interest rate reduces output and inflation directly. If the interest rate change is permanent (or at least highly persistent), the resulting deflation will come to be expected, which in turn further raises the real interest rate and reduces the level of output.
There are two additional points that are worth making about this extended model. …
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