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King, Robert G.. "The New IS-LM Model: Language, Logic, and Limits." Economic Quarterly. Federal Reserve Bank of Richmond. 2000. HighBeam Research. 16 Oct. 2018 <https://www.highbeam.com>.
King, Robert G.. "The New IS-LM Model: Language, Logic, and Limits." Economic Quarterly. 2000. HighBeam Research. (October 16, 2018). https://www.highbeam.com/doc/1G1-73462261.html
King, Robert G.. "The New IS-LM Model: Language, Logic, and Limits." Economic Quarterly. Federal Reserve Bank of Richmond. 2000. Retrieved October 16, 2018 from HighBeam Research: https://www.highbeam.com/doc/1G1-73462261.html
Recent years have witnessed the development of a New IS-LM model that is increasingly being used to discuss the determination of macroeconomic activity and the design of monetary policy rules. It is sometimes called an "optimizing IS-LM model" because it can be built up from microfoundations. It is alternatively called an "expectational IS-LM model" because the traditional model's behavioral equations are modified to include expectational terms suggested by these microfoundations and because the new framework is analyzed using rational expectations. The purpose of this article is to provide a simple exposition of the New IS-LM model and to discuss how it leads to strong conclusions about monetary policy in four important areas.
* Desirability of price level or inflation targeting: The new model suggests that a monetary policy that targets inflation at a low level will keep economic activity near capacity. If there are no exogenous "inflation shocks," then full stabilization of the price level will also maintain output at its capacity level. More generally, the new model indicates that time-varying inflation targets should not respond to many economic disturbances, including shocks to productivity, aggregate demand, and the demand for money.
* Interest rate behavior under inflation targeting: The new model incorporates the twin principles of interest rate determination, originally developed by Irving Fisher, which are an essential component of modern macroeconomics. The real interest rate is a key intertemporal relative price, which increases when there is greater expected growth in real activity and falls when the economy slows. The nominal interest rate is the sum of the real interest rate and expected inflation. Accordingly, a central bank pursuing an inflation-targeting policy designed to keep output near capacity must raise the nominal rate when the economy's expected growth rate of capacity output increases and lower it when the expected growth rate declines.
* Limits on monetary policy: There are two limits on monetary policy emphasized by this model. First, the monetary authority cannot engineer a permanent departure of output from its capacity level. Second, monetary policy rules must be restricted if there is to be a unique rational expectations equilibrium. In particular, as is apparently the case in many countries, suppose that the central bank uses an interest rate instrument and that it raises the rate when inflation rises relative to target. Then the New IS-LM model implies that it must do so aggressively (raising the rate by more than one-for-one) if there is to be a unique, stable equilibrium. But if the central bank responds to both current and prospective inflation, then it is also important that it not respond too aggressively.
* Effects of monetary policy: Within the new model, monetary policy can induce temporary departures of output from its capacity level. However, in contrast to some earlier models, these departures generally will not be serially uncorrelated. If the central bank engineers a permanent increase in nominal income, for example, then there will be an increase in output that will persist for a number of periods before fully dissipating in price adjustment. Further, the model implies that the form of the monetary policy rule is important for how the economy responds to various real and monetary disturbances.
In summary, the New IS-LM model instructs the central bank to target inflation. It indicates that there are substantial limits on the long-run influence that the monetary authority can have on real economic activity and that there are also constraints on its choice of policy rule. But the New IS-LM also indicates that the monetary authority can affect macroeconomic fluctuations through its choice of the monetary policy rule, as well as via monetary policy shocks.
The plan of the article is as follows. Section 1 provides some historical background on the evolution of the IS-LM model since its origin in Hicks (1937). Section 2 then quickly lays out the equations of the closed economy version of the New IS-LM model. Section 3 uses the framework to show how a neutral monetary policy--a policy which keeps output close to its capacity level--implies a specific inflation targeting regime and, if certain exogenous shocks are small, rationalizes a full stabilization of the price level. Following Goodfriend and King (1997), such a policy is called a "neutral monetary policy" and the new model is used to determine some rules for the setting of alternative monetary instruments that would yield the neutral level of output.
The article next turns to understanding the mechanics of the New IS-LM model. Proponents of IS-LM modeling typically stress that sticky prices are central to understanding macroeconomic activity (e.g., Mankiw [1990]) so that the discussion begins in Section 4 with this topic. Firms are assumed to set prices and adjust quantity in response to changes in demand. But in the New IS-LM model, firms are assumed to be forward-looking in their price-setting, in line with research that begins with Taylor (1980). Forward-looking price-setting has major effects on the linkage between nominal disturbances and economic activity, endowing the model with a mix of Keynesian and Classical implications. Section 5 considers the long-run limits on monetary policy given this "supply side" specification and several related topics.
Turning to the aggregate demand side, the new model's IS schedule is also forward looking. Section 6 starts by discussing why this is the inevitable attribute of optimizing consumption-investment decisions and then considers some macroeconomic implications of the new model's IS schedule.
The macroeconomic equilibrium of the New IS-LM model is employed to analyze three key issues that are relevant to monetary policy. Section 7 considers limits on interest rate rules. Section 8 highlights how monetary policy can produce short-run departures of output from its capacity level, either as a result of monetary shocks or as a result of a policy rule which differs from the neutral rules developed in Section 3. It also considers the origin and nature of the tradeoff between inflation and output variability that is present in this model. The article is completed by a brief concluding section.
1. THE EVOLUTION OF THE IS-LM MODEL
Before detailing the model, it is useful to briefly review the historical process that has led to its development and influences its current uses. Since the 1930s, variants of the IS-LM model have been the standard framework for macroeconomic analysis. Initially, Hick's (1937) version was used to explain how output and interest rates would be affected by various shocks and alternative policy responses. Subsequent developments broadened the range of issues that could be studied with the model, notably the introduction of an aggregate production function and a labor market by Modigliani (1944). With the rise of quantitative frameworks for monetary policy analysis--such as the Penn-FRB-MIT model, which was employed by the Federal Reserve System--the role of the IS-LM model changed in a subtle manner. After detailed explanations were worked out in these policy laboratories, the IS-LM model was used to give a simple account of the findings.
While the initial IS-LM model did not determine how the price level evolved through time, the addition of a price equation--or a wage/price block that featured a Phillips (1958) curve--made it possible to explore the implications for inflation. [1] The simultaneous occurrence of high inflation and high unemployment in the 1970s led macroeconomists to question this aspect of theoretical and quantitative macromodels. Further, during the rational expectations revolution spurred by Lucas (1976), fundamental questions were raised about the value of the IS-LM model and the related quantitative macroeconomic policy models. The IS-LM model was portrayed as being fatally inconsistent with optimizing behavior on the part of households and firms (Lucas 1980). The quantitative macropolicy models were criticized for not using microfoundations as a guide to the specification of estimable equations and also for avoiding central issues of identification (Sims 1980, Sargent 1981). The rational expectations revolution suggest ed that new macroeconomic frameworks were necessary--both small analytical frameworks like the IS-LM model and larger quantitative macropolicy models--and that these would lead to a substantial revision in thinking about the limits on monetary policy and the role of monetary policy.
One initial attempt at updating the IS-LM model was initiated in Sargent and Wallace (1975), who incorporated a version of the aggregate supply theory developed by Lucas (1972, 1973) in place of the Phillips curve or wage/price block. According to this rational expectations IS-LM model, systematic monetary policy could not influence real economic activity, although monetary shocks could cause temporary departures of output from its capacity level. This finding that systematic monetary policy was irrelevant led the related literature to be described, by some, as the New Classical macroeconomics. Sargent and Wallace also used their framework to argue against use of the nominal interest rate as the instrument of monetary policy--suggesting that this practice was inconsistent with a unique macroeconomic equilibrium. While this rational expectations IS-LM model was subsequently used to clarify issues of importance for monetary policy--for example, Parkin (1978) and McCallum (1981) showed that an appropriate nomin al anchor could allow the interest rate to be used as the instrument of monetary policy--it did not gain widespread acceptance for three reasons. First, some economists--particularly macroeconomic theorists--saw the model as flawed, because its lack of microfoundations led it to lack the behavioral consistency conditions which are the inevitable result of optimization and the expectational considerations which are at the heart of dynamic economic theory. Second, other economists--particularly applied macroeconomists--were suspicious of the model because it suggested that departures of output from capacity should be serially uncorrelated. Third, many economists--including central bankers-- remained convinced that the systematic choices of the monetary authority were important for the character of economic fluctuations and thus rejected the model due to the "policy irrelevance" implication.
In recent years, there has been the development of small, optimizing macro models that combine Classical and Keynesian features in a "New Neoclassical Synthesis." [2] The New IS-LM model is an outgrowth of this more general research program and is thus designed to incorporate the major accomplishments of the rational expectations revolution, including a more careful derivation from microfoundations, while retaining the stark simplicity that made the earlier IS-LM frameworks much employed tools. One important use of the New IS-LM model is to communicate results from other, more complicated macroeconomic models that are relevant to monetary policy. For example, Kerr and King (1996) first used the core equations of the New IS-LM model to exposit issues involving interest rate rules for monetary policy that had arisen in my research on small, fully articulated macroeconomic models with sticky prices and intertemporal optimization (King and Watson 1996; King and Wolman 1999). [3] The current article shows how the New IS-LM model is also useful in expositing many issues that arise in these sorts of small, fully articulated models and also in larger quantitative macroeconomic models that are currently employed for monetary policy analysis, including the new rational expectations framework of the Federal Reserve (the FRB-US model) and the various U.S. and international models developed by Taylor (1993). In fact, in using the model to discuss the implications of sticky prices, restrictions on interest rate policy rules, and the trade-off between the variability of inflation and output, the article will touch repeatedly on themes which have been central parts of Taylor's research program.
2. THE NEW IS-LM MODEL
Like its predecessors, the New IS-LM model is a small macroeconomic model designed to describe the behavior of economy-wide variables that enter in most discussions of monetary policy. There are five endogenous variables: the log level of real output/spending y, the log price level P, the real interest rate r, the inflation rate [pi], and the nominal interest rate R. [4]
The Core Equations
Three specifications are present in all of the recent papers that employ the New IS-LM model. These are an IS equation, a Fisher equation, and a Phillips curve equation.
The forward-looking IS equation makes current real spending [y.sub.t] depend on the expected future level of real spending [E.sub.t][y.sub.t+1] and the real interest rate [r.sub.t]. There is also an aggregate demand shock [x.sub.dt]: a positive [x.sub.dt] raises aggregate spending at given levels of the endogenous determinants [E.sub.t][y.sub.t+1] and [r.sub.t]. [5]
IS: [y.sub.t] = [E.sub.t][y.sub.t+1] - s[[r.sub.t] - r] + [x.sub.dt] (1)
The parameters s [greater than] 0 determines the effect of the real interest rate on aggregate demand: If s is larger then a given rise in the real interest rate causes a larger decline in real demand. The parameter r [greater than] 0 represents the rate of interest which would prevail in the absence of output growth and aggregate demand shocks. The new IS equation is described as forward-looking because [E.sub.t][y.sub.t+1] enters on the right-hand side.
The Fisher equation makes the nominal interest rate [R.sub.t] equal to the sum of the real interest rate [r.sub.t] and the rate of inflation that is expected to prevail between t and t+1, [E.sub.t][[pi].sub.t+1].
F: [R.sub.t] = [r.sub.t] + [E.sub.t][[pi].sub.t+1] (2)
This conventional specification of the Fisher equation omits any inflation risk premium in the nominal interest rate. [6]
The expectational Phillips curve relates the current inflation rate [[pi].sub.t] to expected future inflation [E.sub.t][[pi].sub.t+1], the gap between current output [y.sub.t] and capacity output [y.sub.t], and an inflation shock [x.sub.[pi]t].
PC: [[pi].sub.t] = [beta][E.sub.t][[pi].sub.t+1] + [varphi]([y.sub.t] - [y.sub.t]) + [x.sub.[pi]t] (3)
The parameter [beta] satisfies 0 [less than or equal to] [beta] [less than or equal to] 1. The parameter [varphi] [greater than] 0 governs how inflation responds to deviations of output from the capacity level. If there is a larger value of [varphi] then there is a greater effect of output on inflation; in this sense, prices may be described as adjusting faster--being more flexible--if [varphi] is greater.
Using the definition of the inflation rate [[pi].sub.t] = [P.sub.t] - [P.sub.t-1], this specification might alternatively have been written as [P.sub.t] = [P.sub.t-1] + [beta][E.sub.t][[pi].sub.t+1] + [varphi]([y.sub.t] - [y.sub.t]) + [x.sub.[pi]t]. This alternative form highlights why (3) is sometimes called a "price equation" or an "aggregate supply schedule." It is a price equation in the sense that it is based on a theory of how firms adjust their prices, as discussed further in Section 4 below. It is an aggregate supply schedule because it indicates how the quantity supplied depends on the price level and other factors. But this article uses the Phillips curve terminology because this is the dominant practice in the new and old IS-LM literature.
The relationship between the output gap and the steady-state rate of inflation gap is given by y - y = 1-[beta]/[varphi] [pi] according to this specification. In fact, experiments with fully articulated models that contain the structural features which lead to (3)--including those of King and Wolman (1999)--suggest a negligible "long-run effect" at moderate inflation rates. Prominent studies of the monetary policy implications of the New IS-LM model--including that of Clarida, Gali, and Gertler (1999)--accordingly impose the [beta] = 1 condition in specifying (3). In this article, [beta] will be taken to be less than but arbitrarily close to one.
Money Demand and Monetary Policy
To close the model and determine the behavior of output, the price level and other variables, it is necessary to specify the monetary equilibrium condition. Researchers presently adopt two very different strategies within the literature on the New IS-LM model.
Specifying money demand and money supply. Under this conventional strategy, the money demand function is typically assumed to take the form
MD: [M.sub.t] - [P.sub.t] = [delta][y.sub.t] - [gamma][R.sub.t] - [x.sub.vt] (4)
with [M.sub.t] - [P.sub.t] being the demand for real balances. This demand for money has an income elasticity of [delta] [greater than] 0 and an interest semielasticity of - [gamma] [less than] 0. [7] There is a shock which lowers the demand for money, [x.sub.vt]: this is a shock to velocity when [delta] = 1 and [gamma] = 0.
The money supply function is assumed to contain a systematic monetary policy component, [f.sub.Mt], and a shock component [x.sub.Mt] :
MS: [M.sub.t] = [f.sub.Mt] + [x.sub.Mt]. (5)
The monetary authority's systematic component may contain responses to the current state, lagged or expected future level of economic activity. Taken together, these equations determine the quantity of money and also provide one additional restriction on the comovement of output, the price level and interest rates.
Specifying an interest rate rule for monetary policy. An alternative--and increasingly popular--strategy is to simply specify an interest rate rule for monetary policy,
IR : [R.sub.t] = [f.sub.Rt] + [x.sub.Rt], (6)
which contains a systematic component, [f.sub.Rt], and a shock component [x.sub.Rt].
Under this rule, the quantity of money is demand-determined at the [R.sub.t] which is set by the monetary authority. Thus, the behavior of the money stock can be deduced, from (4) and (6), as [M.sub.t] - [P.sub.t] = [[delta]y.sub.t] - [gamma][[f.sub.Rt] + [x.sub.Rt]] - [x.sub.vt]. But since the stock of money is not otherwise relevant for the determination of macroeconomic activity, some analysts proceed without introducing money at all. [8]
What Is New about This Model?
The answer to this question depends on the chosen starting point in the history of macroeconomic thought.
Relative to the original model of Hicks, the New IS-LM model is different in that it makes the price level an endogenous variable, which is influenced by exogenous shocks and the monetary policy rule. In the language of Friedman (1970) and other monetarists, the New IS-LM model views the price level as a monetary phenomenon rather than as an unexplained institutional phenomenon. In terms of formal modeling, the idea that the price level is a monetary phenomenon is represented in two ways. First, the model cannot be solved for all of the endogenous variables without the specification of a monetary policy rule. Second, under a money stock rule, even though some individual prices are sticky in the short run, the price level responds to exogenous, permanent changes in the level of the money stock in both the short run and the long run. But, since the 1970s, textbook presentations of the IS-LM model have added a pricing block or aggregate supply schedule, which makes the price level endogenous.
The New IS-LM model also incorporates expectations in ways that the traditional IS-LM model did not. But the rational expectations IS-LM model of Sargent and Wallace (1975) also incorporated the influence of expectations of inflation into both the Fisher equation and the aggregate supply schedule. Modern textbook treatments discuss these expectations mechanisms in detail.
Figure 1 shows two of the New IS-LM model's key equations. As in modern textbooks, there is an IS curve which makes output depend negatively on the (real) interest rate and a Phillips curve or aggregate supply schedule which makes output depend positively on the inflation rate. Relative to these presentations, the New IS-LM model differs (i) in the stress that it places on expectations in both aggregate demand and aggregate supply and (ii) in the particular ways in which expectations are assumed to enter into the model. In particular, the new IS schedule (1) identifies expected future income/output as a key determinant of current output, while this is missing in the SargentWallace model. The new aggregate supply schedule or Phillips curve (3) identifies expected future inflation as a key determinant of current inflation, while in the Sargent-Wallace model it is yesterday's expectation of the current inflation rate that is relevant for supply.
These channels of influence are highlighted in Figure 1. In panel a of the figure, an increase in expected future output shifts the IS curve to the right. requiring a higher real interest rate at any given level of output. In panel b of the figure, an increase in expected future inflation shifts the Phillips curve to the left, requiring a higher current inflation rate at any given level of output.
However, while it is possible to express these behavioral equations in familiar graphical ways, the reader should not be misled into thinking that macroeconomic analysis can be conducted by simple curve-shifting when expectations are rational in the sense of Muth (1961). [9] Instead, it is necessary to solve simultaneously for current and expected future variables, essentially by determining the complete path that the economy is expected to follow. Once this path is known, it is possible to return to the individual graphs of the IS curve or the Phillips curve to describe the effects of shocks or policy rules. …
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