西方经济学评论 2014卷 第1辑 （总第4辑）
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5.Modeling monetary stabilization policy

Now, we are in a position to consider how we can study the effect of monetary stabilization policy by using the analytical framework of the model that was interpreted in section 4.Let us assume that the central bank controls the nominal rate of interest by means of the following feedback monetary policy rule, which is a kind of Taylor rule due to Taylor（1993）.Formalization of the monetary policy by means of the Taylor rule became popular since so called“New Keynesian”dynamic models that are represented by Woodford（2003）and Galí（2008）took the leading position in the mainstream macroeconomics.Choice of the nominal rate of interest rather than nominal money supply as a monetary policy instrument is now common to Post Keynesian as well as New Keynesian literatures.As for the related literatures in Post Keynesian tradition, see, for example, Arestis and Sawyer（2008）, Asada（2010,2011）, Asada, Chiarella, Flaschel and Franke（2010）, Hein（2007）, Isaac（2009）and Setterfield（2009）.

We can interpret this policy rule as a kind of flexible inflation targeting rule, which considers both of the inflation targeting and the employment targeting. In this formulation, the nonnegative constraint of nominal rate of interest is explicitly considered.This type of nonnegative constraint is in particular important in Japan in the 1990s and the 2000s under long period deflationary depression and USA and European countries in the late 2000s after the serious financial crises.

It will be appropriate to replace the inflation expectation formation equation（7）in section 4 with the following new equation in case in which the central bank announces the target rate of inflation to the public.

This equation formalizes a mixed type of inflation expectation formation hypothesis, which means that the inflation expectation formation has both of the“forward looking”and“backward looking”elements.The parameterζis the weight of the“forward looking”element.We can interpret the value of the parameterζ as a measure of the credibility of the inflation targeting by the central bank.The more credible the inflation targeting, the larger will be the value ofζ.See Asada, Chiarella, Flaschel and Franke（2011）.

We obtain the following relationships substituting the equation of price Phillips curve（6）into equations（9）and（10）.

Equations（4）（i）,（4）（ii）,（11）and（12）consist of the following four dimensional system of nonlinear differential equations, whereρin equations（4）（i）and（4）（ii）is no longer constant.

The equilibrium solution（d*, y*, π*, ρ*）of this system such that

satisfies the following relationships.

We can see that the equilibrium value of each variable is independent of the parameter valuesβ1, β2, andζ.Examining the 4×4 Jacobian matrix of the system（13）at the equilibrium point, we can prove the following proposition.We omit the proof because we need some tedious long calculations to prove this proposition that is related to such a high dimensional dynamic system.We can use the method of the proof that is used in Asada, Chiarella, Flaschel and Franke（2010）extensively.

Proposition 1.

（1）Suppose that all of the parameter values β1, β2, and ζ are sufficiently small（sufficiently close to 0）.Then, the equilibrium point of the system（13）becomes locally unstable.

（2）Suppose thatβ1andβ2are sufficiently large andζis sufficiently close to 1.Then, the equilibrium point of the system（13）becomes locally stable.The concept of stability and instability in our model is the traditional one that is applicable to the case in which all initial values of the endogenous variables are pre-determined, unlike the mainstream“New Keynesian”models in which some variables are treated as not-pre-determined“jump”variables.Namely, we consider that the equilibrium point is locally stable if and only if all the roots of the characteristic equation at the equilibrium point have negative real parts.As for the critique of the“New Keynesian”methodology that allows for the“jump”variables, see Asada（2010）, Asada, Chiarella, Flaschel and Franke（2010）, and Asada, Flaschel, Mouakil and Proaño（2011）.

（3）At the intermediate values of the parametersβ1, β2andζ, cyclical fluctuations around the equilibrium point occur.

This proposition means that the central bank's active monetary policy that is combined with the“credible”inflation targeting can“stabilize an unstable economy”even if the dynamics of private debt and capital are explicitly considered unlike the standard models of monetary policy.Needless to say, the sentence“stabilizing an unstable economy”is the quotation of the title of Minsky's book（Minsky,1986）.See also Asada, Chiarella, Flaschel, Mouakil, Proaño and Semmler（2010）.

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