PDPRIETI Policy Discussion Paper Series 19-P-028

Why has Deflation Continued under Extraordinary MonetaryExpansion?

KOBAYASHI, Keiichiro
RIETI

The Research Institute of Economy, Trade and Industry

https://www.rieti.go.jp/en/

RIETI Policy Discussion Paper Series 19-P-028
October 2019

Why has deflation continued under extraordinary monetary expansion?1
Kobayashi, Keiichiro

The Tokyo Foundation for Policy Research, RIETI, Keio University, CIGS
Abstract

We propose a theoretical argument for a new rational expectations equilibrium
hypothesis

intheintergenerational

economy,whereeachgeneration

isintergenerationally altruistic and rational. The intergenerationally-rational
expectations equilibrium implies that deflation can continue under an extreme
increase in money supply.

Keywords: Deflationary equilibrium, transversality condition, zero nominal interest

rate policy.
JEL classification: E31, E50,The RIETI Policy Discussion Papers Series was created as part of RIETI research and aims to contributeto policy discussions in a timely fashion. The views expressed in these papers are solely those of theauthor(s), and neither represent those of the organization(s) to which the author(s) belong(s) nor theResearch Institute of Economy, Trade and Industry.

I thank Makoto Yano and seminar participants at Research Institute of Economy, Trade andIndustry (RIETI) for encouraging and useful comments. All remaining errors are mine. This
study is conducted as a part of the Project “Microeconomics, Macroeconomics, and Political
Philosophy toward Economic Growth” undertaken at RIETI.
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1. Transversality condition and the velocity of money
Observing the monetary policy in Japan for the last three decades, we have a question whether
the velocity of money may be endogenous and responsive to the policy changes. If the velocity
decreases endogenously in response to an additional monetary easing, it may be difficult toescape from deflation, even if the BOJ or the government of Japan firmly commits to the 2percent inflation target by constitutionalize it. In what follows, we propose a theoreticalargument of a new rational expectations equilibrium hypothesis in the intergenerationaleconomy. The intergenerationally-rational expectations equilibrium implies that velocity isendogenous, and deflation can continue under an extreme increase in money supply.
We interpret the problem of endogeneity of money velocity as the violation of thetransversality condition (TVC) in a standard dynamic general equilibrium model. The
quantity theory of money is described as

PY = MV,(1)where P is the price level, Y is the real output (or Gross Domestic Product), M is the nominal
amount of money, and V is the velocity of money.
Here, the TVC can be expressed as that the real value of money, m = M/P, should be finite
in the infinite future. The above equation (1) implies that m = Y/V, which implies that theTVC (or the finite m) means that V is also finite. If m diverges to infinity as time passes, Vmust go to zero.
Why is the TVC relevant to the problem of deflation? The reason is that if TVC is violated,m can go to infinity as M goes to infinity. Then, P can stay at a low level, which means thatthe deflation continues. It is well known that the TVC must be satisfied in the rational
expectations equilibrium, implying that the price level P should go to infinity as M goes toinfinity. Thus, in the standard model, if the BoJ implements an extreme monetary easing, orincreases M indefinitely, then the price level P should go up eventually. In other words, theTVC implies that the inflation is inevitable, if the BoJ implements an extreme monetary easing.
The reality that Japan experienced the coexistence of deflation and money growth seems
inconsistent with the TVC with respect to money. Our objective in the next section is topropose a new concept of the rational expectations equilibrium, in which the TVC is notnecessarily satisfied. In this new equilibrium, the coexistence of deflation and money growth2can be an equilibrium outcome.

２. Intergenerational rationality and deflationary equilibrium
The following argument is based on Kobayashi (2019).
In the usual macroeconomic models, the coexistence of deflation and money growth cannot
be sustained for decades because the coexistence does not satisfy the TVC. The reason why
deflation is impossible under an extreme monetary easing can be rephrased as follows: If
deflation continues under the extreme monetary easing, the value of money increases
indefinitely, which cannot happen in equilibrium because otherwise the money holders(households) can and will purchase the infinite amount of goods and services. As the total
amount of goods and services is finite, this cannot happen. See Bernanke (2000) for an
example of the similar reasoning. This logic can be broken if we consider a new concept ofintergenerational rationality. We will explain how it is broken in what follows.
The textbook macroeconomic model is the infinite-horizon economy, in which the consumers
or the households live for infinite future. But the reality is that all humans are mortal and theinfinite-horizon model is just an approximation. Acemoglu (2009) argues that the following
two assumptions are necessary for the economy to be approximated by the infinite-horizon
model:
1) the individuals live for a finite period, while the household is succeeded by thedescendants, and2) the individuals have the intergenerational altruism in the form that the discounted valueof the lifetime utility of their children enters their own lifetime utility.
Under these assumptions, the utility of individuals extends from generations to generations
and the economy is described as the maximization problem of the utility for the infinitelylived individuals. In the textbook macroeconomics, the economy of the finitely-livedindividuals with intergenerational altruism is considered equivalent to the economy of theinfinitely-lived individuals. We can show, however, that the former includes the latter, but notvice versa.
The optimality of the infinitely-lived individuals requires that the TVC must be satisfied,
while the optimality of the finitely-lived individuals does not require the TVC to hold. The
reason of this difference is summarized as follows.
 The infinitely-lived individuals can only have something they can experience as theirexpectations, because they will be alive when the expectations are realized.
3 On the other hand, the finitely-lived individuals can have something they cannot
experience as their intergenerational expectations, because they will be dead when theintergenerational expectations are realized.
This difference between the expectations of infinitely-lived individuals and theintergenerational expectations of finitely-lived individuals is completely neglected in theexisting macroeconomics literature. This difference is meaningless when we analyze thebusiness cycles or economic growth in the short-run or middle-run, such as four or five years.
But, we argue, when we analyze economic dynamics of the intergenerational time horizon,
this difference matters a lot.
Let us consider what the finitely-lived agents can hold as their expectations on the value of apiece of paper, which is called “money.” For simplicity of argument, let us assume that the“money”’ does not generate any utility. In the economy with the infinitely-lived individuals,
the value of “money” is permanently zero, because the worthless paper today is worthless
tomorrow.
However, in the economy with finitely-lived individuals, the people can hold the following
expectations: “Although the ‘money’ is worthless for me, I believe that my descendants will
become very happy if they hold ‘money’.” This expectation is not consistent with what thecurrent generation can experience and therefore it looks an irrational expectation. But thecurrent generation cannot experience what the next generation will experiences, meaning that
there is no way for the current generation to confirm the truth of their expectation ex post.
To confirm the expectations ex post is physically impossible, because they will be dead when
their descendants live. In this situation, what guarantees the rationality of expectations? The
only means to guarantee the rationality is the consistency of the value function: the valuefunction, or the lifetime utility, for the current generation must be consistent with theirexpectation on the value function for the next generation, in equilibrium. The meaning of thisconsistency condition will be made clear in the following argument.
Let us consider again the example of the piece of paper, called “money.” When a finitely-lived
agent believes “my descendants will be very happy with holding ‘money’,” what is the agent’s
value function? He has the intergenerational altruism such that he feels happiness when heexpects that his descendants will feel happiness. Then, he feels a desire for “money,” because
he wants to obtain it to bequeath to his descendants. Now, because of this new desire, he feelsthat “money” is valuable for him, because he wants “money” to bequeath to his descendants,
but not to increase his own consumption. In this way, a finitely-lived agent holds the4conviction that “money” is valuable for him. This conviction is consistent with his expectationon the utility of his descendants that “they will be happy with holding ‘money’”Thus, the consistency of expectation is satisfied, and the expectation (“my descendant will behappy with holding ‘money’”) is justified as a rational expectation.
This logic is summarized as the following circular argument, which is the same as thosetypically adopted in the rational expectations hypothesis.
 “Money’’ is valuable for me, as I want it not because it increases my own utility, but
because I am altruistic to my descendants and I want to bequeath “money” to them,because I believe that “money’’ will be valuable for my descendants.
 On the other hand, my expectation that “money’’ will be valuable for my descendants is
consistent with the fact that “money” is valuable for me. This consistency supports theexpectation as a rational expectation.
 In this way, the fact that “money” is valuable for me and the expectation that “money” isvaluable for my descendants support each other as the grounds of justification. This is acircular argument.
This circular argument generates the value of “money” as a bubble. The same logic holds forthe money in the real world. It is shown as follows that once the money has the value of thebubble, the deflation cannot be stopped even if the Bank of Japan increases the money supplyextremely. As stated in the previous paragraph, the logic for the effectiveness of extreme
monetary easing in fighting deflation is the following:
If deflation continues under the extreme monetary easing, the value of money
increases indefinitely, which cannot happen in equilibrium because otherwise themoney holders (households) can and will purchase the infinite amount of goods andservices. As the total amount of goods and services is finite, this cannot happen.
This logic can be overturned in our model of the intergenerational economy, where people
have non-satiated demand for money because they want to bequeath it as much as possible.
In this economy, even when the total value of money supply is increasing indefinitely, themoney holders (i.e., households) do not want to increase the purchase of the goods andservices indefinitely, but they just store the additional money. Then, the demand for the goods
and services stays finite, leading to the finite price level, while the indefinite amount of money
is stored to be bequeathed to the next generation. This situation can continue as a long-term
steady state.
5This argument implies that there can emerge the deflationary equilibrium, where the people
hoard money indefinitely, in the economy of finitely-lived individuals with theintergenerational altruism and rationality. It is also shown that the TVC is not satisfied. TheTVC is not necessary to be satisfied in the intergenerational model, because the TVC isnecessary for the optimality in the infinite-horizon model, not the intergenerational model.
In our intergenerational model, the violation of the TVC is consistent with the optimality inthe households’ decision, because they have the bubbly demand for money, which makes them
indifferent between hoarding money and increasing consumption.

３. Policy debate on the Japanese deflation redux
If the intergenerational model above is the true description of the Japanese economy, it gives
us a new insight for the policy debate on the decade-long deflation in Japan. Our model
implies that the deflationary equilibrium where deflation and money growth coexist cancontinue for a long period as a stable steady state. In this deflationary equilibrium, the TVC
is violated. The existence of this deflationary equilibrium implies that the deflation cannot bestopped by the extraordinary monetary expansion by the central bank.
In the 1990s and 2000s, many economists argue that an extreme monetary easing can help
the Japanese economy to escape from the deflation (see for example, among many others,
Krugman [1998], Bernanke [2000], Eggertsson and Woodford [2003], Auerbach andObstfeld [2005]). These arguments are based on the TVC without exception. They go as
follows: the coexistence of deflation and monetary easing violates the TVC, while the TVC
must be satisfied in equilibrium; thus, the deflation must stop eventually in equilibrium, aslong as the central bank continues the extreme monetary easing.
However, our intergenerational theory claims that there exists a long-term equilibrium wherethe TVC is violated. Given that this theory is correct, the extreme monetary easing may not
be able to stop deflation. Our theory implies that the popular opinion, which has been
dominant for the last 20 years, that we need further monetary easing to fight deflation, may
not be correct.
Then, what causes the persistent deflation in our intergenerational economy?
The deflationary equilibrium in our intergenerational economy is a steady state, which can6

continue in the long-run, whereas in the standard Keynesian argument, deflation occurs whenthe economy deviates from the long-term steady state. In the long-term steady state, thefollowing Fisher equation holds:

1+i = (1+ π) (1+ r),（2）where i is the steady-state value of the nominal interest rate, πis the inflation rate, and r is
the real interest rate. In the long-term steady state, the real interest rate r is given by themarket equilibrium and it cannot be affected by the monetary policy. Given that r is fixed, thedecision by the central bank to set i decides the value of π. In the last 25 years in Japan, thenominal interest rate has been fixed at zero, i.e., i = 0. Then, the Fisher equation (2) impliesthat the value of π, the long-term inflation rate, becomes negative:

π＝－r/(1+r) < 0This argument shows that our model of the intergenerational economy implies that the zerointerest rate policy generates the expectation of the long-term deflation. In the existingmodels, this conclusion from the Fisher equation is rejected because the long-term deflation
under monetary easing violates the TVC. However, this conclusion cannot be rejected in theintergenerational model, because the TVC is not necessarily satisfied in equilibrium in ourmodel.
In this case, the extraordinary monetary expansion, such as the quantitative easing, is not able
to overturn the deflationary expectations. We may need a fundamentally different policy
measures to fight the deflationary equilibrium.

References

Acemoglu, Daron (2009) Introduction to Modern Economic Growth, Princeton University
Press, Princeton, New Jersey,.
Auerbach, Alan J., and Maurice Obstfeld (2005) “The Case for Open-Market Purchases in a7

Liquidity Trap,” American Economic Review, Vol. 95, No. 1, pp. 110--137.
Bernenke, Ben (2000) “Japanese Monetary Policy: A Case of Self-Induced Paralysis?” in R.
Mikitani and A. S. Posen, eds., Japan's Financial Crisis and Its Parallels to U.S. Experience,
Washington: Institute for International Economics.
Eggertsson, Gauti B., and Michael Woodford (2005) “The Zero Bound on Interest Rates andOptimal Monetary Policy,” Brookings Papers on Economic Activity, Vol. 34, No. 1, pp. 139211. The Brookings Institution.
Kobayashi, Keiichiro (2019) “Deflationary equilibrium with ever-growing government
liabilities, and intergenerational rationality,” work in progress.
Krugman, Paul R., (1998) “It's Baaack: Japan's Slump and the Return of the Liquidity Trap,”

Brookings Papers on Economic Activity, Vol. 29, No. 2, pp. 137-206. The Brookings
Institution.

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