NIRA OPINION PAPER
No.38 | May 2018

Can Japan’s Monetary Policy
overcome the Dilemma it faces?
-Suggestions offered by Estimation of the Equilibrium Interest Rate Ryuzo Miyao
Professor, Graduate School of Economics, The University of Tokyo

Mototsugu Shintani
Professor, Research Center for Advanced Science and Technology, The University of TokyoJapan’s monetary policy faces a dilemma in the second term of the Bank ofJapan Governor Kuroda, and the second term of the framework that he has instituted.
The realization of the 2% price stability target will take time; however, a further
strengthening of monetary easing in order to prioritize the early achievement of thistarget will increase concerns over secondary effects. On the other hand, the hasty
normalization of monetary easing or a change in the policy framework will create
instability in the monetary environment and slow down Japan’s economic recovery.
One key to overcoming this dilemma is whether or not the effects of monetaryeasing increase in the future without a change in the policy. If the performance of theeconomy improves, the economic stimulus effect of monetary easing will become
stronger even if the operational target for the policy interest rate remains the same forthe time being. If the benefits of the monetary easing policy increase in magnitude, theproblem of secondary effects may be relatively mitigated. In this paper, the authors
estimate the equilibrium interest rate (also known as the natural rate of interest), a
neutral interest rate level that neither stimulates nor restrains the economy, andexamine whether or not the effects of monetary easing will increase in the future.
The results of these estimates, based on multiple models, suggest that Japan’sequilibrium interest rate has recently commenced an upward trend. The same trend
could also be inferred from the potential growth rate, corporate capital investment andother economic indicators. If this steady increase in Japan’s equilibrium interest ratecontinues into the future, the policy effects, i.e. the benefits of monetary easing, canalso be expected to increase.

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With the Bank of Japan’s Governor Haruhiko Kuroda beginning his second term, a second
round of monetary policy is commencing under his leadership, and the coming five years of policy
management is a subject of close attention. The achievement of the BOJ’s 2% price stability target
will take some time, and concern over potential secondary effects will intensify if monetary easing
is strengthened in order to prioritize the early achievement of this goal. On the other hand, if the
Bank goes as far as hastily normalizing the easing policy or changes its policy framework,
instability will be generated in the financial conditions, and this would act to dampen economic
recovery. One key factor in overcoming this dilemma will be whether or not the effects of monetaryeasing will increase without a change in the Bank’s policy. This paper will estimate the equilibrium
interest rate (also known as the “natural” rate of interest), which is a neutral interest rate levelthat neither stimulates nor restrains the economy in order to examine the potential for the benefitsof monetary easing to increase into the future1.

Work will not disappear from Human Society
Following the appointment of Haruhiko Kuroda to the Governorship of the BOJ in 2013,
the Bank displayed a change in its policy management approach towards the prioritization of therapid realization of a 2% price stability target, and the implementation of all necessary policy forthe achievement of this target. The impression made by the transition in the Bank’s policy
approach at a Monetary Policy Meeting in April 2013, directly following Governor Kuroda’s
appointment, towards large-scale easing – both quantitative and qualitative – and a stated goal of
doubling the inflation rate to 2% in two years, remains fresh in the memory. Easing was expanded
in October 2014, and in January 2016 the Bank further strengthened easing, moving to a negativeinterest rate policy. However, secondary effects manifested themselves in unexpected forms (forexample, a negative 10-year government bond interest rate), and in September 2016 the Banktransitioned to a policy of short- and long-term interest rate control (yield curve control), whichhas persisted to the present.
Over the course of this period, the Japanese economy continued a prolonged recovery,
driven at first by household consumption, and, following this, by improvement in corporate profitsand employment. At the same time, while the inflation rate became positive and temporarily rose
to close to 1%, considered overall, the upward pressure has been very relaxed. The latest
projections by the Bank of Japan itself predict an inflation rate of 1.8% for both fiscal years of 2019and 2020 (Outlook for Economic Activity and Prices, April 2018). It appears that the stablerealization of the Bank’s 2% price stability target will take some time.
The second term of the Kuroda regime faces the following dilemma: If the Bank maintains
the same logic as it did during Governor Kuroda’s first term, and further strengthens monetary
For more details regarding the estimates discussed in this paper, please refer to the background paper “Kinko
rishiritsu no suikei shuho oyobi suitei kekka ni tsuite [On the Estimation Methods and Resutls of Equilibrium Interest

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Rates],” is available on NIRA’s homepage. (in Japanese)
http://www.nira.or.jp/president/opinion/entry/n180524_892.html

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easing in order to prioritize the rapid achievement of the 2% target, it is predicted that the risk of
secondary effects – the creation of an asset price bubble, a worsening in the profit margin offinancial institutions, and a decline in fiscal discipline – will intensify. On the other hand, if the
Bank places the greatest emphasis on the risk of secondary effects and hastily normalizes easingor even modifies its 2% target policy framework, the monetary environment will be rendered
unstable, and economic recovery will be delayed. Neither strengthening easing nor pulling backfrom the policy represents an easy solution, and it can be predicted that this will represent adifficult task for policy management. This is the dilemma currently facing the Bank of Japan2.

Overcoming the Dilemma: Will the Benefits of Monetary Easing Increase?
Is there a means of overcoming this dilemma? One key will be whether or not the benefitsof monetary easing, i.e. the economic stimulus effect, increase without a change in the policy.
Generally, the degree of easing in monetary policy can be evaluated by comparing the levelof the policy interest rate (typically, the short-term interest rate) and the equilibrium interest rate
(more specifically, the equilibrium real interest rate), a neutral interest rate level that does notaffect the economy or prices. If the policy interest rate (the real rate defined as the nominal rate
less expected inflation rate) is lower than the equilibrium interest rate, the monetary policy stancecan be judged as expansionary; by contrast, if the policy interest rate is higher, monetary policy
can be judged as contractionary. Therefore, if the equilibrium interest rate were to increase due tofactors such as an increase in the performance of the economy without any change in the target
level of the policy interest rate, the degree of monetary easing would increase, and the economic
stimulus effect would be boosted. If, following this scenario, the benefits of the easing policy
increase while concern regarding the secondary effects remains constant, the issue represented bythose secondary effects would, relatively speaking, be eased. As a result, while the dilemma would
remain, it could be overcome.
However, there is some room for argument as to whether or not concern regarding
secondary effects can be regarded as a given, i.e. as fixed, under a long-term easing regime. The
main risks related to unconventional monetary policy are indicated as being: (i) financial
imbalances (asset price bubbles, etc.); (ii) impact on the financial system (decline in profits forfinancial institutions, etc.); and (iii) effects related to fiscal policy (risk related to monetaryfinancing, etc.). It is naturally the case that each of these areas will require careful examinationin future: In relation to (i), as to whether or not expectations will become excessively bullish in theevent that the fundamentals of the economy strengthens; in relation to (ii), as to whether or not
the vulnerability of the financial system will increase, given the possibility that the low-profit
This paper will focus on yield curve control, the BOJ’s major future policy framework, and discuss the effect ofmonetary policy by considering the gap between the policy interest rate and the equilibrium interest rate. While thepolicy effects of the “quantitative” aspect of quantitative and qualitative monetary easing which has been emphasized
by the Bank – large-scale expansion of the monetary base and buybacks of long-term government bonds – are still
being verified, a clear economic stimulus effect (stock prices, exchange rate, etc.) has been reported (Miyao, R.,
Hidentoteki kin’yu seisaku – Seisaku tojisha toshite no shiten [“Unconventional Monetary Policies – A Perspective froman Involved Party”], 2016, Yuhikaku Publishing, in particular Chapter 3). The Bank of Japan has announced that it
will continue its policy of expansion of the monetary base until the actual inflation rate stably exceeds its target of 2%,
and expects recovery in the economy to continue to be supported by the effect of the quantitative approach.

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NIRA OPINION PAPER
No.38 | May 2018environment for financial institutions will become structural: and in relation to (iii), as to whether
or not the nation falls into a state of fiscal dominance (a state in which the government loses fiscal
discipline and the central bank follows the government in a subservient role)3.

Overview of Equilibrium Interest Rate: Long-term Trend Factors and Other
Fluctuating Factors
In this section, we provide a detailed explanation of the equilibrium interest rate, thispaper’s main focus4.
As indicated above, the term “equilibrium interest rate” generally refers to a neutral realinterest rate that does not affect the economy or prices, acting neither to ease nor to tighten.
Theoretically, the equilibrium interest rate can be defined as a real interest rate that balancessavings and investment in a situation in which prices are elastic and full employment has beenachieved. If the actual real interest rate is higher than the equilibrium interest rate, output will
fall below the full employment level (this is termed “equilibrium output” or “natural output”),
acting to push prices down. Alternatively, if the real interest rate is lower than the equilibrium
interest rate, it will act to increase output and prices.
Under the framework of an economic growth model, this equilibrium interest rate
corresponds to the real interest rate on the optimum growth path in the long-run (i.e., the realinterest rate consistent with the balanced growth path, on which prices are flexible and supply
and demand are matched). Because the equilibrium interest rate is a concept that corresponds toequilibrium output (that is, full employment output), the fact that it corresponds to the potential
growth rate (the growth rate under equilibrium output) can be intuitively understood. The
equilibrium interest rate can formally be derived explicitly from the optimum household
consumption and savings behavior that forms the foundation of optimum growth theory (theEuler equation for consumption). As a result, the equilibrium interest rate can be expressed as
the total of a component that corresponds to the long-term potential growth rate (theproductivity growth rate, etc.) and a component that is explained by short-term fluctuating
factors (changes in household preferences, fiscal policy, and other demand shocks). In otherwords, it can be expressed as follows:
The equilibrium interest rate = A long-term trend component (corresponding to the potential
growth rate) + A cyclical component (fluctuations due to demand shocks, etc.).
Discussions based on the approximation “equilibrium interest rate (or natural rate ofinterest) ≒ potential growth rate” are frequently encountered. This can be understood as an
For more detail, see, for example, Miyao, R. “ICT no shinten to kin’yu seisaku unten (“The Development of ICT and
the Management of Monetary Policy”),” NIRA Opinion Paper No. 33, December 2017.
4 For discussions regarding the equilibrium interest rate, see Oda, S. and Muranaga, J., “Shizen rishiritsu ni tsuite:
Riron seiri to keisoku (“The Natural Rate of Interest: A Survey of Theory and Measurements”),” Bank of Japan
Working Paper Series No. 03 – J – 5, October 2003, and Iwasaki, Y. et al, “Wa ga kuni ni okeru shizen rishiritsu no
doukou (“Trends in the Natural Rate of Interest in Japan”),” Bank of Japan Review, 2016 – J – 18, October 2016.
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approach that focuses on long-term trend factors, making it possible to ignore the short-term
fluctuating factors in the second term of the equation above.
The approach taken to the calculation of estimates below will reflect this idea of dividing
the equilibrium interest rate into long-term trend factors and other fluctuating factors.

Approach to the Estimation of the Equilibrium Interest Rate
This section will introduce methods employed in the estimation of the equilibrium
interest rate. The main approaches to estimation of the equilibrium interest rate are: (1) The
univariate time-series approach (the Hodrick-Prescott filter [hereafter, referred as “HP filter”]);(2) The Laubach-Williams model; and (3) The dynamic stochastic general equilibrium (DSGE)
model. An overview of the characteristics of each of these approaches will be offered.
(1) Univariate time-series approach (HP filter)
The univariate time-series approach (HP filter) is a method of statistically extracting
trend components from actually observed real interest rate data. Based on the assumption thatthe real interest rate is constantly fluctuating around the equilibrium interest rate, an estimatedvalue for the equilibrium interest rate is isolated using the HP filter.
The major feature of the HP filter is the method’s simplicity, and it is also sometimes
used to estimate potential GDP and potential growth. It should be noted that this approachrelies solely on statistical procedure of data smoothing and does not involve any economic theory.
(2) The Laubach-Williams model
The Laubach-Williams model is an approach that explicitly incorporates standard
economic theory (IS curves, Philips curves, etc.) in the estimation of the equilibrium interest
rate.
As already indicated, the equilibrium interest rate is a neutral real interest rate that
does not affect the economy or prices, acting neither to ease nor to tighten. The LaubachWilliams model assumes an IS curve for aggregate demand in the economy. If the real interest
rate is higher than the equilibrium interest rate, aggregate demand or the gap between supply
and demand will decrease; if the real interest rate is lower, aggregate demand or the gap
between supply and demand will increase. On supply side, the model incorporates a traditional
Philips curve so that the inflation rate is determined by the adaptive expectation of inflation bymarket participants and the output gap (i.e., real GDP minus potential GDP). In addition, thetrend component of the potential growth rate is assumed to be described by a random walkprocess. Demand shocks are similarly defined as random walk variables. Considered from theperspective of the equation above, in the Laubach-Williams model, the equilibrium interest rate
is formularized in such a way that both the trend component in the first term and the cyclicalcomponent due to demand factors in the second term are incorporated (and in each case theeffect of shocks is formularized as a persisting stochastic trend).
The distinctive feature of the Laubach-Williams model is that while it is more or less
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informal, it explicitly displays the structure of an economic model. It does not incorporate thedynamically optimized behavior of households and firms as does the DSGE model discussed
below. Nevertheless, IS and Philips curves are both relational formulas employed in standard
macroeconomic theory, and the consideration of such theoretical mechanisms is a feature offeredby the Laubach-Williams model that is not offered by the univariate time-series approach. It is
more general than the univariate time-series approach in the sense that it does not only
incorporate a trend component due to the potential growth rate but also other sources offluctuations due to demand shocks. The fact that the US Federal Reserve Bank has published
up-to-date estimates based on the Laubach-Williams model (on the personal webpage of Federal
Reserve Bank of San Francisco President John Williams) suggests the model’s importance.

(3) The DSGE model
Estimation of the equilibrium interest rate using the DSGE model explicitly considers
the dynamically optimized behavior of households and firms. In essence, the representative
household seeks to maximize the utility it obtains from consumption and leisure into the future.
The representative firm seeks to maximize its profit in each period, and sets prices withconsideration of adjustment costs into the future. The model employed in this paper assumes
that the central bank follows monetary policy rules that consider the zero interest rate
constraint. Given the model’s complete specification of the structure of the economy, ultimately
determining the equilibrium interest rate requires the solution of a complex nonlinear equation,and its estimation also demands a sophisticated method. In addition, equations corresponding toIS curves and Philips curves can be obtained by linear approximation, making it possible todiscuss the relationship of correspondence between the DSGE model and the Laubach-Williams
model discussed above.
The DSGE model is the main analytic tool driving contemporary macroeconomic
analyses. Its major distinctive feature is that it is a structural model that incorporates acomplete description of the behavior of economic agents. The use of the model also enables theanalyst to avoid “the Lucas critique” of policy analyses. At the same time, numerous variations inmodel settings can be considered, and the results of estimations are dependent upon thepreconditions of the model. It is therefore important to test the robustness of the model structure
and assumed parameters. The analysis conducted in this paper will proceed with attention torobustness.

Results suggest that the Equilibrium Interest Rate has displayed an Upward Trend
in Recent Years
We will now consider the results of estimations based on the three methods discussed above
in sequence.
First, Figure 1 shows values estimated using the HP filter (blue solid line, HP 1 series). Basedon the HP1 series, the equilibrium interest rate, which had exceeded 5% in around 1990, declined
monotonously until 1999. Following this, despite slight increases in the first half of the 2000s and
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around 2010, figures have been largely static, and have recently declined to become negative.

Figure 1 The equilibrium interest rate based on the HP filter(Note) The real interest rate is a series obtained by subtracting the expected inflation rate (estimated using an
autoregressive model) from the uncollateralized overnight call rate.
HP1 is a series of estimated values for the equilibrium interest rate (smoothness parameter = 14,400); monthly,
January 1981 to December 2017.
(Source) Estimates by the authors.

However, because the HP filter is a method that extracts the trend component from actual
real interest rate data, persistent deviation from the real interest rate can by definition not betolerated. In particular in this case, the results show that the equilibrium interest rate has recently
declined to become negative, but this reflects the fact that the observed real interest rate has
displayed a declining tendency. It must therefore be borne in mind that results reflect the specificcharacteristics of the HP filter. To go further, given that the results of estimations using the HP
filter are known to be unstable at the end point (the final period of the sample), it is necessary to
be aware that the results may be significantly corrected by the addition of data.
Next, Figure 2 shows results for the equilibrium interest rate calculated using the
Laubach-Williams model (real-time estimates)5. The estimates based on the Laubach-Williams
model show that following a peak of around 5% in the first half of the 1990s, the equilibrium
interest rate declined basically consistently, dipping slightly into negative figures in the early
2000s. This is consistent with the estimates obtained using the HP filter. Following this, the rate
became positive, and remained largely static, with slight fluctuations. Immediately following the
global financial crisis, the rate declined rapidly to below −1%, after which it increased largely
The Kalman filter is employed when potential variables are calculated based on the Laubach-Williams model. Twotypes of series can be calculated: Real-time estimates, using only the data available at the time of the evaluation (“onesided estimates”), and smoothed estimates, using all of the data for a sample period, including the future (“two-sided
estimates”). Because real-time estimates are used in international comparisons employing the Laubach-Williams
model, real-time estimates are reported in this paper. Smoothed estimate results are shown in Figure 3 in the
background paper.

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monotonously, reaching a level of around 2% most recently. In the background here is an increasein estimated values for the potential growth rate. However, in the case of the estimates obtainedusing the HP filter, the rate was either largely static or displayed a moderate decline in the period
following the global financial crisis. The two set of results contrast on this point. In addition,
because the potential growth rate rose to be higher than the equilibrium interest rate from 2000,
the other cyclical factors (demand shock factors) became negative, and this appears to havecontinued to act as a factor driving the equilibrium interest rate downwards. Furthermore, theinterest elasticity parameter for the IS curve was changed, and the qualitative result remainedrobust (see Figures 4 and 5 in the background paper).
Figure 2 The equilibrium interest rate based on the Laubach-Williams model(Note) Values estimated for the equilibrium interest rate based on the Laubach-Williams model (real-time, quarterly
estimates, 1982 Q1 to 2017 Q4).
(Source) Estimates by the authors.

Lastly, Figure 3 shows the equilibrium interest rate calculated using the DSGE model6.
While the rate declined somewhat below 1% in the mid-1980s, following this it displayed anincreasing tendency, until it exceeded 3% at the beginning of the 1990s. Following this the rate
progressively declined until the latter half of the 1990s, taking a negative value in the latter halfof the 1990s and the first half of the 2000s, but it did not decline below -1%. Immediately following
the global financial crisis, the rate displayed a rapid decline to close to -2%. Following this, ittransitioned to an upward footing, with the most recent figures between 0% and 1%. Estimates
were also conducted using the DSGE model based on other settings (a linear model, a nonlinear
model without the zero interest rate constraint, and a combination of the zero interest rate
constraint and a linear model), and the qualitative result remained robust (see Figure 7 in the
Estimates obtained using a nonlinear model with the zero interest rate constraint. Here, the steady-state value forthe equilibrium interest rate for the entire period was 0.46%. For details of the method of solving the model and theestimation method, see the Technical Appendix in the background paper.

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background paper).
Figure 3 The equilibrium interest rate based on the DSGE model(Note) Values estimated for the equilibrium interest rate based on the DSGE model (nonlinear with the zerointerest rate constraint, quarterly estimates, 1983 Q2 to 2017 Q4)(Source) Estimates by the authors

Other Economic Indicators also Point to an Upward Trend in the Equilibrium
Interest Rate
In addition to the estimation results discussed above, there are some other economic
indicators closely related to the equilibrium interest rate. The potential growth rate is one of these
indicators. As indicated in the equation discussed above, the potential growth rate corresponds tothe long-term trend component of the equilibrium interest rate, and numerous discussions employ
the approximation “equilibrium interest rate ≒ potential growth rate.” Figure 4 shows the potential
growth rate as calculated by the Cabinet Office and the Bank of Japan. Both series are estimated using
standard production functions and move closely to each other. From an initially high level, the rate declines
significantly in the first half of the 1990s, dropping further at the time of the global financial crisis, following
which, it has risen in recent years. Overall, this trend is consistent with the results of the estimations basedon the Laubach-Williams model and the DSGE model, shown in Figures 2 and 3 respectively.

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Figure 4 The potential growth rate has also displayed a recent upward trend(Note) Half-yearly data, first half fiscal 1983 to first half fiscal 2017
(Source) Cabinet Office, Bank of Japan.

Corporate capital investment trends also offer a useful reference as another economic
indicator. Figure 5 shows corporate capital investment (real value). It can be seen that capital
investment has increased in vigor in recent years. Standards for the System of National Accountsof Japan were revised at the end of 2016, and research and development expenses are now
included in the new series (2008 SNA). An increase in research and development investment hascontributed to the recent invigoration of capital investment, supporting the increase in thepotential growth rate on the twin fronts of capital deepening and total factor productivity.
Figure 5 Corporate capital investment is also displaying a continuing increase(Source) Cabinet Office, “National Accounts of Japan”
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Figure 6 shows labor productivity for Japan as a whole. Here, labor productivity is real
GDP divided by the figure obtained by multiplying the number of employed persons by the numberof hours worked (man hours). Labor productivity has continued to increase stably from 2000 to thepresent, displaying steady growth without a reduction in pace even with a recent increase in thenumber of employed persons. We may infer that this stable improvement trend on the supply side
as a whole has also been a factor supporting the increase in the equilibrium interest rate.

Figure 6 Labor productivity (man hour-based) is also continuing a stable increase(Note) Quarterly data, labor productivity = real GDP (trillion yen)/[Number of employed persons (10,000 people) ×total actual working hours (2015=100)](Source) Cabinet Office, “National Accounts of Japan”; Statistics Bureau, Ministry of Internal Affairs andCommunications, “Labor Force Survey”; Ministry of Health, Labour and Welfare, “Monthly Labour Survey”

Economic Trends show the Benefits of Monetary Easing to be Increasing
Taking into consideration estimates of the equilibrium interest rate obtained using three
approaches and the evidence of other economic indicators, we may infer that overall, the Japanese
economy has continued a steady improvement in performance, and the equilibrium interest rate
itself is trending upwards.
If this trend continues, we can predict that even if there is no change in monetary policy– that is, even if the current long-term interest rate target is maintained – the degree of monetaryeasing will increase, and its effect in stimulating the economy will also be boosted. There are ofcourse a range of routes available for the propagation of the effects of monetary easing other than
the traditional interest rate channel (a gap between the policy interest rate and the equilibrium
interest rate), including stock prices, the exchange rate, and bank credit. As the US and otheroverseas economies continue to improve, overseas potential growth rates and equilibrium interest
rates have also ceased their decline or are beginning to recover (and as a result, it is predicted that
US interest rates will commence a gradual increase). The additional effect of recovery in the global
economy will presumably further increase the effects of easing.
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This increase in the benefits of monetary easing increases the potential for overcoming
the monetary policy dilemma discussed at the beginning of this paper. This is because an increasein policy effects will ease the issue of secondary effects to some extent. Naturally, it will benecessary to closely examine whether the upward trend in the equilibrium interest rate willcontinue into the future, and whether the risk of secondary effects will increase. On the other hand,announced policy changes or revisions of the framework can be expected to entail considerable
costs, whether in the direction of easing or tightening. We must not forget that a scenario in whichmonetary policy management that appears staid is in fact overall optimal and will continue to
produce significant effects is certainly possible.

Ryuzo Miyao
Professor, Graduate School of Economics, The University of Tokyo. Ph.D. (Economics),
Harvard University. Former Member of the Policy Board, Bank of Japan (March 2010 –March 2015). Specializes in monetary economics and empirical macroeconomic analysis.

Mototsugu Shintani
Professor, Research Center for Advanced Science and Technology, The University of Tokyo.
Ph.D. (Economics), Yale University. Specializes in macroeconomics and econometrics.

This is a translation of a paper originally published in Japanese.
NIRA bears full responsibility for the translation presented here. Translated by Michael Faul.

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