Stock prices and monetary policy in Japan:
An analysis of a Bayesian DSGE model
Satoshi Hoshino∗,a,c and Daisuke Ida†,b,cabcFaculty of Economics, Okayama Shoka University

Faculty of Economics, Momoyama Gakuin University

Research Fellow, Graduate School of Economics, Kobe University

April 16, 2021

Abstract
This paper reevaluates the role of asset price stabilization in Japan during the 1980s
through a Bayesian estimation of the dynamic stochastic general equilibrium model. Our
results show the presence of the wealth channel from increased stock prices in Japan. In
addition, we argue the possibility that the Bank of Japan (BOJ) may have conducted
its monetary policy by targeting the stock price stability in addition to inflation and theoutput gap. The BOJ’s response to stock price movements as a matter of policy, however,is subject to considerable uncertainty. Our results indicate that while the BOJ may havereacted to stock prices deviated from their fundamental values, it could not prevent a stock
price bubble simply by implementing a contractionary monetary policy shock. Therefore, we
conclude that the BOJ’s monetary policy stance aimed at stabilizing stock price fluctuations
and minimizing macroeconomic volatility, whereas endogenous volatility was caused by badshocks.

JEL codes: E52; E58;
Keywords : Monetary policy; Bayesian estimation; DSGE model; Stock prices;
Wealth effect∗E-mail: hoshino@po.osu.ac.jp†

E-mail: ida-dai@andrew.ac.jp

1

Introduction

The objective of this paper is to reassess whether the Bank of Japan (BOJ) considered stock
price stabilization in its monetary actions during Japan’s 1980s asset bubble. Researchers havedisagreed on whether the BOJ should have reacted more aggressively to fluctuations in asset
prices during the latter half of the 1980s, when the Japanese economy experienced a boom
and burst in stock prices. Indeed, the boom in stock prices led to an economic boom via thewealth effect brought about by rapidly increasing asset prices. Unfortunately, the bubble instock prices also caused irrational behavior on the part of firms and banks. Consequently,
the Japanese economy became trapped in secular stagnation when the bubble burst and asset
prices collapsed in 1990 (Ogawa, 2003).
As mentioned above, evaluation of the stock price boom of the 1980s has been generated
a debate about whether the BOJ should have raised its policy rates in response to the boomin the stock market. This evaluation is separated by dichotomous viewpoints about raising
the interest rate: the view of the Federal Reserve System (FED) and that of the Bank ofInternational Settlement (BIS). Some economists support the view that the BOJ would have
had difficulty raising the policy rate in response to a sudden increase in stock prices because
the inflation rate remained stable during the period. This evaluation is considered as the FEDview (Bernanke and Gertler, 2000). In contrast, other economists assert that what the BOJ’s
failure to increase the interest rate to moderate the extraordinary boom in stock prices caused
the secular stagnation that followed. That group argued that even though inflation was stable,
the BOJ might have prevented the stock price bubble if the central bank responded correctly
to it. This assertion is regarded as the BIS view (Cecchetti et al., 2002). There seems to be
no consensuses on whether the BOJ should have attempted to stabilize the fluctuating stock
prices that occurred during the 1980s.
This paper reevaluates the performance of the BOJ’s monetary policy from the 1980s to
1990s using a Bayesian estimation of the dynamic stochastic general equilibrium (DSGE)
model.1 In the DSGE model, stock price movements are characterized by both a demand
and a supply side. On the one hand, the demand side of stock prices is based on the role of thewealth effects of stock prices, which implies that an increase in stock prices leads to increased1

See also Kaihatsu and Kurozumi (2014), Hirakata et al. (2016), Hirose (2008), Iiboshi et al. (2006), Mutoet al. (2016), and Sugo and Ueda (2008) for Bayesian estimation of the DSGE using Japanese time series data.

1

consumption spending in the private sector (Castelnuovo and Nistico, 2010). On the other
hand, the supply-side channel of stock prices implies that an increase in stock prices induces adecline in real marginal costs that reduces inflation (Carlstrom and Fuerst, 2007). Our study
contributes to previous studies because none of previous studies directly incorporated stock
price stabilization into the monetary policy rules of DSGE models.
While we acknowledge the importance of both channels in the Japanese economy, this paper
focuses on identifying of the deep parameter that captures the demand channel of stock prices
because we want to know whether that channel had a substantial effect on movements in stock
prices. In addition, since our objective is to evaluate whether the BOJ attempted to stabilize
the stock price boom of the late 1980s, we consider whether one can appropriately identify the
BOJ’s intention to stabilize stock prices using a model with an wealth effect. More precisely,
our research question is to evaluate whether the BOJ responded to stock prices in addition
to its standard policy goals, such as inflation and output stabilization. To do this, we add
a monetary policy rule to incorporate the role of stock price stabilization with the standard
policy objectives and identify the coefficient for stock price stabilization in the policy rule.
To examine the role of asset price stabilization in the Japanese economy, we estimate theDSGE model developed by Castelnuovo and Nistico (2010), who incorporated the BlanchardYaari type perpetual youth model into the standard new Keynesian (NK) model to consider thewealth channel of stock prices. They found that the FED may have responded systematicallyto fluctuations in asset prices. We evaluate the BOJ’s monetary policy stances during 1980s
using the theoretical framework that those researchers developed. We use the model developed
by Castelnuovo and Nistico (2010) so we can consider both the demand and the supply channelof stock prices in a single DSGE model. As we mentioned earlier, while the demand side of
the wealth channel can be directly identified by Bayesian estimation, the supply side of thechannel is theoretically considered in the model. Therefore, Castelnuovo and Nistico (2010)’s
model is quite suitable for our purpose.
Our results identify the presence of the wealth channel resulting from increased stock prices
in Japan. In addition, we point out the possibility that the BOJ’s monetary policy decisions
at the time gave weight to stock price stabilization in addition to more traditional policy goals
such as inflation and the output gap. However, our results indicate that while the BOJ might
have reacted to stock prices deviated from their fundamental values, it could not have prevent2

a stock price bubble by implementing only a contractionary monetary policy shock. Therefore,
our study emphasizes that the BOJ’s monetary policy stance aimed to stabilize fluctuations
in stock prices and minimize the macroeconomic volatility, whereas endogenous volatility wascaused by bad shocks.
The contribution of our paper is as follows. Our paper is related to the arguments by
Bernanke and Gertler (2000) and Jinushi et al. (2000). Their studies argue that the BOJ was
unable to sufficiently raise the policy rate, which caused both the boom and the crash in stock
prices in the late 1980s. However, their evaluations are derived from the simulation results
using the estimated simple Taylor rule. Furthermore, while Okina et al. (2001) discuss whether
the BOJ should have responded to the drastic increase in stock prices, that discussion was notbased on a structural macroeconomic model. While Miyao (2002) found that BOJ monetary
policy was characterized by active policy stances in the late 1980s, his finding is based on
the estimation results suggested by the structural vector autoregressive (VAR) model. In thatsense, our study addresses the challenge to evaluating reactions to stock prices using monetary
policy rules based on the Bayesian DSGE model. Therefore, our study complements their
discussions based on evaluation using a Bayesian DSGE model. To the best of our knowledge,
ours is the first study that evaluates whether the BOJ should have directly reacted to stock
price fluctuations in that we evaluate that issue by using an estimated DSGE model.
Our study is closely related to the work of Hirose (2008). He estimated a medium-scale
DSGE model with a sunspot shock as well as a financial accelerator effect.2 He showed thatthe BOJ’s estimated reaction function was close to the performance suggested by the optimal monetary policy rule that minimizes the central bank’s loss function. He concluded thatbased on the simulation result, BOJ monetary policy could have minimized the macroeconomic
volatility during the period. However, Hirose (2008) did not explore how the BOJ reacted tostock prices in the latter of 1980s. In contrast to Hirose (2008), this study identifies the BOJ’s
attitude toward stock price fluctuations during the period by incorporating stock price stabilization into the Taylor rule. Our result implies the possibility that BOJ responses considered
stock price fluctuations during the late 1980s. In our analysis, this possibility is characterized
by the coefficient of stock price stabilization in the estimated BOJ reaction function.
2

Muto et al. (2016) also build a DSGE model with a financial accelerator and evaluate the effect of thefinancial accelerator on the Japanese economy by Bayesian estimation.

3

The structure of this paper is as follows. Section 2 provides facts about the Japanese
economy from the 1980s to the 1990s and shows how a change in stock prices affects theJapanese economy. We briefly review the literature related to our study and address thecontribution of our paper. In Section 3, we briefly explain the DSGE model and describe
the Bayesian estimation methods. Section 4 provides detailed explanations about Bayesianestimation of the DSGE model, and Section 5 reports the main results of this paper. In Section
6, we discuss whether the BOJ should have responded to the stock price gap based on theestimation results obtained in the previous section. Section 7 concludes. Appendix A provides
a detailed model description of Castelnuovo and Nistico (2010).

2

Stock prices and monetary policy in Japan

2.1

A brief review of the Japanese economy in the 1980s

This section briefly explains the Japanese economy during the 1980s. The Japanese economy
experienced both boom and burst during this period. Figure 1 shows several time-series datathat capture the story of the Japanese economy during the 1980s and 1990s. Following thePlaza Accord in 1985, the Japanese economy faced the risk of deflation from sharp appreciationin the exchange rate. In fact, the yen appreciated sharply against the dollar in response to thePlaza Accord, from approximately 250 yen in 1985 to around 120 yen in the subsequent year.
As shown in Figure 1, after the Plaza Accord, the inflation rate was near zero in accordancewith sharp appreciation in the nominal exchange rate. Accordingly, the GDP gap was also
negative in 1986-1987 following the Plaza Accord.
[Figure 1 around here]
To combat this risk, the BOJ aggressively cut the official discount rate that represented its
monetary policy stance during the 1980s. Indeed, as shown in the left lower panel of Figure 1,
the official discount rate dropped sharply from 6.5 % in 1985 to 2.5% in 1987, and this monetaryeasing continued until April, 1989. The left upper panel of Figure 1 shows that as noted earlier,while the GDP gap was negative in response to the Plaza Accord, the gap was improved bymonetary easing. Several studies point out that the continuation of monetary easing from 1987
to 1989 induced the asset price bubble, whereas the sharp increase in the official discount rate
generated the collapse of the bubble. The BOJ decided to raise the policy rate in April, 1989,
4and it raised its policy rate sharply. Indeed, the official discount rate reached 6.25% in 1990.
As argued in several previous studies, while extended monetary easing created that stock pricebubble, a sharp increase in the official discount rate caused it to collapse. As pointed out inMiyao (2002), this fact would reveal that the BOJ’s monetary policy stance was active in asense that the BOJ’s monetary policy was easing during 1986-1987 and contractionary during
1989-1990.
We calculate the stock price gap, which is defined as the deviation of actual stock prices fromdetrended ones. It may be one proxy for the deviation of stock prices from their fundamental
values. The right lower panel of Figure 1 shows that the stock price gap significantly increased
with monetary easing during these periods. Bernanke and Gertler (2000) and Jinushi et al.
(2000) argue that the BOJ could have prevented the asset price bubble if it had raised its policy
rate in accordance with an increase in stock prices.
Why did the BOJ not aggressively raise the official discount rate in response to asset pricemovements? According to Okina et al. (2001), there are several reasons. One is related to achange in the inflation rate during the late of 1980s. Based on the FED view, as long as the
inflation rate is stable, the central bank has difficulty raising the policy rate even if movements
in asset prices are fluctuating because of nonfundamental components (Bernanke and Gertler,
2000). Thus, the FED view supports the policy stance that the central bank has an incentive
to conduct monetary tightening only if such a boom in asset prices leads to inflation risk. In
fact, inflation risk did not emerge in this period. Therefore, as pointed out by Okina et al.
(2001), it is possible that the BOJ lost the chance to increase the official discount rate for thisreason.
Our study is motivated to answer the question of whether the central bank actually contemplated responding to an increase in stock prices even if low inflation was maintained.

2.2

Stock prices and monetary policy: Literature review

This section briefly reviews the literature related to our study and clarifies how this study isrelated to previous studies in terms of examining the role of asset price stabilization.3 Indeed,
several papers investigate whether the central bank should have considered the effect of asset
prices on the real economy. As noted earlier, it has been debated whether central banks should3

See also Shibamoto et al. (2020) for a detailed discussion about BOJ’s monetary policy during the 1980s.

5react to fluctuations in asset prices. Bernanke and Gertler (2000) asserted that, based on theframework developed by Bernanke and Gertler (2000), the central bank should not stabilize
asset prices unless they affect an increase in future inflation expectations. Conversely, Cecchetti
et al. (2002) argued that the central bank should respond to asset prices as a precaution, because
the bursting of asset price bubbles can cause severe economic stagnation. In addition, according
to Chadha et al. (2004) and Haugh (2018), the central bank might consider the effect of stock
price misalignment that causes asset prices to deviate from their fundamental values on thereal economy.
No consensus has been reached in terms of the theoretical aspects of the NK model. For
instance, several studies support the assertion of Bernanke and Gertler (2000). They argue thatthe central bank can stabilize the economy if it reacts strongly to inflation. Thus, the response
to asset prices in the policy rule is redundant when the central bank aggressively raises thepolicy rate in response to inflation. Several studies support this view (Carlstrom and Fuerst,
2007; Gilchrist and Leahy, 2002; Faia and Monacelli, 2007; Iacoviello, 2005).
On the other hand, some previous studies assert that the central bank can obtain gains
from asset price stabilization (Airaudo, 2013; Gambacorta and Signoretti, 2014; Kannan et al.,2012; Pfajfar and Santoro, 2014). For instance, Airaudo et al. (2013) showed that a mild
response to asset prices in a monetary policy rule can achieve a unique REE and rule out
nonfundamental volatility in an NK model with financial market imperfections. As suggested
by Kannan et al. (2012), when the model contains heterogeneities of households, the central
bank can obtain gains by implementing an augmented monetary policy rule that contains both
asset price stabilization and a macro-prudential tool such as a credit growth rate.
Our study is related to the work of Castelnuovo and Nistico (2010) in terms of asset pricestabilization. They argued that including a stock-price gap in the monetary policy rule isconsistent with post-WWII stock market boom and bust cycles by using a DSGE model with
Bayesian techniques. We use the same framework as Castelnuovo and Nistico (2010) and findthat using Japanese time-series data, positive and significant responses to stock prices areambiguous. Thus, we conclude that while the BOJ might have reacted to fluctuations in stock
prices, the response was affected by a great amount of uncertainty. This is in stark contrast to
the findings in the work of Castelnuovo and Nistico (2010).
In summary, it seems that there is no consensus about whether the central bank should

6react aggressively to asset price fluctuations in terms of the DSGE model. Note that in thispaper we do not provide the normative answer of whether the central bank should react tostock prices aggressively; rather, we simply evaluate the BOJ’s monetary policy stance during
the 1980s by focusing on stock price stabilization in the monetary policy rule.

3

Model description

This paper focuses on the wealth channel of stock prices to evaluate the BOJ’s monetary policy
stance. To do so, we adopt the framework of Castelnuovo and Nistico (2010), who incorporatea discrete-time perpetual youth model developed by Blanchard (1985) and Yaari (1965) intoa standard NK model. We briefly explain the framework of the perpetual–youth NK model.
Readers who want to know detailed derivations of the model are referred to Nisticò (2012) andCastelnuovo and Nistico (2010). Readers familiar with this model can skip to Section 4, which
provides explanations of the model estimation.

3.1

Model summary

The model is based on a canonical DSGE model with the wealth channel of stock prices.
The wealth channel is captured by the parameter ξ, which represents the probability of being
replaced the next period begins. Carlstrom and Fuerst (2007) model the NK model with stock
price dynamics, which focuses on the supply side of stock price that the dividend is negatively
affected by the real marginal cost. In contrast to Carlstrom and Fuerst (2007), Castelnuovo
and Nistico (2010)’s framework can consider both demand and supply channels of stock prices.
Therefore, the model that we employ is based on Castelnuovo and Nistico (2010) and Nisticò
(2012). As in Castelnuovo and Nistico (2010), we consider a stochastic trend in productivity
to estimate the DSGE model. This enables us to estimate the model without implementing indata prefiltering. The model description is explained as follows.
The economy consists of an indefinite number of cohorts that are subject to the constraintof a constant probability ξ of being replaced when the next period begins. Following the terminologies established by Castelnuovo and Nistico (2010), the interaction between “newcomers”
owning zero financial assets and “old traders” that accumulates their wealth causes the wedge
between the stochastic discount factor pricing all securities and the average marginal rate of
substitution in consumption that is equalized in a representative agent (RA) model. In this7

case, individual consumption smoothing that is optimal in an RA model does not carry overin aggregate terms because agents in the financial markets change over time and have different
wealth and different consumption levels. The case for ξ = 0 corresponds to the RA model.
Each household obtains utility from consumption and disutility from labor supply. Moreprecisely, following Nisticò (2012), each household has Cobb-Douglas preferences over consumption and labor supply. Household consumption is captured by habit formation. As in astandard NK model, nominal price rigidity is introduced by the assumption of staggered pricecontracts.
The production sector consists of two types of firms: retailers and intermediate goods
firms. Retailers use intermediate goods to produce final goods under a perfectly competitivemarket. Following Calvo (1983), intermediate goods firms set their nominal prices based on a
staggered manner. Thus, a fraction 1 − θp of all firms optimally adjusts their price, whereas theremaining fraction θp of firms that do not optimally change their prices follows the indexation
rule associated with past inflation as well as steady state inflation. In addition, following
Castelnuovo and Nistico (2010), households specialize in supplying a different type of laborand each cohort spans all labor types. For each labor type there exists a an infinitely lived
monopoly labor union that determine the nominal wage. Each union faces Calvo’s (1983)
nominal wage rigidity. Following Erceg et al. (2000), a fraction of 1 − θw can change nominal
wages in its union, whereas remaining fraction θw cannot optimally choose their wages follows
the indexation rule associated with past price inflation as well as productivity growth andsteady state inflation.

3.2

Log-linearized model

We briefly explain the log-linearized equations.4 Following Castelnuovo and Nistico (2010), we
express log-deviations from the detrended steady state with lower case letters. In this section
we focus on the equations expressed by a gap term, which implies the deviation of the levelvalue from its detrended steady state. The output gap is expressed by x̂y,t = ŷt − ŷt∗ . Similarly,
we also define the real wage gap as x̂w,t = ŵt − ŵt∗ and the stock price gap as x̂s,t = q̂t − q̂t∗ .
Here, the variables with a hat denote the log-deviation from the detrended steady state. The
variables with an asterisk denotes the counterparts under frictionless equilibrium. Following
4

See the Appendix A or Castelnuovo and Nistico (2010) for a detailed derivation of the structural model.

8Castelnuovo and Nistico (2010), frictionless equilibrium is defined as flexible prices and wages
in addition to nonstochastic markup on prices and wages and no financial shocks. Variables
under frictionless equilibrium are defined in Appendix A.
The log-linearized equations are summarized as follows:
1 − h/γh(1 − h/γ)(1 − g/y)x̂y,t =
Et x̂y,t+1 − x̂y,t +ψx̂s,t1 − h/γ + ψ
γ
1 − h/γ + ψh(1 − h/γ)2 (1 − g/y)  n+ x̂y,t−1 −R̂t − Et π̂t+1 − R̂t∗ ,γ
1 − h/γ + ψµp (1 − β̃)(1 − β̃)(1 − α)x̂s,t = β̃Et x̂s,t+1 +Et x̂y,t+1 −Et x̂w,t+1
α + µpα + µp− R̂tn − Et π̂t+1 − R̂t∗ + ztν ,π̂t = β̃ (Et π̂t+1 − ιp π̂t ) + ιp π̂t−1 + λp x̂w,t +

αλpx̂y,t + ztp ,1−αγŵt = β̃ Et ŵt+1 − ŵt + Et π̂t+1 − ιw π̂t + Et zt+1
− ιw ztγ + ŵt−1


ϕ
1
γ
γ
+
x̂y,t
− π̂t + ιw π̂t−1 − zt + ιw zt−1 + λw
(1 − h/γ)(1 − g/y) 1 − α
λw h/γ−x̂y,t−1 − λw x̂w,t + ztw .
(1 − h/γ)(1 − g/y)

(1)

(2)

(3)

(4)

Here, π̂t denotes the inflation rate, and R̂tn denotes the nominal interest rate. ŵt is the real
wage rate and R̂t∗ is the natural rate of interest, which is defined as the real interest rate underfrictionless equilibrium. As we explain below, ztj (for j = a, g, v, r, b, p, w) denotes structural
shocks that follow the autoregressive (AR)(1) process. The deep parameters in the above
structural equations are defined as follows:β̃ =µp (1 − θp )(1 − θp β̃)(1 − α)β(1 − h/γ)
, λp =,
1 − h/γ + ψ
θp (µp + α)λw =µw (1 − θw )(1 − θw β̃)
1 − β(1 − ξ) ω, ψ=ξ.
θw (µw + ϕ(1 + µw ))1−ξc

In addition, h is the degree of habit formation in consumption, g/y is the ratio of demandfor consumption goods relative to output excluding household consumption, and γ is the productivity growth in the steady state. µp is the price markup and µw is the wage markup. ιpis the degree of indexation of past prices in the price index and ιw is the degree of indexationof past wages in the wage index. α is the degree of diminishing return to scale in production
9

function. ω/c denotes the ratio of the aggregate wealth to aggregate consumption in the steadystate.
Equation (1) is the dynamic IS curve with the wealth effect of stock prices. Equation (2)represents stock price dynamics. Equation (3) is the price new Keynesian Phillips curve andEquation (4) is the wage new Keynesian Phillips curve.
To close the model, we specify the monetary policy rules. This study employs the standard
monetary policy rule suggested by Taylor (1993). In particular, we consider whether eachcentral bank should react to the stock price gap. More specifically, we specify a log-linearized
monetary policy rule as follows:nR̂tn = φr R̂t−1+ (1 − φr ) (φπ π̂t + φx.y x̂y,t + φx.s x̂s,t ) + ztr ,(5)where φπ is the coefficient of the rate of inflation, φx.y is the coefficient of the output gap, andφx,s denotes the coefficient of the stabilization weight on the stock price gap.
The seven structural shocks are considered as follows:γ+ εγt ,
ztγ = ργ zt−1pztp = ρp zt−1
+ εpt ,w
ztw = ρw zt−1
+ εw
t ,
g
ztg = ρg zt−1
+ εgt ,bztb = ρb zt−1
+ εbt ,
νztν = ρν zt−1
+ ενt ,rztr = ρr zt−1
+ εrt .

where εjt follows N (0, σj2 ) for all j = a, g, v, r, b, p, w. As we will argue, the measurement error
shock of the growth rate of stock prices are defined in Section 4.

4

Asset price stabilization in Japan: A Bayesian estimation

This section represents the estimation strategy. Since our model includes the trend due to the
production technology, we must rewrite it to the detrended equilibrium conditions. The lowercase variables denote detrended macrovariables. We introduce the detrended macro variables
as follows: yt = Yt /At , ct = Ct /At , dt = Dt /At , wt = Wt /At , qt = Qt /At , ωt = Ωt /A, and10mrst = M RSt /At . Here At is the level of the technology, Ct is consumption, Dt denotes thedividend, and Ωt is financial wealth, respectively.
Then, we estimate the DSGE model with the wealth channel of asset prices by Bayesian
methods.5 To evaluate the likelihood function, we apply the Kalman filter to the system
consisting of log-linearized equilibrium and observation equations. Then, 1000,000 draw fromthe posterior distribution of parameters to be estimated is obtained by the Metropolis-Hastings(MH) algorithms to approximate the moments. The scale parameter in the MH algorithms is
set so that the acceptance ratio is maintained around 25%. The first half draws are discarded
and the remaining half draws are used for our analysis.
We estimate the key structural parameters using seven quarterly Japanese time-series data.6
Yt is real per capita GDP, Ct is real per capita consumption, and SPt is real per capita Nikkei
stock average (NIKKEI 225). As for these real series, we divide these nominal series with the
GDP deflator. Regarding the per capita terms, each series is divided by population over 15
years old. Wt is the real wage, lt is hours worked, DEFt is the GDP deflator, and Rtn is the callrate. Like previous studies that examine the Japanese economy in the DSGE frameworks, weselect the sample period from 1981:Q1 to 1998:Q4 to avoid the problems from the nonnegativity
constraints on nominal interest rates.
The observation equations are given by100∆ ln Yt





γ





ztγ + ŷt − ŷt−1





0




 

 
 

 

 
 
ztγ + ĉt − ĉt−1
 100∆ ln Ct   γ    0 

 

 
 

 

 
 
 100∆ ln SPt   γ    met 
ztγ + q̂t − q̂t−1

 
 
 


 

 
 
 100∆ ln Wt  =  γ  + 
 +  0 ,
ztγ + ŵt − ŵt−1

 
 
 


 
 

 
 100∆ ln lt
  0   1/(1 − α) (ŷt − ŷt−1 )   0 

 
 
 


 

 
 
 100∆ ln DEFt   π  



π̂
0
t

 
 
 

n
Rtn
R
R̂tn
0
n

where γ = 100 ln γ, π = 100 ln π, and R = 100 ln Rn .7 met is the measurement error for the5

Our estimation is conducted by Dynare (Adjemian et al., 2011).

6

We explain detailed explanation of data descriptions in the Appendix B.

7

We use the growth rate of hours worked in the observation equation to maintain the specification of theCastelnuovo and Nistico (2010)’s model.

11stock price growth rate, which is given bymq2
met = ρmq met−1 + εmq∼ i.i.d.N (0, σmq),t , εt2 is the white noise. The meawhere ρmq ∈ [0, 1) represents the autoregressive coefficient and σmq

surement error follows the first order autoregressive process used by Matsumae et al. (2011).8
Following previous studies, we assume that some parameters in the model are fixed. For
example, we set the capital share, α = 0.37, the discount factor, β = 0.995, and price andwage markup, µp = µw = 0.2, following Sugo and Ueda (2008), and the steady state exogenous
demand factors to output ratio g/y = 0.3 follows the sample mean.
Following previous studies, we set the prior distributions of estimated parameters that we
estimate below. Table 1 reports the priors of each parameter. The priors of the turnover rate
ξ, leisure weight in the household’s utility χ and monetary policy response to stock price gap
φx.s follow those of Castelnuovo and Nistico (2010). More precisely, ξ, χ, and φx.s follow theuniform distribution from 0 to 1.0, the gamma distribution with a mean of 1.4 and the standard
deviation of 1.0, and the normal distribution with mean of 0 and standard deviation of 0.025,
respectively. Regarding the priors of the almost structural parameters {h, θp , θw , ιp , ιw }, wefollow those of Sugo and Ueda (2008). As argued in previous studies that focus on the Japanese
economy using a Bayesian DSGE model, except for φx.s , the parameters of the monetary policy
rule are the same distributions of Iiboshi et al. (2006).
Regarding the priors of seven structural shocks, the persistence of each shock ρx , x ∈{γ, p, w, g, b, ν, r} are the beta distribution with the mean of 0.5 and the standard deviation of
0.2 and the standard deviation of shocks σx , x ∈ {γ, p, w, g, b, ν, r} are the inverse gamma withthe mean of 0.5 and the standard deviation of infinity. Finally, While previous studies usedthe DSGE models for the Japanese economy that did not incorporated the nonfundamental
financial shock ztν , we assume that the prior distribution of the financial shock also has same
distribution as other shock to ensure the same conditions.
8

As argued by Castelnuovo and Nistico (2010), the measurement error is also introduced for the stock prices,

but it is the white noise. In contrast, the measurement error in our model is the AR(1) process because thecontamination from the errors would continue to carry over from the previous period.

12

5

Results

This section provides the main results of the paper. Section 5.1 provides the posterior estimatesof the structural model. Section 5.2 explores whether the BOJ reacted to the stock market. In
Section 5.3 we examine dynamic and cyclical properties of the estimated model by using theimpulse response function and the variance and historical decomposition.

5.1

Posterior estimates

Table 1 summarizes the values of estimated parameter and those 90% posterior interval.9 To
confirm the importance of stock prices in the model, we focus firstly on the turnover rate ξ,
which is characterized by wealth effect of stock prices through the household’s demand side.
The posterior mean ξ = 0.046 and its 90% interval is [0.026, 0.066] which suggests the presenceof the wealth effects. Thus, we identify the effect of the stock prices on real activities throughthe variation in the household’s consumption. In the US economy, Castelnuovo and Nistico(2010) estimated ξ to be about 0.13. This results suggest that the wealth effects in the Japanese
economy is smaller than that in US economy. We will discuss the importance of the reaction
to stock prices φx,s in Section 5.2.
The posterior mean of most structural parameters is similar to that obtained in the DSGE
model for Japan, but some differ from previous studies. The wage stickiness θw = 0.216 is lower
than Hirose and Kurozumi (2012) and Kaihatsu and Kurozumi (2014). The former estimatedvalue is 0.522 and the latter one is 0.503. Our estimated value of the price indexation ιp is
0.041, which is smaller than that reported in Hirose and Kurozumi (2012) and Kaihatsu andKurozumi (2014). The former and the latter estimated values are 0.631 and 0.408, respectively.
These differences may be caused by the selection of the data on prices. More precisely, although
Hirose and Kurozumi (2012) and Kaihatsu and Kurozumi (2014) incorporate the CPI into theobservation equation, our analysis use the GDP deflator as the data on prices. Indeed, Hirakata
et al. (2016) used the GDP deflator, and we confirmed that their estimated value of the priceindexation was the similar result as the value estimated in our study.10
9We have confirmed that the estimated parameters are correctly identified in our model. Additional resultson this identification problem are available upon request. See also footnote 10.
10

Although Hirakata et al. (2016) select the sample period from 1981Q1 to 2013Q4, the sample period in our

analysis is from 1981Q1 to 1998Q4.

13

The leisure weight in the utility, χ = 0.031, is quite low compared with that estimatedby Castelnuovo and Nistico (2010), who analyzed the US economy using the estimated DSGE
model (χ = 1.4456). The difference might have been caused by the inclusion of the period before
Jitan, which means the reduction in the hours worked in a week due to the 1987 amendments
to the Labor Standards Act in Japan. Therefore, the leisure weight might be underestimatedby including the periods of long working hours.
Next, we examine the parameters of the financial shock, which directly effects stock prices
and is the specific shock in our analysis. Although the financial shock is relatively persistent,
it does not fluctuate so much (i.e., ρν = 0.958 and σν = 0.561). This is because in theobservation equation the measurement error for the stock prices absorbs its volatility. The
standard deviation of the financial shock would be estimated to be relatively the low value.
Indeed, the standard deviation of the measurement error for the stock prices is an extremely
high value (σmq = 6.986).

5.2

The Bank of Japan’s response to the stock market

Following Table 1, we have found that a positive value of ξ significantly accounts for thewealth effect of stock prices in Japan. Dose this wealth effect also justify the BOJ’s stock pricestabilization? Table 1 reports the estimated value of stock price stabilization, φx,s . Since theestimated value of φx,s is 0.164, this might indicate that the BOJ responded to movements instock prices. However, the result also shows that the estimated value might be an insignificant
response of the BOJ to fluctuations in stock prices because the credible interval [−0.096, 0.423]
contains zero. Therefore, while the BOJ reacted to an increase in stock prices in the 1980s,
this result indicates that there is great uncertainty about the stabilization of stock prices.
Next, we compare several models with the benchmark model. Table 2 reports the comparison of Bayesian estimation results restricted by several key parameters with the benchmark
result. “Baseline” implies the estimation results without any parameter restrictions. The second column of the table shows the estimation result with the restriction to ξ. Thus, this model
corresponds to the model without wealth effect of stock prices. Note that it still contains thestabilization of stock prices in this restricted model. The third column implies the alternativemodel with the restriction of no stock price stabilization. The final column represents the
restricted model, where wealth effect and stock price stabilization are absent. The last row of

14

the table reports the log-marginal likelihood for each model.
[Table 2 around here]
The likelihood of the model with φx,s = 0 leads to the smallest log-marginal likelihood ofother specifications. Accordingly, the model with ξ = 0 and φx,s > 0 outperforms other models.
This result might indicate that the BOJ responded to fluctuations in stock prices during the
1980s. In addition, comparing the model ξ = 0 with that with ξ = φx,s = 0 implies that theformer model outperforms the latter one. Put differently, the model in which both wealth effectand stock price stabilization are absent results in worse performance than that with ξ = 0.11
This result also indicates that the BOJ contemplated the stabilization of stock prices during
the period.
Finally, we attempt to investigate whether the BOJ could have reacted more aggressively tothe sharp increase in stock prices in the late 1980s. To do this, we consider the counterfactual
estimations as if the BOJ has responded strongly to asset prices during the period. Table 3
reports the estimation results of the case as if the BOJ has adopted the stronger response to
stock prices. The second column of the table shows that the BOJ’s reaction to stock prices
is stronger than the baseline case, namely, φx,s = 0.164. The comparison of the model with
φx,s = 0.25 with the models that include the value of φx,s above 0.25 shows that a moreaggressive response to stock prices cannot improve the performance of the model. However,even in this case, the model with a stronger response to stock prices outperforms the baselinemodel. Further discussion is provided in the next section.
[Table 3 around here]11

We confirmed the problem of parameter identification under these constraints. However, this confirmationsuggests that the case of ξ = 0 or ξ = φx,s = 0 may be weakly identified due to measurement errors in stock
prices. Our model that takes such measurement error into account is based on Castelnuovo and Nistico (2010).
We re-estimated the model without taking into account the measurement error of stock prices, but we confirmedthat excluding this measurement error does not affect the results obtained in this paper. Detailed estimation
results of the DSGE model excluding the measurement error of stock prices are available upon request. In few
restricted models, a few parameters did not meet the convergence diagnostic criteria. We confirmed, however,that this problem can be mostly solved by increasing the sampling of the MH algorithm. Therefore, we can saythat our main message is unaffected by these issues.

15

Therefore, we can say that these results imply that the BOJ contemplated the greater
uncertainty that could result from the effect of stock price fluctuations on the Japanese economy.
This result is stark contrast with the assertion of Bernanke and Gertler (2000) who point out thepossibility that the BOJ could have prevented a sharp increase in stock prices if it implemented
precautionary monetary tightening.

5.3

Variance and historical decomposition

In this subsection, we evaluate the contribution of the shocks to the business cycle fluctuationsin the Japanese economy, and discuss variance and historical decomposition of the several
key variables. Table 4 represents the variance decomposition of the key macrovariables that
we pick up at the quarterly forecast horizons of T = 8 and T = 32. Table 4 shows for thevariance decomposition of the nominal interest rate, the monetary policy shock account for its
almost variation at both the short and the medium term. However, the financial shock also
generates the fluctuations in the interest rate and the contribution increases, especially in themedium term. The financial shock leads to the nonfundamental disturbances in stock prices.
Thus, the central bank manipulates the interest rate in response to the variation in the stock
prices generated by the financial shock. These findings support the result that monetary policy
responds to the asset prices as stated in the previous discussion.
[Table 4 around here]
As mentioned above, the financial shock effects the nonfundamental component of the stock
prices. This is supported by the results of the variance decomposition of the stock price gap.
However, the fluctuations in the stock price gap is mainly caused by the exogenous demand
shock. Since we do not incorporate real investment as the observation data and endogenous
variable into our analysis, the estimation results would overestimate the effects of the exogenous
demand shock in the demand side of the economy. For the variance decomposition of the stock
price growth, the structural shocks do not explain much of the variations because of introducing
the measurement error to the observation equation. The fluctuations in the output growth areprimarily generated by the neutral technology shock. This result is consistent with Hirose andKurozumi (2012) and Kaihatsu and Kurozumi (2014).
Figure 2 illustrates the historical decomposition of the nominal interest rate and shows thatthe monetary policy shock plays the most vital role in its fluctuations over the periods. The
16

historical decomposition shows the significant effect of the financial shock on the policy rate.
We can see that this shock creates the downward pressure on the policy rate in the late 1980s.
This result may be interpreted as the scenario that the BOJ combated a sharp increase instock prices, but it could not substantially raise the nominal interest rate due to bad shocks
associated with financial frictions during 1987-1990. By contrast, it follows from Figure 2 that
precautionary monetary easing during 1992-1993 can be explained by the negative contributionsof the financial shocks. This implies that the BOJ’s precautionary monetary easing policy rate
results in an active reduction in its policy rate down by reacting to the recession associatedwith the collapse of the asset price bubble.
[Figure 2 around here]

5.4

Dynamic and cyclical properties of the estimated modelThis subsection investigates the quantitative properties of the estimated model. Figures 3-6
summarize impulse responses of the nominal interest rate, stock price gap, inflation, stock pricegrowth, and output growth to the shock to monetary policy, preference, financial conditions,and neutral technology. “Baseline” represents the impulse responses of the model variables tothe shocks under the estimated parameters in the benchmark model. We firstly focus on theimpulse responses in the benchmark model.
Figure 3 shows the impulse response to a monetary policy shock in an estimated DSGE
model. The contractionary monetary policy shock increases the nominal interest rate, thestock price gap, and growth and decreases the inflation and output growth. The increase in
the nominal interest rate causes the increases in dividends and consequently the stock pricegap and growth. This is because the contractionary monetary policy decreases the payments
for labor compensation more than the decrease in the output. Moreover, the impulse responses
illustrates that this shock generates the trade-off between stabilization of the inflation and thestock price gap. These results suggest that the central bank must sacrifice the price stability toprevent fluctuations in stock prices as long as a monetary policy rule contains the stabilization
term that responds to the stock price gap. As the results show, inflation and the stock pricegap are characterized by persistent responses, compared to the case for other shocks.
[Figure 3 around here]17

As shown in Figure 4, the preference shock leads to stock price fluctuations though a change
in the discount factor. Except for the stock price growth, the positive preference shock increases
macrovariables. However, the impulse responses of stock price gap and growth appear to beinconsistent with the ones that we expect. Figure 5 shows the financial shock, which induces
the nonfundamental disturbances for the stock prices. This shock results in increases in stock
prices, inflation, and the output gap through the wealth effects of stock prices, which increase
the demand for output. In response to both shocks, although the central bank increases its
nominal interest rate, the policy reaction is more persistent in the case of the financial shock
than that of other shocks. Put differently, the financial shock is the more persistent effects on
the interest rate than any other structural shock.
[Figure 4 around here][Figure 5 around here]
As shown in Figure 6, the positive neutral technology shock increases output growth andstock prices via an increase in the dividend, whereas it declines the inflation. Thus, the central
bank also faces a policy trade-off between inflation and stock price stabilization in the case of
the technology shock. In contrast to the monetary policy shock, since the neutral technology
shock is less persistent than other shocks, inflation and the stock price gap promptly converge
to stationary steady states.12
Figures 3-6 also reveal whether monetary policy stabilizes the real economy by reacting tostock prices. These figures summarize the impulse responses under the different values of φx.s :Baseline (φx.s = 0.164), φx.s = 0.25, and φx.s = 0.5. As the value of φx.s increases, it indicatesthat monetary policy reacts more strongly to the stock market conditions.13[Figure 6 around here]
These impulse responses reveal that as the central bank respond strongly to the fluctuationsin the stock price gap, the nominal interest rate tends to react more strongly and are more
persistent, whereas the growth rate of stock price and output are no significant changes relative
12

While the persistence of the monetary policy shock is 0.325, it of the neutral technology shock is 0.079.

13

In this simulation, while we change only the value of φx.s in the baseline model, we do not consider there-estimation of the model under the different value of φx.s .

18

to that of the baseline model. These results suggest that even if the monetary policy reacts
strongly to the fluctuations of stock price gap, it is difficult for the central bank to stabilize
sufficiently the stock price and output volatility in the periods.

5.5Role of measurement error for stock prices

In the previous section, we estimated a DSGE model that takes into account the measurement
error of stock prices. The specification of the baseline model is based on Castelnuovo andNistico (2010). The estimation results appear to show that the BOJ’s response to stock prices
is positive, whereas there is a large uncertainty about its statistical significance. This is because
the result also shows that the estimated standard deviation of the measurement error of stock
prices is quite large. We conjecture that the estimation results may be strongly affected by thismeasurement error. Therefore, to check for robustness, we estimate the DSGE model without
the measurement error of stock prices.
Table 5 shows the estimation results of the DSGE model excluding the measurement errorof stock prices.14 There are several caveats to this robustness check. First, the performanceof the model obtained in Table 3 is better than that of the model excluding the measurement
error. Second, all log marginal likelihoods are worse than the ones obtained in Table 3, however.
Thus, the performance of the model excluding the measurement error of stock prices is worse
than that of the benchmark. Third, the estimates of the stabilization coefficients of stock prices
are much smaller than those in Table 1. For example, in the baseline specification excluding
the measurement error of stock prices, φx,s is 0.008, which is much smaller than 0.164 in Table
1. This robustness check indicates that the main message of this paper remains unaffected by
the exclusion of the measurement error for stock prices.
[Table 5 around here]
14

In this robustness analysis, the posterior distribution of the MH algorithm was drawn 500,000 times and thesecond half of the distribution was used for the analysis. The results showed that most of the parameters met
the diagnostic criteria for convergence of the distribution, but some did not. However, we would like to mention
that this robustness check does not affect the main conclusion of this paper.

19

6

Policy reevaluation: Bad policy or bad luck?

In this section, we discuss the role of stock price stabilization during the 1980s based on
the simulation results obtained in the previous section. The main purpose of this section isto reevaluate the BOJ’s monetary policy during the 1980s based on the implication of theseresults. As discussed in Bernanke and Gertler (2000), Jinushi et al. (2000), and Okina et al.
(2001), it has been discussed the possibility that both the delay and the shortage of monetary
tightening policies from 1985 to 1987 led to the stock price bubble. In addition, sharp increases
in the official discount rate in subsequent periods resulted in the bursting of the bubble in1990. The problem is whether the BOJ could have prevented the stock price bubble in thelate 1980s, had it decided to pursue aggressive increases in the policy rate in response to stock
prices during the period.
For instance, Bernanke and Gertler (2000) argued that the BOJ should have reacted to thestock price boom in the latter of the 1980s using the estimation result of the BOJ’s reaction
function suggested by the Taylor rule.15 They asserted that the BOJ should have aggressively
raised its interest rate in the late 1980s.16 Miyao (2002) found that the BOJ’s monetary policy
was characterized by active policy stances in the late 1980s by estimating the VAR model. He
pointed out that the BOJ’s monetary policy was easing in 1986-1987 and it was tightening in
1989-1990. Summing up, these results seem to stress the importance of the BOJ’s active policy
stance in these periods.
On the other hand, Hirose (2008) estimated the financial accelerator effects in a DSGE
model with a sunspot shock and found that the estimated monetary policy rule during 1980s
was similar performance the optimal monetary policy rule that minimizes the welfare loss.
Therefore, he concluded that the since the monetary policy could reduce the macroeconomic
fluctuations in Japan, the endogenous volatility during the period were associated with theexogenous shocks that was induced by “bad luck” rather than “bad policy”.
15

In their estimation, they introduced the exchange rate into the reaction function because the exchange rate

plays a significant role in the Japanese economy during the latter of the 1980s.
16

However, Bernanke and Gertler (2000) also pointed out that an increase in the policy rate should be justified

if the BOJ combats the inflationary risk induced by stock price boom. Thus, they claimed that the central bankshould not react to a fluctuation in asset prices as long as asset price fluctuations do not connect to the inflationary
risk (namely, the FED view).

20

As shown in Figure 3, our model suggests that the BOJ could not prevent stock pricebubble even if it put a larger weight on stock price stabilization in its reaction function. Figure
3 showed that a reaction function with a larger weight on stock prices leads to a persistentdecline in the inflation rate, whereas it creates a more increased response of the stock pricegap. This result might imply that even if the BOJ decided active monetary tightening in 1987,
such a policy prescription could not prevent a drastic increase in stock prices that deviate fromtheir fundamental values.
Figure 7 illustrates the impulse response to monetary policy shock under several parameter
restrictions.17 The first case corresponds to the case for no asset price channel. In this case,monetary tightening with stock price stabilization causes a decline in the stock price gap. A
contractionary policy shock prevents a stock price boom in the case of ξ = φx,s = 0. ξ = 0
implies that the model reduces to the RA model. This case corresponds to Carlstrom andFuerst (2007). However, in the presence of stock price channel (i.e., ξ > 0), even a positive
weight on stock prices in the reaction function cannot prevent a positive response of the stock
price gap regardless of monetary tightening. Okina et al. (2001) argued the possibility thatthe BOJ could not have prevented the stock price bubble even if it decided to raise the official
discount rate gradually in response to a sharp increase in stock prices. They asserted, instead,that a sharp increase in the policy rate might have been required to restrain the stock pricebubble. Our result has shown that the BOJ might not have prevented the stock price bubble
even if it decided to raise the policy rate sharply. In that sense, we might say that our result
supports the assertion of Okina et al. (2001) in terms of a Bayesian DSGE investigation.
[Figure 7 around here]
How come the positive weight on stock prices did not prevent a stock price boom? In
our model, it is possible that monetary tightening policy leads to a positive response of thestock price gap. A contractionary monetary policy causes a decline in output and inflation.
The decline in the inflation rate reduces the real marginal cost. In our model, stock pricedynamics proportionally change with the dividend, which is related positively to output andnegatively to the real marginal cost.18 Since monetary tightening induces a decline in the real17

In this simulation, we reestimate the model under each restriction.

1−αThe log-linearized dividends are rewritten as follows dˆt = ŷt −(ŵt + αˆ
lt ). The dividend is theα + µpremaining of the income net of the cost in the production.
18

21

marginal cost, which increases the dividend. When the effect of a decline in the real marginal
cost dominates that of decreased output, therefore, stock prices may increase in response tomonetary tightening. Figure 8 plots the historical decomposition of the dividend. This figure
shows that the dividend increases regardless of monetary tightening during 1989-1990. It
follows from Figure 8 that the fluctuations in financial shocks during this period contributed
significantly to this increase in dividends. This empirical finding is consistent with the model
prediction and the assertion of Okina et al. (2001).
[Figure 8 around here]

7

Concluding remarks

This study reexamined the role of stock price stabilization in Japan. To do this, we adopted
a DSGE model that included the wealth channel through stock prices. Our results showed
the presence of the wealth channel through an increase in stock prices in Japan. In addition,
we argued for the possibility that the BOJ conducted its monetary policy by giving weight
to stock price stabilization as a policy objective in addition to controlling inflation and theoutput gap. However, our results indicate that while the BOJ might have reacted to stock
prices that deviated from their fundamental values, it could not prevent a stock price bubble
purely by implementing a contractionary monetary policy shock. Therefore, we conclude thatthe BOJ’s monetary policy stance aimed to stabilize fluctuations in stock prices and minimize
the macroeconomic volatility, whereas endogenous volatility was caused by bad shocks.

Acknowledgements
We would like to thank Hirokuni Iiboshi and Shin-ichi Nishiyama for helpful comments andsuggestions. This paper was supported by JSPS KAKENHI Grant Number JP20K01784. Allremaining errors are my own.

22

A

Appendix A: Castelnuovo and Nistico (2010) model

In this appendix, we provide a detailed explanation of the framework of the perpetual-youth
NK model developed by Castelnuovo and Nistico (2010).

A.1

Households

The representative household obtains utility from consuming final goods and spending leisure.
Thus, the household’s preference is given by
E0

∞
X

b

β t (1 − ξ)t ezt [log (Ct (j, k) − hCt−1 ) + χ log (1 − lt (k))] ,t=0

where β is subjective discount factor, ξ is turnover rate, ztb is a shock to preference, Ct (j, k) is
individual consumption, Ct is aggregate consumption, h is a parameter of habit persistence, χis the weight of leisure, lt (k) is hours worked.
The household’s budget constraint is given by
Z 1
Pt+1 Bt+1
1
Ct (j, k) + Et ft,t+1+
Qt (i)Zt+1 (j, k, i)di = Wt (k)lt (k) − Tt +Ωt (j, k),
Pt
1
−
ξ
0
where ft,t+1 is stochastic discount factor, Pt is price level, Bt is the household’s nominal bondholdings, Qt (i) is real stock price, Zt (j, k, i) is equity share issued by intermediate good firms,
Wt (k) is real wage, Tt is a lump sum transfer and profit, and Ωt (j, k) is financial wealth anddefined as follows
Z 1Ωt (j, k) ≡ Bt (j, k) +(Qt (i) + Dt (i)) Zt (j, k, i)di.
0No-arbitrage condition is given by
Et ft,t+1 =

1
,
Rtn

where Rtn is the gross nominal interest rate.
The first-order conditions are summarized as follows
Pt Qt = Et ft,t+1 Pt+1 (Qt+1 (i) + Dt+1 (i)) ,Et ft,t+1 = βEt

Pt C̃t (j, k)bb
ezt+1 −zt ,Pt+1 C̃t+1 (j, k)where C̃t (j, k) ≡ Ct (j, k) − hCt−1 .
23

A.2

Retailers

Retailers produce final goods Yt using intermediate goods Yt (i) to maximize their profit underR1
the perfect competitive market. Their profit is given by Pt Yt − 0 Pt (i)Yt (i)di. Here, Yt ishRi(1+µpt )p1, where µpt is
production function of retailers which is given by Yt = 0 Yt (i)1/(1+µt ) di
the time varying price markup. The first-order condition for retailers is given byYt (i) =Pt (i)Pt−(1+µpt )/µpt
Yt ,

(A.1)

which denotes the demand for intermediate goods. Given the perfect competitive market, theprice level is given
Z 1
Pt =

−1/µpt−µpt

Pt (i)

.

(A.2)

0

A.3

Intermediate good firms

Intermediate goods firm i produce output Yt (i) by using labor service lt (i). The production
function of the intermediate goods firms is
Yt (i) = At lt (i)1−α ,where α ∈ (0, 1), Yt (i) is an intermediate good and At is a neutral technology level and thelogarithm of it is given by
ln At = ln γ + ln At−1 + ztγ ,where γ is the growth rate of technology and ztγ is the stochastic term of technology.
The intermediate good firms set their prices to maximize their discount future profit in themonopolistically competitive market as given the demand for intermediate goods (A.1 ). Their
price setting follows Calvo (1983). Specifically, while a fraction 1 − θp of all firms reoptimize
their price, the remaining fraction θp firms that do not optimally set their price follows theindexation rule associated with past inflation and the steady state inflation rate. Regarding
the firms that reoptimize their price, the first-order condition for Pto is given by∞
X

Pt+s Yt+s|tEt
θps ft,t+1
µpt+s
s=0



Pto
Pt+s



Pt+s−1
Pt−1

24

ιp
π

s(1−ιp )− (1 + µpt+s )mct+s|t= 0,where Pto is the reoptimized price, ιp is the degree of price indexation and mct+s|t is the economy
wide marginal cost and expressed as follows
−α/(1−α)(1+µpt )/µpt
 o 

Pt
Pt+s−1 ιp s(1−ιp ).
πmct+s|t = mct+s
Pt+s
Pt−1
Here, mct is average marginal cost and given byWt
mct =(1 − α)At



Yt
At

α/(1−α).

Given staggered price manner, the price level (A.2 ) is transformed as follows
o p
n
p
p −µt
ιp
.
π 1−ιp )−1/µt + (1 − θp )(Pto )−1/µt
Pt = θp (Pt−1 πt−1

A.4

Labor unions

Labor unions negotiate with intermediate goods firms with respect to wage setting and set nominal wages in order to maximize the discount future income in the monopolistically competitivew

w

market as given the demand for the labor service lt (k) = (Wt (k)/Wt )−(1+µt )/µt lt . Here,i−µwti(1+µwt )
hR
hR
w
w
1
1
is the aggregate labor hours and Wt = 0 Wt (k)−1/µt dk
lt = 0 lt (k)1/(1+µt ) dk
is the aggregate real wage. Note that they are not always free to change the wage and their wage
setting follows the price setting manner of Calvo (1983). While a fraction 1 − θw of all firms
reoptimizes their wage, the remaining fraction θw unions that do not optimally change theirwage follows the indexation rule related with the past inflation and the productivity growth.
As for the labor unions that reoptimize their wage, the first-order condition for Wto is given by


ιw

∞
X
lt+s|ts(1−ιw )so Pt+s−1 At+s−1w
Et
θw ft,t+s w
Pt Wt
(πγ)
− (1 + µt+s )Pt+s M RSt+s|t = 0,µt+s
Pt−1 At−1
s=0

where Wto denotes the optimized real wage, µw
t+s is the time varying wage markup, ιw is thedegree of the wage indexation, and M RSt+s|t is the average marginal rate of substitution
between consumption and labor hours. The relationship between average and economy-wide
real marginal costs M RSt is characterized as follows:
M RSt+s|t = M RSt+s
1 − lt+s

Pt WtoPt+s Wt+s

1 − lt+s−(1+µwt+s )/µwt+s ,Pt+s−1 At+s−1 ιws(1−ιw )(πγ)
Pt−1 At−1

where M RSt+s|t is the average M RS and M RSt+s is the economy-wide M RS and defined asfollows
M RSt+s ≡ χ

25

C̃t+s
.
1 − lt+s

Given staggered wage setting, the aggregate wage index is transformed as follows
i w
h 
w −µt
−1/µw
t
+ (1 − θw )(Pt Wto )−1/µt.
Pt Wt = θw Pt−1 Wt−1 (πt−1 γezt−1 )ιw (πγ)1−ιw

A.5

Market clearing condition

The market clearing condition for the final goods is given19g

Yt = Ct + gezt At .

A.6

Log-linearized model

A.6.1

Key equations

ŷt =

ĉt −

g
c
ĉt + ztg ,yyh
1 − h/γ(1 − h/γ)2  nR̂t − Et π̂t+1(ĉt−1 − ztγ ) =ψ q̂t −γ
1 − h/γ + ψ
1 − h/γ + ψ
1 − h/γhγ+
Et ĉt+1 − ĉt + Et zt+1
1 − h/γ + ψγb− (1 − h/γ)(1 + ψb ) Et zt+1
− ztb ,

(A.4)



γ
q̂t = β̃Et q̂t+1 + (1 − β̃)Et dˆt+1 − R̂tn − Et π̂t+1 + Et zt+1
+ ztν ,

(A.5)

1−αdˆt = ŷt −m̂ct ,
α + µp

(A.6)

ˆlt =

mw
ˆ t = ϕˆlt +

1
ŷt ,
1−α

(A.7)

1
h/γ
ĉt −
(ĉt−1 − ztγ ) − ŵt ,1 − h/γ
1 − h/γ

(A.8)

α
ŷt .
1−α

(A.9)

m̂ct = ŵt +
19

(A.3)

Unlike Castelnuovo and Nistico (2010), our analysis assume that a public sector does not consume thefraction of total output and its consumption is stochastically decided.

26

A.6.2Frictionless equilibriumh/γ(1 − α)ŷ ∗1 − α + (α + ϕ)(1 − h/γ)(1 − g/y) t−1




g/y
h g
(1 − α)(1 − g/y)h γ
gzt − zt−1 + zt ,+1 − α + (α + ϕ)(1 − h/γ)(1 − g/y) 1 − g/yγγŷt∗ =

h/γ(1 − α)ŵ∗1 − α + (α + ϕ)(1 − h/γ)(1 − g/y) t−1




g/y
h g
α(1 − g/y)h γ
gzt − zt−1 + zt ,−1 − α + (α + ϕ)(1 − h/γ)(1 − g/y) 1 − g/yγγ(A.10)ŵt∗ =





1
1
g
γ
g
∗
Et ŷt+1 − Et zt+1 + Et zt+1
1 − h/γ 1 − g/y
y


h/γ
g
−
ŷt∗ − ztg(1 − h/γ)(1 − g/y)y

1 − h/γ + ψg g∗−ŷt − zt
(1 − h/γ)2 (1 − g/y)
y




g g
(1 − h/γ + ψ)h/γ1γ∗+ŷt−1 − zt−1 − zt
(1 − h/γ)2
1 − g/yy(1 − h/γ + ψ)(1 + ψb ) bEt zt+1− ztb ,−
1 − h/γ(A.11)

R̂t∗ =

γ∗∗.
q̂t∗ = β̃Et q̂t+1+ (1 − β̃)Et ŷt+1− R̂t∗ + Et zt+1

27

(A.12)(A.13)

A.6.3

Steady states

The steady states in the log-linearized equilibrium conditions are as follows.
c
g
=1− ,
y
y
ω
Rn (µp + α)=,c
(Rn − γπ)(1 + µp )c/y
ξ{1 − β(1 − ξ)} ω
ψ=
,
1−ξ
c
β(1 − h/γ),β̃ =1 − h/γ + ψ
1−α,ϕ=χ(1 − h/γ)(1 + µw )(1 + µp )c/yψβ(1 − ξ)ρb
ψb =,(1 + ψ − h/γ){1 − β(1 − ξ)ρb }

B

λp =

µp (1 − θp )(1 − β̃θp )(1 − α),θp (α + µp )λw =µw (1 − θw β̃)(1 − θw ).
θw {µw + ϕ(1 + µw )Appendix B: Data sources

We provide the detailed explanation how to make a data set to estimate the DSGE model. The
data series we use in this paper are as follows:20• Gross Domestic Product (Source: Cabinet Office, “National Account.”)• GDP deflator (Source: Cabinet Office, “National Account.”)• Call rate (Source: Bank of Japan)• Nikkei 225 (Source: Federal Reserve Bank of St. Louis)• Nominal consumption (Source: Cabinet Office, “National Account.”)• Nominal wage (Source: Ministry of Health, Labor and Welfare, “Monthly Labour Survey.”)• Labor hour (Source: Ministry of Health, Labor and Welfare, “Monthly Labour Survey.”)20

For time series data of real GDP, GDP deflator, and nominal consumption, simple retrospective series up

to 1993Q4 are used for estimation to maintain consistency in the base year.

28• Population over 15 years old (Source: Statistics Bureau, Ministry of Internal Affairs andCommunications, “Labor Force Survey.”)

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31

Table 1: Priors and posteriors

Prior
Parameters

Type

Posterior

Mean

SD

90% interval

0.046[0.026, 0.066]

ξTurnover rate

UniformhHabit persistence

Beta

0.700

0.150

0.174

[0.076, 0.266]

χLeisure weight

Gamma

1.400

1.000

0.031

[0.001, 0.061]

θpIntermediate good price stickiness

Beta

0.375

0.100

0.883

[0.855, 0.914]

θw

Wage stickiness

Beta

0.375

0.100

0.216

[0.110, 0.320]

ιpIntermediate good price indexation

Beta

0.500

0.250

0.041

[0.000, 0.084]

ιw

Wage indexation

Beta

0.500

0.250

0.057

[0.001, 0.110]

φr

Monetary policy rate smoothing

Beta

0.800

0.100

0.958

[0.931, 0.987]

φπMonetary policy response to inflation

Gamma

1.700

0.100

1.671

[1.507, 1.832]

φx.y

Monetary policy response to output gap

Gamma

0.125

0.050

0.137

[0.049, 0.220]

φx.s

Monetary response to stock price gap

Normal

0.000

0.025

0.164

[-0.096, 0.423]

γ

Steady state rate of balanced growth

Gamma

0.480

0.100

0.468

[0.344, 0.591]

πSteady state inflation rate

Gamma

0.240

0.100

0.256

[0.125, 0.385]

Steady state interest rate

Gamma

1.090

0.100

1.101

[0.940, 1.258]

ργPersistence in ztγ

Beta

0.500

0.200

0.079

[0.015, 0.141]

ρp

Persistence in ztp

Beta

0.500

0.200

0.109

[0.022, 0.191]

ρw

Persistence in ztw

Beta

0.500

0.200

0.555

[0.320, 0.784]

ρgPersistence in ztg

Beta

0.500

0.200

0.958

[0.926, 0.993]

ρbPersistence in ztb

Beta

0.500

0.200

0.361

[0.049, 0.665]

ρνPersistence in ztν

Beta

0.500

0.200

0.958

[0.928, 0.989]

ρrPersistence in ztr

Beta

0.500

0.200

0.325

[0.129, 0.519]

ρmq

Persistence in met

Beta

0.500

0.200

0.367

[0.203, 0.530]

σγStandard deviation of ztγ

Inverse gamma

0.500

inf

1.010

[0.870, 1.145]

σpStandard deviation of ztp

Inverse gamma

0.500

inf

0.431

[0.363, 0.495]

σwStandard deviation of ztw

Inverse gamma

0.500

inf

0.504

[0.368, 0.638]

σgStandard deviation of ztg

Inverse gamma

0.500

inf

1.770

[1.529, 2.006]

σbStandard deviation of ztb

Inverse gamma

0.500

inf

0.447

[0.159, 0.715]σνStandard deviation of ztν

Inverse gamma

0.500

inf

0.561

[0.352, 0.766]

σrStandard deviation of ztr

Inverse gamma

0.500

inf

0.123

[0.106, 0.141]

σmq

Standard deviation of memqt

Inverse gamma

0.500

inf

6.986

[6.033, 7.936]

R

n

32

[0, 1]

Mean

Table 2: Comparison of models

Baseline

ξ=0

φx.s = 0

ξ = φx.s = 0

ξ

0.046

0

0.050

0

h

0.174

0.145

0.162

0.149

χ

0.031

0.027

0.029

0.042

θp

0.883

0.319

0.882

0.296

θw

0.216

0.525

0.187

0.436

ιp

0.041

0.050

0.042

0.058

ιw

0.057

0.046

0.059

0.057

φπ

1.671

1.691

1.681

1.776

φx.y

0.137

0.148

0.136

0.159

φx.s

0.164

0.452

0

0

φr

0.958

0.849

0.964

0.797

Log-marginal likelihood−641.23−626.92−641.53−631.01

Table 3: Comparison of models

φx.s = 0.164

φx.s = 0.25

φx.s = 0.5

φx.s = 0.75

φπ

1.671

1.662

1.675

1.687

φx.y

0.137

0.139

0.132

0.132

φr

0.958

0.954

0.967

0.976

Log-marginal likelihood−641.23−640.31−641.27−643.20

33

Table 4: Variance decomposition

Shock

Stock price gap

Stock price growth

Inflation

T =8

T = 32

T =8

T = 32

T =8

T = 32ztγ

Neutral technology shock

4.8

3.4

3.9

3.9

0.2

0.2

ztp

Price markup shock

3.1

2.8

0.1

0.1

92.1

85.5

ztw

Wage markup shock

14.5

10.2

0.3

0.3

0.2

0.2

ztg

Exogenous demand shock

45.3

49.9

0.3

0.3

1.2

1.8

ztb

Preference shock

7.2

5.0

0.0

0.0

0.0

0.0

ztν

Financial shock

18.7

14.0

0.7

0.7

4.4

8.3

ztr

Monetary policy shock

5.9

14.6

0.0

0.0

1.5

3.6

Output gap
Shock

Output growthInterest rate

T =8

T = 32

T =8

T = 32

T =8

T = 32ztγ

Neutral technology shock

7.0

6.9

82.5

82.5

0.0

0.0

ztp

Price markup shock

1.6

1.6

0.5

0.5

4.9

4.1

ztw

Wage markup shock

22.2

22.0

2.5

2.5

0.3

0.4

ztg

Exogenous demand shock

14.8

14.6

4.6

4.6

2.2

9.6

ztb

Preference shock

8.2

8.1

3.7

3.7

0.1

0.0

ztν

Financial shock

36.0

36.1

5.1

5.1

2.4

9.0

ztr

Monetary policy shock

9.9

10.3

0.9

0.9

89.7

76.5

Table 5: Comparison of models: Robustness check

Baseline

ξ=0

φx.s = 0

ξ = φx.s = 0

φx.s

0.008

0.001

0

0

Log-marginal likelihood−643.76−641.09−642.02−636.69

34

4

7

3

6
5

2

4
1

3

0

2

-1

1
0

-2

-1
-3

GDP gap-2-4

Inflation rate-3
81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

9

40

8

30

7

20

6

10

5
0
4
-10

3
2

Official discount rate

1

Call rate

-20
-30

0

Stock price gap-40
81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

Source: Bank of Japan (call rate, GDP gap, offical discount rate), Cabinet Office National
Accounts (GDP deflator), Nikkei industry Research Institution via FRED, Federal Reserve
Bank of St. Louis (Nikkei Stock Average Nikkei 225)

Figure 1: Time series data in the Japanese economy: From 1980s to 1990s

35

1.5

Percentage deviation from the steady state (%)

1

0.5

0

-0.5

-1

Technology shockPreference shock

Financial shock

Monetary policy shock

Other shocks

Nom inal interest rate

-1.5
81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

Figure 2: Historical decomposition of nominal interest rate

36

97

98

Figure 3: Impulse responses to the monetary policy shock37

Figure 4: Impulse responses to the preference shock38

Figure 5: Impulse responses to the financial shock39

Figure 6: Impulse responses to the neutral technology shock40

Figure 7: Impulse responses to the monetary policy shock

41

15

Percentage deviation from the steady state (%)

10Technology shockPreference shock

Financial shock

Monetary policy shock

Other shocks

Dividend

5

0

-5

-10
81

82

83

84

85

86

87

88

89

90

91

92

93

94

Figure 8: Historical decomposition of dividend

42

95

96

97

98