Hidden Stagflation∗
Yuta Takahashi and Naoki Takayama†
Institute of Economic Research, Hitotsubashi University
October 13, 2023
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Abstract
There is a widespread perception that the Japanese economy has been underperforming due to chronic deflation. From this perspective, it is puzzling that consumption growth began to further stagnate precisely when the economy emerged fromdeflation around 2014. We attribute this puzzling phenomenon to technology stagnation specific to manufacturing goods and the zero lower bound constraint on nominalinterest rates. Our extended New Keynesian model reveals that this technology stagnation alone can account for approximately half of the observed rise in inflation andmore than 40% of the decline in consumption growth.
JEL Classification: E31, E43, E52, E58

1

Introduction

The Japanese economy has faced low growth and low inflation since the stock market crash of
1990. Initially termed “the lost decade,” this prolonged period of poor economic performance
eventually came to be known as “the two lost decades” and, more recently, it has been referred
to as secular stagnation. To combat this stagnation, the Japanese government implemented avariety of fiscal, monetary, and deregulation policies. A pivotal change occurred in December∗
We acknowledge comments from Daisuke Adachi, Kosuke Aoki, Jonas Arias, Francesco Bianchi, Toni
Braun, Larry Christiano, Shigeru Fujita, Ippei Fujiwara, Masao Fukui, Fumio Hayashi, Masashi Hino, Hibiki
Ichiue, Daisuke Ikeda, Hiro Ishise, Takashi Kano, Mitsuru Katagiri, Shinnosuke Kikuchi, Olivier Loisel, JeanBaptiste Michau, Tomohide Mineyama, Sophie Piton, Hikaru Saijo, Toshiaki Sekine, Etsuro Shioji, Ludvig
Straub, Nao Sudo, Michael Song, Satoshi Tanaka, Takashi Unayama, Yuichiro Waki, and Johannes Wieland.
In addition, we thank Yukimi Ueda for the excellent research assistance.
†
Institute of Economic Research, Hitotsubashi University. Emails: yuta.takahashi@r.hit-u.ac.jp andntakayama@ier.hit-u.ac.jp.

1

2012, when Prime Minister Abe assumed office. Advocating drastic expansionary policies,
he openly pressured the Bank of Japan (BOJ) to adopt more aggressive monetary policies.1
To achieve this goal, his cabinet appointed Kuroda as the governor of the BOJ. Upon
his appointment in April 2013, Governor Kuroda introduced a new package of unconventional monetary policies termed quantitative and qualitative easing (QQE).2 Shortly after
the introduction of QQE, the economy finally began to emerge from deflation (see Figure1a). Given this sequence of events, both policy authorities (such as BOJ (2016) and Caldara
et al. (2020)) and academia (including Bernanke (2017a) and Hausman and Wieland (2015)
and Ito (2021)) credit QQE for this uptick in inflation. For example, Bernanke offered thefollowing assessment of QQE:
Kuroda’s program of “qualitative and quantitative easing” has had important
benefits, including higher inflation and nominal GDP growth and tighter labormarkets. Bernanke (2017b)
However, the uptick in inflation did not translate into a discernible improvement in the real
economy, as illustrated in Figure 1b. Real consumption per capita has remained stagnant
since the introduction of QQE, although it had been increasing until around 2010. In line withthis observation, Hausman and Wieland (2015) analyze Japan’s cross-sectional consumption
data and find little evidence that Kuroda’s expansionary monetary policy significantly affected consumption. These findings are puzzling, particularly given the widespread belief
that Japan’s economic underperformance stems from deflation.
In this paper, we offer a resolution to this puzzling phenomenon. The key to our resolution
lies in the observation that a specific subcategory of goods has been pivotal in driving
both the inflation uptick and the dip in consumption growth. In Figure 2, we disaggregate
inflation and consumption data into manufacturing and non-manufacturing goods. The left
panel of Figure 2 highlights how the inflation rate for the manufacturing good, which waspreviously negative, turned positive around the time QQE was introduced. Concurrently,
the consumption growth of the manufactured good—which had greatly outpaced that of
the non-manufacturing good—began to level off, as depicted in the right panel of Figure
2. These trend shifts indicate a potential stagflation scenario—a combination of stagnant
1

The Abe administration continued until September 2020. Prime Minister Abe introduced a policy
package widely known as “Abenomics.” Broadly speaking, the core of the package was characterized bythree components: (i) aggressive monetary policy, (ii) flexible fiscal policy, and (iii) growth strategies bystimulating private investment.
2
Kuroda was the governor until April 2023. During him term in office, the BOJ strengthened its monetary
policy in various ways. The BOJ introduced a negative interest rate on reserves and yield curve control.
Consequently, not only short-term interest rates but also long-term interest rates have been pushed down tonear-zero. Moreover, the BOJ’s asset purchase program to acquire various financial assets, including ETFs
and REITs, has also been expanded on an unprecedented scale.

2

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Figure 1: Japanese Macroeconomy
Notes: See Section 3.1 and Appendix A for details on the variables used in these graphs. The blue-colored
areas represent periods of QE by Governor Shirakawa and the red-colored areas represent periods of QQE
by Governor Kuroda. The average growth rate of real consumption per capita before QE is around 0.8%.
After QQE, the average growth declined to around 0.2%.

consumption and higher inflation. More specifically, the data suggests that a supply shockto the manufacturing goods sector has reduced its consumption growth and pushed inflation
upward.
To formally explore the possibility of stagflation, we introduce a theoretical frameworkthat builds upon New Keynesian models. Contrary to the canonical New Keynesian model,
our model delineates three distinct goods: generic outputs, manufacturing goods, and nonmanufacturing goods. Drawing upon the modeling assumptions used in New Keynesianmodels with investment-specific technology shocks (for example, Justiniano et al. (2011) andChristiano et al. (2014)), producers of the consumption goods employ linear, yet distinct,
technologies to transform generic output into each category of consumption goods. This
linear technology assumption implies that the relative price of the manufacturing good reflects the technology specific to the manufacturing good, which is an important aspect for
our analysis.3 The generic output is produced by combining intermediate goods suppliedby monopolistic intermediate-good firms. These firms choose their prices to maximize theirprofit subject to the pricing friction given by Calvo (1983).
We employ this framework to investigate the Japanese economy from 1994 to 2018. As
emphasized earlier, the foundation of our discussion is the fact that the prices of manufactured goods steadily declined until around 2010 and have remained relatively stablesince then. Based on our theoretical model, this persistent decline mirrors the technologicalprogress specific to the manufacturing good. On the flip side, the cessation of the relative3

According to Greenwood et al. (1997), it is common in the macroeconomic analysis to infer this type of
directed technology progress from relative prices.

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Figure 2: Manufacturing and Non-Manufacturing Goods
Notes: The average growth of consumption of the manufacturing good before the introduction of quantitativeeasing by Shirakawa was 7%. After the introduction of QQE, it was merely 0.7%.

price decrease for the manufacturing good suggests that manufacturing-specific technology
has reached an impasse. Thus, according to our model, the data suggests that the Japanese
economy has been experiencing a negative and permanent technology shock since around2010. We refer to this technological stagnation as the manufacturing-specific technology
stagnation (MST stagnation).
Now, we proceed to derive the theoretical implications of the MST stagnation for aggregate inflation and consumption. The MST stagnation reduces the efficiency of production of
the manufacturing good, thereby leading to a decline in its relative price. When the elasticity
of substitution between consumption goods is one, a value strongly supported by our data,
the MST stagnation leaves labor supply, saving, and consumption of the non-manufacturing
good unaffected. This property, combined with the fact that the nominal interest rate iseffectively pegged in Japan, implies that only inflation and consumption of the manufacturing good are responsive to the MST stagnation. Consequently, these effects ripple throughaggregate inflation and consumption.
Having established the theoretical implications, we quantify the impact of the MST
stagnation on inflation and consumption growth. We find that the MST stagnation alone
accounts for approximately 50% of the observed increase in inflation and 40% of the observed
decline in consumption growth since 2014. In other words, in the absence of the MST stagnation, the aggregate inflation rate would have barely risen above 0%. Thus, our resolution
to the puzzle is encapsulated in the title of this paper: the increase in inflation and weak
consumption can be attributed to stagflation. However, since this resolution has largely goneunnoticed, we termed it “hidden stagflation.”
Our quantification depends heavily on the structure of the model, which prompts us to4

validate the theoretical model. Specifically, we extensively utilize the intertemporal Euler
equation. As widely recognized in the literature, the Euler equation has a range of sharp
predictions that are often met with skepticism. For example, a one percentage point permanent increase in inflation should be associated with a one percentage point permanent
decline in consumption growth in the long run. Furthermore, our theoretical model has asimilar sharp cross-sectional implication. If a city experiences a one percentage point higher
inflation than other cities, that city should exhibit a one percentage point greater decline in
the growth of consumption compared to the other cities. Remarkably, we find that our data
supports these sharp predictions.
Before concluding this paper, we undertake two sets of additional exercises to prove therobustness of our analysis. First, we verify that the MST stagnation is observed in manyother datasets and other developed countries, including Germany and the United States.
These robustness exercises are particularly important because the premise of our analysis
is that the MST stagnation has occurred in Japan. Second, we explore two extensions of
the model. We allow the representative consumer to have a more general utility function
and introduce multiple investment goods. By introducing capital, we can also examine
the effects of technology stagnation specific to information and communication technology(ICT) investment goods, which is also substantiated in our data. Our quantification results
are either only slightly changed or even reinforced by these extensions.
In addition to the papers already mentioned, our study belongs to several lines of research.
First, our study is related to the literature that analyzes the Japanese economy. A seminal
work in this area is that of Hayashi and Prescott (2002), who examine the slowdown of
economic growth by using a real business cycle model. They argue that the lost decade waslargely driven by the permanent decline in the growth of total factor productivity (TFP).
A follow-up study by Kawamoto (2005) scrutinizes the premise in Hayashi and Prescott(2002) that TFP growth has declined. Additionally, there are papers that examine sourcesof the TFP stagnation (Sekine et al. (2003), Nakakuki et al. (2004), Fukao and Kwon (2006),
Caballero et al. (2008), and Muto et al. (2023)). From a theoretical perspective, Aoki et al.
(2017) and Illing et al. (2018) propose alternative models for the stagnant growth in Japan.
These papers typically focus on the slowdown from 1990, but our study focuses on slower
economic growth and higher inflation since around 2011.
Another more specific strand of related studies is the recent literature that analyzes
Japan’s unconventional monetary policies or Abenomics. Hausman and Wieland (2014),
Hausman and Wieland (2015), and Ito (2021) provide an initial assessment of Abenomics,
and Michelis and Iacoviello (2016) study the effect of the explicit inflation target rule adopted
by the BOJ in December 2012. Other related studies include that of Fukui and Yagasaki
5

(2023), which identifies the effect of the ETF purchase of the BOJ on stock and bond prices.
We propose a new channel that explains the rise in inflation and consumption stagnationand provide a quantitative analysis.
In a broader context, our research aligns with the growing body of literature on secularstagnation, often delineated by low output, low inflation, and low nominal interest rates(Summers (2016)). Studies such as Michau (2018), Caballero and Farhi (2018), Eggertsson
et al. (2019b), Eggertsson et al. (2019a), and Asriyan et al. (2021), propose a theory forsecular stagnation. These papers often focus on low output level and low inflation, but noton the growth rate of output. A notable exception is Benigno and Fornaro (2018). Their
model has multiple steady states, one of which has low growth and low inflation. Our paper
proposes a different mechanism that explains the rise in inflation and lower consumption
growth in Japan from a supply shock specific to a certain sector. Consequently, our paper
resonates with studies that advocate that secular stagnation results from issues in the supply
side of the economy (Gordon (2015), Barro (2016), and Ramey (2020)).
The remainder of this paper is organized in the following manner. In Section 2, we introduce our theoretical framework. Section 3 empirically analyzes the Japanese macroeconomy
through the lens of the model and provides the quantification results. Section 4 confirms therobustness of our empirical findings regarding the MST stagnation. Section 5 reveals thatthe results of the quantification are not overturned by extending the theoretical framework.
Section 6 concludes by discussing the implications of our study for the monetary policy.

2

Theoretical Framework

Our theoretical framework is a modified version of New Keynesian models that incorporate
investment-specific technology shocks (e.g., Justiniano et al. (2011) and Christiano et al.
(2014)). In these existing models, a final good is either consumed by a representative consumer or linearly transformed into an investment good. Unlike these models, we introduce a
generic output that is linearly converted, with different efficiency, into two types of consumption goods: manufacturing and non-manufacturing goods. In our baseline model, we do notinclude capital accumulation, but subsequently extend the model to incorporate it in Section
5. A key assumption shared by our model and the existing models is that the government
can control aggregate inflation, but not relative prices. Apart from this assumption, ourmodel closely aligns with the canonical New Keynesian model. In fact, when the relative
price of the manufacturing good is equal to one, our model boils down to the canonical New
Keynesian model.

6Generic-output producer. At date t, a generic output, Yt , is produced by a perfectlycompetitive representative firm. The representative firm produces the generic output by comR
ε/(ε−1)bining intermediate goods (Yt (k))k∈[0,1] with technology, Yt = k∈[0,1] Yt (k)(ε−1)/ε dk,
where ε > 1. The representative firm maximizes its profit given the price of the generic output, Pt , and the prices of the intermediate goods, (Pt (k))k∈[0,1] . The demand for intermediate
good k is given by
Yt (k) = (Pt (k) /Pt )−ε Yt .
(1)
The constant returns-to-scale production function implies that in equilibrium, the price ofR
1/(1−ε)the generic output satisfies Pt = k∈[0,1] Pt (k)1−ε dk.
Intermediate-goods firms. Intermediate good k is monopolistically supplied by intermediategood firm k. Labor is the only input, and the production function is identical across all
intermediate-goods firms:
Yt (k) = At Lt (k) ,(2)where Lt (k) is the labor demand of firm k and At represents the economy-wide technology.
The process of At can be non-stationary. As in other New Keynesian models, we assume
that the intermediate-goods firms are subject to pricing frictions, which are spelled out in
Calvo (1983): the firms can reset their prices only with probability Θ at each date t. A firmable to reset its price at date t selects its price P̃t to maximize
max
Pet

Et

∞
X

t
υt+k
Θk




e
Pt Yt (k) − Wt Lt (k) ,k=0t
subject to (1) and (2). Variable υt+k
is the nominal stochastic discount factor between datet and t + k.

Consumption-goods firms. There are two consumption goods indexed by i ∈ {m, n} inthis economy: the manufacturing good m and the non-manufacturing good n. There is a
representative firm that produces good i. Each firm has a linear technology function, whichconverts the generic output to the consumption good i. The non-manufacturing-good firm
has technology Yn,t = Mn,t and the manufacturing-good firm has technology Ym,t = Am,t Mm,t .
Here, Yi,t stands for the amount of production by firm i and Mi,t represents the amountof generic outputs used as intermediate goods for production. Variable Am,t represents
manufacturing-specific technology (MST), which increases the quantity or quality of the
manufacturing good produced, given the same amount of generic outputs used. We allow
Am,t to be non-stationary. When Am,t = 1 for all t, then the model boils down to the7canonical New Keynesian model.
Similar to the evolution of the relative price of the investment good revealed by Greenwood et al. (1997), the relative price of the manufacturing good has been declining substantially over a long period of time (See Section 3). Because of this similarity, we assume thatthese representative consumption-goods firms can set their prices freely, following Justiniano
et al. (2011) and Christiano et al. (2014). Then, in an equilibrium, the relative price of the
manufacturing good is given by4
pm,t ≡ Pm,t /Pn,t = A−1
m,t .

(3)

This characteristic implies that the relative price is always efficient and can be used forrecovering Am,t .
Representative consumer. There is a representative consumer in this economy, whose
lifetime utility function is given by
U = E0∞X

β t (γn ln Cn,t + γm ln Cm,t − v (Lt ))with γn + γm = 1,

(4)

t=0

where Cn,t is the consumption of the non-manufacturing good, Cm,t is the consumption of
the manufacturing good, Lt is labor supply, the function v (·) is disutility from labor, and β
is the discount factor. All quantity variables are articulated on a per-capita basis.
There are two aspects worth mentioning regarding the specification of the utility function.
First, we assume that the elasticity of intertemporal substitution parameter (EIS parameterfor short) is one. This assumption guarantees the existence of a balanced growth path (BGP)of the economy, which is frequently made in medium-scale macroeconomic models.5 Second,
the instantaneous utility function implies that the shares of nominal consumption expenditure are constant. While the assumption may appear restrictive, it is supported strongly inour data (see Section 3.2).
The flow budget constraint at date t is given by
Pm,t Cm,t + Ps,t Cs,t + Bt = Wt Lt + Rt−1 Bt−1 ,(5)where Bt is the government bond, Rt is the nominal interest rate, and Wt is the wage rate.
Additionally, we assume that the representative consumer cannot short-sell the bond, Bt ≥ 0.
4

While relative prices are often used to estimate this type of directed technology progress in the literature(Greenwood et al. (1997)), this method may provide inaccurate estimates of technology progress. To assure
credibility, we provide various robustness exercises in Section 4.
5
In Section 5, we consider the cases in which the EIS parameter is not unity.

8

The representative consumer maximizes her utility U subject to the flow budget constraints
and the short-selling constraints.
Government. As shown in Section 3.2, the effective lower bound on the nominal interest
rate has been binding since the mid 1990s. In light of this observation, we simply assume thatthe nominal interest rate is pegged, Rt = R̄ ≥ 1. This assumption can be also interpreted
in the following manner: The government implements a Taylor rule with a large coefficienton the inflation rate. Then, as shown by Benhabib et al. (2001), there are two steady states:
target inflation equilibrium and deflationary equilibrium. Given this monetary policy rule, it
can be considered that the Japanese economy remains stuck at the deflationary equilibrium
and the nominal interest rate is at the effective lower bound. Since these two policies areobservationally equivalent, we adopt the former interpretation for simplicity. Moreover, as
in the standard New Keynesian model, the net bond supply is zero.
Market Clearing Conditions and Equilibrium. The market clearing conditions forgeneric output and consumption goods are
Mn,t + Mm,t = Yt ,Ci,t = Yi,t ,and the labor market clearing condition isZ
Lt =Lt (k) dk.

k∈[0,1]

We adopt the standard competitive equilibrium concept for our analysis. Moreover, because
technology processes (At , Am,t ) are non-stationary, our analysis focus on a BGP of the economy and the fluctuations around it. A BGP is a particular type of competitive equilibrium
in which all the endogenous variables grow at constant, but not necessarily the same, rates.
Let gX denote the growth rate of variable X along the BGP. By allowing a slight abuse ofnotation, let gXt denote the growth rate of variable X at date t.
Macroeconomic Variables. Because there are multiple goods in this economy, we mustspecify how they are aggregated to define inflation and consumption. We define these variables as mimicking the national accounts. The growth rate of aggregate consumption is
calculated as the weighted average of consumption growth rates, using the relevant nominal

9

consumption shares as done in the official national accounts:6
gCt ≡ γn gCn,t + γm gCm,t .
Lastly, we define the inflation rate as the weighted average of the individual inflation
rates using the same weights:
πt ≡ γn πn,t + γm πm,t ,(6)
where πi,t is the inflation rate of good i, πi,t ≡ ln Pi,t /Pi,−1 .

3Empirical Analysis

In this section, we analyze the uptick in inflation through the lens of the theoretical model
developed in Section 2. Our analysis begins with an overview of the data, followed by adetailed quantification. Finally, we conduct validation exercises to assess the robustness of
our model.

3.1

Data

We mainly rely on the National Accounts of Japan (JSNA) with the benchmark year of 2011,
which covers the period from 1994 to 2018.7 Throughout our paper, we use the JSNA priceindexes and real sequences. We categorize consumption expenditure into two groups: manufacturing and non-manufacturing. The former category includes expenditure on durables
produced by the manufacturing sector and the latter includes all other consumption expenditures.8 We choose this categorization based on the evidence presented in Figure 3. It
6

In this economy, aggregate consumption corresponds to real GDP, not Yt .
Those familiar with the Japanese economy may question the extent of the impact of the hike in value
added tax (VAT), which was implemented in April 2014. We eliminate the mechanical components of priceincreases due to the hike (see Appendix A.1.2 for the details), but cannot eliminate the impacts on prices
and quantities resulting from endogenous reactions by households. However, the impacts of the VAT hikes
on the annual growth rate of consumption are expected to be small. For example, Cashin and Unayama(2016) study the VAT hike in April 1997 and find that the consumption level of durables rose right before theimplementation of the VAT hike (March), but declined when the VAT hike was implemented (April). Thus,
if we take the annual average growth rate, the impact of the VAT hike on consumption growth is minute.
8
In this paper, we ignore the durability of the manufacturing good. This simplifying assumption isfrequently used in macroeconomic analysis (e.g., Nakamura and Steinsson (2010), Wolman (2011), andHerrendorf et al. (2021)). Moreover, if we incorporate the durability of the manufacturing good, as doneby Erceg and Levin (2006), our New Keynesian model has an unrealistic implication. Specifically, if thenominal interest rate is pegged, a persistent shock to the TFP growth rate has unrealistically huge effects on
the economy. A similar phenomenon occurs in the three-equation New Keynesian model. There are many
ways to fix this unrealistic implication of the model due to the durability of the manufacturing good. See
Section 3 of the Online Appendix, which explains this unrealistic implication and how to fix it by introducing
cognitive discounting (Gabaix (2020)). We could, in principle, combine these models and analyze permanent
7

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Figure 3: Inflation by Subcategory

illustrates that the average inflation levels for non-durable goods, semi-durable goods, andservices are approximately equal. This allows us to group them together as a composite
good, thereby simplifying our analysis.9 For the sake of brevity, we call the category nonmanufacturing “good” although it includes services and some of the manufacturing goods.10
Appendix A provides additional details regarding the the data construction.
A quick look at Japanese data yields three findings. First, the data substantiate the useof the Cobb-Douglass preference in our model. Although the price of the manufacturing gooddecreased by 64% from 1994 to 2011 compared to the price of the non-manufacturing good,the share of the manufacturing good has remained virtually unchanged during this period(see Figures 4a and 4b). This empirical pattern suggests that the elasticity of substitution
between the consumption goods is approximately one.11 We set γm to the average value ofthe share of the manufacturing good in total expenditure—γm = 10.1%.
Second, as mentioned in the introduction, the inflation rate of the manufacturing good
πm,t increased sharply compared to that of the non-manufacturing good πn,t since around2010. Equation (3) implies that this sharp rise in the relative price reflects the technology
stagnation of the manufacturing-good firm. To visualize the stagnation at a glance, we depict
the MST in Figure 4c. As evident from Figure 4c, the growth rate of Am,t declined permanently in the last decade. The growth rate from 2014 onward decreased by 5.9 percentage
points compared to that up until 2010. In the next subsection, we explore the implications
technology shocks, which requires a global, not local to a steady state, analysis. Such analysis is left for
future research.
9
The same analysis is undertaken without constructing this composite good. The quantitative results arelargely unchanged. To simplify the notation and our analysis, we group them together.
10
One may wonder whether calling the composite good as a non-manufacturing good is suitable. One justification is that its sizable component is food and services, which are often not considered to be manufacturing
goods. See, for example, Herrendorf et al. (2014).
11
The same observations hold true for the United States, which led Wolman (2011) to adopt the CobbDouglas preference.

11

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(c) Logarithm of MST

Figure 4: The Prices and the Share of the Consumption of the Manufacturing Goodof this dramatic and permanent change in MST.
The final observation is that Japanese consumers have faced nominal interest rates at theireffective lower bound. Figure 5a displays the policy interest rate, the 10-year government
bond interest rate, and the average deposit interest rate faced by Japanese households. In
the late 1990s, in response to the banking crisis, the BOJ drove its policy rate to near-zerorange and has been effectively trapped in the range.12 However, the zero interest rate alone
was not sufficient to revive the economy. To stimulate the economy, the BOJ has introduced
various unconventional monetary policies. In recent years, the BOJ has focused on measures
to lower longer-term interest rates to deal with the ongoing economic downturn and deflation.
While the 10-year government bond interest has been positive most of the time, thedeposit interest rate has hovered near-zero since the early 1990s. Thus, from the consumers’
viewpoint, the nominal interest rate has been at the effective lower bound. Furthermore,
there is another factor preventing the BOJ from changing its nominal interest rate. The Abeadministration pressured the BOJ to adopt an explicit 2% inflation targeting rule. As longas the aggregate inflation rate remains below the target level, the BOJ has been politicallyunable to raise nominal interest rates. These considerations support one of our modelingassumptions that the BOJ effectively pegs its nominal interest rate at the the lower bound.13
One might question whether the deposit interest rate accurately reflects the marginal
12

In 2006-2007, the BOJ attempted to move away from the near-zero policy rate that had been in place.
Unfortunately, the onset of the global financial crisis necessitated a halt in the attempt.
13
Since 2022, Japan’s inflation rate has exceeded the 2% target. However, as of August 28, 2023, the BOJ
has not raised the policy rate, while other central banks have significantly tightened monetary policies. On
August 2, 2023, Deputy Governor Uchida explained the BOJ’s policy, stating, “. . . sustainable and stableachievement of the price stability target of 2 percent has not yet come in sight.” This situation highlights
the difficulty the BOJ faces in raising the nominal interest rate. The transcript can be downloaded from this
URL.

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Figure 5: Monetary Policy and Asset Composition of Japanese Households
Notes. The deposit interest rate and the policy rate are downloaded from the website of the BOJ. The ID for the deposit interest
rates is IR02’DLDR120. The policy rate is taken from the official discount rate (ID: IR01’MADR1Z@D) until September 1995
and the call rate (uncollateralized overnight, ID: FM02’STRACLUCON and FM01’STRDCLUCON) since October 1995. Theinterest rate for the 10-year government bonds are downloaded from the website of the Ministry of Finance, Japan. The Annual
Report on National Accounts for 2018, Part of Stock II Accounts classified by Institutional Sectors in JSNA, provides the data
for Figure 5b.

interest rate that Japanese households face. Figure 5b displays the asset composition ofJapanese households, revealing that their assets primarily comprise deposits and cash, followed by illiquid claims of insurance and pension contracts. Deposits and cash account for
approximately 50% of the total financial assets of Japanese households and claims of insurance and pension constitute roughly 30%. This portfolio pattern is in stark contrast to thatof the United States where deposits and cash accounts for merely around 10% and claims of
insurance and pension constitute a similar share of nearly 35%.14 Furthermore, data froma survey conducted by the Japan Securities Dealers Association indicates that over 70% ofhouseholds did not possess any equity during this sample period.15 These facts suggest thatthe marginal interest rate most relevant to households is likely the deposit interest rate,
which has been at its effective lower bound: ln Rt = r̄.16
14This claim is based on Table B.101.h of Financial Accounts of the United States from the webpage of
the Board of Governors of the Federal Reserve System.
15
The survey data can be retrieved from Figure 6 (page 149) in the PDF file, https://www.jsda.or.jp/
shiryoshitsu/toukei/2021jikeiretuhyou.pdf.
16
In our analysis, the term "consumption" does not include rent. However, it is important to note that thesefactors might indirectly influence overall consumption patterns. Specifically, a decrease in the interest rates
on long-term government bonds could potentially lead to reduced mortgage rates for existing homeowners,
generating income effects and thereby leading higher consumption. However, according to the findings ofHausman et al. (2019), such transmission to mortgage rates for existing homeowners has been rather limited.
Consequently, although this transmission channel is theoretically plausible, its quantitative impact in thecontext of Japan appears to be limited.

13

3.2

Quantification

Building upon our model, we are now ready to derive the theoretical implications of apermanent decline in the growth rate of Am,t (the MST shock for short) for aggregate inflationand consumption. Our analysis hinges on the following insight: when an MST shock occurs,
it impacts the efficiency of the manufacturing-good firm, which is evident from the change in
its relative price. Since the manufacturing-good firm is not subject to any pricing frictions,this movement of the relative price is, in fact, efficient. Moreover, the unit elasticity of
substitution between goods and the pegged interest rate implies that income effects on labor
supply, savings, and consumption of the non-manufacturing good offset the corresponding
substitution effects. Thus, only consumption and the price of the manufacturing good are
influenced by the MST shock. Consequently, this relative price change directly influences
aggregate inflation and consumption. Below, we formalize this insight.
Recall the optimality conditions for the representative consumer are
Pn,t Cn,tCn,twt
Pm,t Cm,t=, v ′ (Lt )
=
γm
γn
γn
Pn,t
Bt
Cn,t+1 R̄Pn,t= 1, lim E0 β t
= 0,
Et
t→∞
Cn,t Pn,t+1
Pn,t Cn,t(7)(8)

and the flow budget constraints (5). Let (Cn,t , Cm,t , Lt , Bt ) denote an optimal (state-contingent)
allocation given some equilibrium price system, Pn,t , Pm,t , wt , R̄ . Suppose that the price of′due to the decline in Am,t . Then, an allocathe manufacturing good Pm,t increases to Pm,t′′′tion Cn,t , Cm,t , Lt , where Cm,t = Pm,t /Pm,t Cm,t , satisfies all the above conditions and the′, wt , , R̄ . Thus, labor supply, saving, and consumption ofbudget constraints given Pn,t , Pm,t
non-manufacturing goods do not react to a shock on Pm,t . Moreover, the demand for genericoutput remains unaffected:
Mt =

′
′
Pm,t
Cm,t
Pm,t C m,t
1
′
C
=
=
.
m,t
′
Am,t
Pn,t
Pn,t

We take advantage of this property to fully characterize the dynamic responses of theminimum-state-variable solution to the MST shock.17 Suppose that an unexpected shock
occurs at date t0 and the growth rate of Am,t shifts from gAm,t to gAm,t + ĝAm,t , whereĝAm,t = 1 − ρt−t0 +1 ĝAm .
17(9)Here, we focus our analysis on minimum-state-variable (MSV) solutions since we are primarily interested
in the permanent change in aggregate inflation. Although accommodating sunspot shocks could potentiallycause fluctuations in the inflation rate of the non-manufacturing good, the long-run implications remain
consistent. Additionally, Angeletos and Lian (2023) reveal a certain fragility of non-MSV solutions thatprovides a justification for focusing on the MSV solutions.

14

Parameter ρ ∈ (0, 1) governs how quickly ĝAm,t converges to ĝAm . Since only consumption
and inflation of the manufacturing good are affected by the changes in Am,t , equilibrium
consumption and inflation under the MST shock are simply given byĝCm,t = ĝAm,t∗π̂m,t= −ĝAm,t∗ĝCn,t
=0

∗
π̂n,t
= 0,

(10)
(11)

where ĝCm,t represents the impulse response of consumption growth of the manufacturing
good to the MST shock relative to the initial equilibrium consumption growth. Similarly,
the other variables with the “hat” notation (ˆ) stand for the corresponding impulse responses.
Using equations (10) and (11), we can obtain the impulse responses to aggregate inflationand consumption growth:
Proposition 1. Consider MST shock (9). Then, the impulse responses of aggregate inflationand consumption growth to the MST shock are given byπ̂t = −γm ĝAm,t(12)

ĝCt = γm ĝAm,t .

(13)

Figure (6) illustrates the MST shock (9) and the impulse response of aggregate inflation(12). Aggregate inflation depends solely on the MST shock and gradually converges to a
new steady-state level. As indicated by equation (13), the impulse response of aggregate
consumption mirrors that of the inflation rate. 18
Having established the theoretical implications, we quantify the impact of the MST shockusing Proposition 1. We assume that the MST shock occurs in year 2011 (t0 = 2011) andalmost converges to its steady-state value, ĝAm , by the year 2014, as suggested by Figure 3.
Let ĝC∞ and π̂∞ denote the associated new steady-state values:ĝC∞ = γm ĝAm

(14)π̂∞ = −γm ĝAm .

(15)

We measure the size of the MST shock, ĝAm , as the difference in average growth rate of the
MST until 2010 and since 2014: ĝAm = −5.9%.
Table 1 encapsulates the findings of our steady-state analysis. According to the data,18

One might be wondering how this paper is related to the Neo-Fisherian debate (Uribe (2022)). The
debate is regarding how the permanent changes in policy nominal rates affect other interest rates andinflation in the short run. In our context, the nominal interest rate is pegged so that our paper is notdirectly related to the debate. In terms of the dynamics, our model implies that the permanent shock on
the growth rate of MST increases the inflation in both the short and long run, which is largely consistent
with the data.

15

7
0.6
6
0.5
5
0.4
4

0.3

3

0.2

2

0.1

1

0

0

-0.1
2006

2008

2010

2012

2014

2016

2018

2006

2008

2010

2012

2014

2016

2018

(b) Aggregate Inflation Rate, π̂t(a) ShockFigure 6: Impulse Responses
Notes: we set ρ to 0.5.

there was a rise in the aggregate inflation rate by 1.24 percentage points. Notably, roughly
half of this increase can be attributed to the MST shock alone. To delve deeper into this
impact, we explore a counterfactual scenario in which the MST did not experience stagnation
since 2011. Our analysis suggests that in such a scenario, the aggregate inflation rate would
have lingered around 0.4%, a rate considerably closer to zero than the actual, although still
positive. Therefore, we conclude that the MST shock has been a pivotal factor in driving
the inflation observed in Japan since 2014.19
However, the rise in inflation caused by the MST shock is by no means a signal thatthe economy is performing well. In fact, according to our model, the MST shock reduces
aggregate consumption growth by −0.59 percentage points. It might be tempting to compare this number with the change in the growth rate of aggregate consumption per capita.
However, such a comparison could lead to an overestimation, since during the Abenomics
period, labor market participation for older people and women increased more rapidly thanearlier. The observed increase might partially be a result of the government effectively increasing the retirement age to 65 years from April 2013 onward, a factor that our current
model does not account for. 20 Therefore, it would be prudent to compare ĝC∞ /L∞ with its
data counterpart, which more accurately captures the effect of the MST shock.21 According
to our analysis, 40% of the observed decline in consumption growth is explained by the MST
19

While we assume that the manufacturing good is perishable, durability of the manufacturing good does
not affect our steady-state analysis. This is because along the BGP, the growth rates of purchase of durable
good and its stock are equal.
20
There seem to be other factors such as delayed exit from labor market of Japanese baby boomers who
are rather concentrated cohort born in 1947-49. This baby boomer generation has remained in the labormarket well beyond the retirement age.
21
When we conduct validation exercises in the next subsection, we examine the change in the growth rateof manufacturing consumption per capita. This is the correct counter-part because we use the Euler equationof the representative consumer.

16

MST-Induced Change in Model

Data Counterpartπ̂∞

0.59% pt

1.24% ptĝC∞

−0.59% pt−0.59% ptĝC∞ /L∞−0.59% pt−1.41% pt

0% pt−0.17% pt

π̂∞ + ĝC∞ /L∞

Table 1: Steady-State Result for Macro Variables
Notes. The data-counterpart of π̂∞ is the difference between the average inflation before 2011 and since 2014.
The data counterparts of the other variables are similarly computed.

shock. Thus, the model can simultaneously account for the rise in inflation and the weak realconsumption, thereby providing a resolution to the puzzle. The puzzling weak consumption
accompanied with the rising inflation can be interpreted as a manifestation of stagflationthat results from the MST shock.
Discussions There are five aspects worth mentioning with regard to Proposition 1 andour baseline results. First, within our framework, the impulse responses are not sensitively
affected by the representative consumer’s expectations of the evolution of the MST shock.
To help understand this aspect, consider the canonical three-equation New Keynesian model
under a Taylor rule that satisfies the Taylor principle. Imagine the following two cases: TFP
temporarily rises only today, or TFP has permanently risen from today onward. The inflation
rate declines today in the first case, whereas it rises in the second case. Note that in bothcases, the TFP level increases today. The response of inflation depends delicately on whether
the representative consumer perceives that the TFP shock is temporary or permanent.22 In
contrast, our model does not have this sensitivity issue. A negative MST shock increases
the relative price of the manufactured good.Consequently the inflation rate today always
increases, irrespective of whether the MST shock is perceived as a temporary or permanent
shock. In this dimension, our impulse response analysis is robust.
Second, our analysis does not eliminate the possibility that the Japanese economy is ina liquidity trap with a permanently negative output gap. To elaborate on this aspect, notethat along the BGP, Yt is expressed in the following manner: Yt = Γ × At × L∗ , where L∗ isthe efficient level of employment along the BGP and Γ represents the distortion stemming
22

These results are well-known in the literature, but for completeness, we derive them in Section 3.1 of
the Online Appendix.

17

from the nominal pricing friction.23 If Γ is less than one, the real GDP is lower than theefficient level. In other words, the economy has a permanently negative output gap. Because
our argument holds for any level of Γ, our quantification results remain valid even if theeconomy is in a liquidity trap with a permanently negative output gap.
Third, Proposition 1 holds even if the saving function of the representative consumer
is not horizontal. The key property underpinning Proposition 1 is that the MST shock
affects only the consumption of the manufacturing good, not saving, labor supply, or the
consumption of the non-manufacturing good. In Appendix B, we introduce an overlapping
generations model in which the asset supply curve is upward-sloping and demonstrate that
Proposition 1 still holds.
Fourth, our argument relies on the premise that the BOJ is constrained at its effective
lower bound, Rt = R̄. Interestingly, even if the BOJ is not constrained and is free to choose
any interest rate rule, it is optimal for the BOJ not to respond to the MST shock. This isbecause the MST shock impacts efficiency without causing any distortions. Consequently,
the BOJ should disregard the relative price movements triggered by the MST shock. This
result follows from Aoki (2001). Furthermore, Wolman (2011) shows that in our context,
the optimal trend inflation rate is negative as long as there is the MST progress. Conversely,
when the MST slows down, the optimal trend inflation rate rises. Both studies indicate thatthe BOJ should aim to minimize efficiency losses due to price distortions and ignore efficient
price fluctuations.
Finally, our baseline results have policy implications for Japan. A conventional interpretation of the recent increase in inflation attributes this increase to the unconventionalmonetary policies by Governor Kuroda. However, our baseline results suggest an alternative
explanation: the BOJ’s monetary policy is effectively constrained, thereby leading Japan toexperience a rise in inflation driven by the MST shock. Consequently, Japan has concurrently faced an inflation and a stagnation in real consumption. As such, Governor Kuroda’s
triumphant declaration that “Japan’s economy is finally no longer in deflation” appears premature and potentially misleading. Our findings serve as a cautionary note against drawing
simplistic conclusions regarding the Japanese economy based solely on the analysis of theheadline aggregate inflation rate.24
23

When Am,t = 1, then Γ corresponds to the GDP gap.
This quote is from Governor Kuroda’s speech at the 2019 Michel Camdessus Central Banking Lecture,
International Monetary Fund. The transcript can be downloaded from https://www.boj.or.jp/en/about/press/koen_2019/data/ko190723a1.pdf.
24

18

3.3

Validation of the Key Mechanism

Thus far, we have used our model to explore the implications of the MST stagnation when
the interest rate is effectively pegged. To derive Proposition 1, we rely heavily on the
Euler equations of the representative consumer. Unfortunately, the Euler equations have
sharp implications for the change in inflation and consumption growth rate. Since these
implications have not yet been empirically established in the existing literature, readers mayquestion the reliability of our findings. To ensure our study’s credibility, we conduct two
validation exercises in this subsection. In the first exercise, we examine the model’s timeseries implications. In the second exercise, we study the cross-sectional implications of themodel.
We begin by deriving the implications for the steady-state changes. The steady-stateversion of the intertemporal Euler equation isgCi = ln β + r − πi .

(16)

Let operator d stand for the change from an initial steady-state value to a final steady-statevalue. It should be noted that this d operator conceptually differs from the “ ˆ ” operator,
which extracts steady-state changes solely induced by the MST shock. Applying the doperator to equation (16), we obtain
dgCi = d ln β − dπi .

(17)Here, we assume that the nominal interest rate is pegged, dr = 0, and allow the possibility
that the discount factor β changes.25 According to equation (17), an increase in the long-run
inflation by one percentage point leads to a corresponding decline in consumption growth by
one percentage point. This sharp theoretical prediction closely resembles the classic Fisher
effect, where nominal interest rates and inflation move together in the long run.26 In ourmodel, when the nominal interest rate is instead pegged, inflation and consumption growth
move exactly in opposite directions in the long run, a prediction we refer to as the Fisher-like
effect.
The presence of dβ prevents us from directly applying equation (17) to the data. We
eliminate this unobserved term by using equation (17). Equation (17) holds for i = n, m, so
that
dgCm − dgCn = − (dπm − dπn ) .
(18)
25

For example, Braun and Nakajima (2012) and Werning (2015) propose heterogeneous-agent models inwhich the discount factor of “the representative agent” in their models is endogenously determined.
26
See Uribe (2022) for empirical evidence supporting this classic Fisher effect.

19πm − πngCm − gCn

Until 2010

Since 2014

Change

−6.3%
6.6%

−0.7%
0.6%

5.6% pts−6.0% pts

Table 2: Time-Series Evidence

We examine whether this modified version of the Fisher-like effect is supported by our data.
Table 2 presents the data counterpart of dπm − dπn and dgCm − dgCn . As evident from Table
2, equation (18) holds true: the relative inflation rate increases by 6.2 percentage points, andthis relative increase is accompanied by an almost equal decline in the associated relative
consumption growth by 6.0 percentage points. In the long run, the relative consumption
growth rate and the relative inflation rate move precisely in opposite directions, thereby
confirming the Fisher-like effect in our time-series data.27
While the time-series evidence is clear at first glance, it essentially provides us witha single data point. Therefore its reliability must be carefully scrutinized. To gain morecredibility, we present additional cross-sectional evidence. We begin by extending the model
geographically, assuming that there is a representative consumer for each city indexed by a.
Then, the Euler equation (16) holds for all city a:agCma = ln β + r − πm
,

(19)

a
is the corwhere gCma is the growth rate of manufacturing consumption in city a and πm
responding inflation rate. Note that the nominal interest rate is common across cities.28
Again, applying the d operator to equation (19), we obtain the following equation:adgCma = d ln β − dπm.

(20)

If city a experiences inflation that is higher by one percentage point than that in the other
cities, its corresponding consumption growth rate will be lower by one percentage point thanthat of the the others. Consequently, our model also has a sharp prediction for cross-sectional
patterns of inflation and consumption growth. Assuming that the changes in the discountfactor are common across a, we examine whether equation (20) is supported by the data.
The exact same inflation measure of the manufacturing good by each city, as the nationalcounterpart, is unfortunately unavailable. Thus, we aggregate the city-level inflation rates of27

When the discount factor is truly exogenous, we can directly take equation (17) to the data. The inflation
rate of the manufacturing good increased by 6.2 percentage points and the corresponding consumption growthrate declined by 5.9 percentage points. Thus, we confirm the Fisher-like effect for the case in which β isexogenous as well.
28
Indeed, deposit interest rates differ only slightly among cities in Japan.

20

-5

-10

-15

-20

-25
5

10

15

20

25

Figure 7: Cross-Sectional Fisher-Like Effecthome appliances and furniture, computer hardware, and audio-visual equipment to constructa. Similarly, we apply the same aggregation method tothe empirical counterpart of dπmconstruct the empirical counterpart of dgCma . See Appendix A.4 for a detailed explanationof our construction of these variables.
a
In Figure 20, we plot the change in inflation, dπm, on the horizontal axis, and thecorresponding change in real consumption, dgCma , on the vertical axis for each major city a.
Most observations lie on the −45 degree line. Indeed, the naive regression indicates that theslope is approximately −1, as predicted by the cross-sectional version of Fisher-like effect,(20). While the confidence interval of the coefficient of the naive regression is not tight,[−1.6, −0.6] , we find evidence that the implication of the cross-sectional Fisher-like effect(20) is at least consistent with our data.

4

Robustness of the MST Stagnation

In line with previous literature, we assume that the relative output price of the manufacturing good reflects the MST, Am,t . However, there are several factors that could lead toinaccuracies in this method of recovering the MST. For example, trade and market power
have a direct impact on output prices. The observed increase in the relative price of the
manufacturing good may result from factors unrelated to technology. This raises legitimate
concerns regarding our finding that the MST has stagnated. To ensure the credibility of ourfindings, we conduct four robustness exercises in this section.
First, we compare the MST obtained through our method with the TFP of manufacturingsectors published by the Japan Industrial Productivity Database 2021, which is a KLEMStype data. We refer to the database simply as KLEMS. Second, we scrutinize the impact
21

of both international and domestic sectoral trade on relative prices, utilizing data from theWorld Input Output Database (WIOD) and Japan’s import price index.29 Third, we explore
the effect of markups on relative prices, motivated by the recent research (Loecker andEeckhout (2021); Loecker et al. (2020)) that reveals that markups in the U.S. have increased
significantly. It is natural to imagine that a similar phenomenon may have occurred in Japan.
If this is the case, our relative price would reflect relative market power, not technology. We
examine whether it is a legitimate concern. Finally, we demonstrate that the MST stagnation
is a common phenomenon observed across developed countries. Based on these additional
analyses, we affirm that our finding of the MST stagnation is indeed robust.

4.1

TFP Estimate by KLEMSKLEMS directly measures sectoral output and various inputs, and subsequently deduces sectoral TFP in domestic production through growth accounting decomposition. This approachis advantageous as it is less susceptible to issues arising from the use of relative prices offinal goods. For example, if the relative price of the manufacturing good decreases due to a
decline in the prices of imported final goods, this movement is not considered a technologicalimprovement in the sectoral TFP by KLEMS.30 Furthermore, this approach only requiresthat sectoral production functions exhibit constant-returns-to-scale. Because of these favorable properties, TFP sequences by KLEMS-type data are frequently used in the literature(e.g., Carvalho and Gabaix (2013).)
Figure 8 displays our estimated MST and the manufacturing TFP obtained from KLEMS.31
Until 2010, both increased steadily and significantly, even though their average growth rates
differed. However, since around 2011, they began stagnating, and since 2014, they havealmost stopped improving. Thus, we confirm that the TFP by KLEMS has also stagnatedas our estimated MST. In fact, this finding is consistent with the previous studies by Basu etal. (2013) and Fernald (2015) who argue that the low-frequency movement of relative prices
reflect technological progress.
29

See Timmer et al. (2015) for a detailed description of the dataset.
Sectoral linkage might affect both the relative prices and sectoral TFP. This issue is scrutinized in thenext subsection.
31
We calculate the KLEMS counterpart of the productivity of manufacturing good by taking a weighted
average of the sectoral TFP from KLEMS, which aligns with our definition of the manufacturing good. We
use weights that are proportional to consumer purchases from the manufacturing sectors. See Appendix A.3
for a more detailed explanation.
30

22

0
-0.2
-0.4
-0.6
-0.8
-1
-1.2
1995

2000

2005

2010

2015

Figure 8: Comparison of the Estimates of Technology

4.2

Evidence from WIOD and Import PriceIn the first exercise above, we do not directly account for the effects of international anddomestic sectoral trade and/or exchange rates. In this subsection, we aim to do so by
employing the methodology developed by Auer et al. (2019).32
Auer et al. (2019) delineate a model that explicitly captures international and domestic
sectoral linkages of production networks. In their model, the unit nominal cost function
for a given sector s in country i is given by Wi,s,t = Fi,s (χi,s,t , Pi,s,t ) , where χi,s,t denotes
the effective cost of non-material inputs (e.g., labor, capital, and technology) and Pi,s,t is avector of intermediate input prices, Pi,s,t = (Pji,ks,t )j,k . This price vector encapsulates theglobal input-output linkages. Under certain conditions, they show that the inflation of sector
s in country i can be decomposed as a weighted average of the growth rate of χi,s,t and theinflation rates:XCγji,ks,t−1 πj,k,t
πi,s,t = γi,s,t−1∆ ln χi,s,t +
{z
} j,k
|
Own Contribution
|
{z
}

C
with γi,s,t−1+X

γji,ks,t−1 = 1,

(21)

j,k

Linkage Contributions

C
where γi,s,t−1
is the share of the non-material inputs in the gross output, and γji,ks,t−1 isthe share of the material input from sector k in country j in the gross output. Notably,
all the variables, except ∆ ln χi,s,t in equation (21) are observable in the WIOD. Therefore,
we are able to infer ∆ ln χi,s,t by solving equation (21). Equation (21) enables us to determine whether inflation in a sector is driven by the cost of its own non-material inputs,C
γi,s,t−1∆ ln χi,s,t , or by the factors originating from international and domestic sectoral tradePlinkages, j,k γji,ks,t−1 πj,k,t .
Our analysis focuses on the decomposition of the inflation rate of the sector in the WIOD
industry classification that most closely aligns with our narrow definition of the manufac32

For the sake of completeness, we provide a detailed explanation in Section 1 of the Online Appendix.

23

turing sector (i.e., durable goods sector). Specifically, we examine sector C26, “Manufactureof computer, electronic, and optical products” in Japan. Additionally, to facilitate easiercomparison, we subtract the inflation rate of the non-manufacturing good πn,t from bothsides of equation (21).
In Figure 9a, the relative price, the level of the own contribution, and the level of thelinkage contributions are depicted. Due to the coverage of the latest edition of the WIOD,
we can only plot them from the year 2000 until the year 2014. Nevertheless, Figure 9a
provides useful information. First, the relative price of sector C26 exhibits a similar pattern
to the relative price of the manufacturing good: it declined consistently until around 2011,
and then ceased to do so. According to decomposition (21), own contribution has increased
sharply since 2012, thereby causing the relative price to stop declining.
Unfortunately, current data limitations prevent us from ascertaining whether the observed trends have persisted after 2014. In an effort to supplement our analysis from adifferent perspective, we turn our attention to the import price index. In Figure 9b, we depict the import price of “Computers and Peripheral Equipment” relative to the import priceof “Electric and Electronic Equipment,” excluding “Computers and Peripheral Equipment.”
It is important to note that this relative price tends to be less influenced by international anddomestic sectoral linkages, given that both categories of goods are imported and produced
similarly. Intriguingly, Figure 9b echoes the same empirical pattern as that highlighted in
Figure 2a. The relative import price declined substantially until around 2014, but remained
stable thereafter. Note that the price of imported computers had declined sharply relative toother electric and electronic equipment. Thus, Figure 9b implies that computer-specific technological progress had been fast but began stagnating, which confirms the MST stagnation.
Moreover, the same empirical pattern is observed even if the relative price is constructedbased on the contract currency. We conclude that the MST stagnation is not entirely driven
by international and domestic sectoral linkages and currency depreciation.

4.3

MarkupNow we turn to focus on the concern regarding market power in domestic markets. We adapt
our model by incorporating the exogenous markup µi,t of good i. Consequently, the relative
inflation rate of the manufacturing good becomes
πm,t − πn,t = gµm,t − gµn,t − gAm,t .

(22)

The relative price increases due to either the relative increase of the markup of the manufacturing good producer, gµm,t − gµn,t , or the relative technology stagnation, gAm,t . As such, our
24

1.2

0

1
-0.2
0.8
-0.4
0.6
-0.6

0.4

-0.8

0.2

-1

0

2000

2005

2010

2015

1995

(a) Decomposition Exercise

2000

2005

2010

2015

(b) The Relative Import Prices

Figure 9: Effects from Trade
Notes. To draw the level ofP
the relative price, the own contribution
and the linkage contributions, we first compute πi,t − πn,t ,C
γi,s,t−1(χ̂i,s,t − πn,t ) andj,k γji,ks,t−1 πj,k,t − πn,t , where πn,t is the manufacturing inflation rate in Japan, i is Japan,
and s corresponds to sector C26. Then, we compute the cumulative sums of the relative inflation rate and these contributions
to recover the levels. The import price index is available from the website of the BOJ.

measure of MST might be distorted due to the presence of the relative change in markup.
To examine this potential bias, we use the sectoral markups µn,t estimated by KLEMS.
KLEMS measures the sectoral markup i as
µi,t =

Gross Operating Surplusi,t + Labor Costi,t +Intermediate Input Costi,t.
Capital Costi,t +Labor Costi,t +Intermediate Input Costi,tWe aggregate these sectoral markups as we did in Section 4.1 to construct the markup
for both the manufacturing and the non-manufacturing goods. We plot the time-series of
the relative markup and the relative price of the manufacturing good in Figures 10a and10b. The growth rate of the relative markup of the manufacturing sector, gµm,t − gµn,t ,has remained essentially constant, contrasting with the noticeable movement in the relative
price.
Our finding aligns with the results presented in Nakamura and Ohashi (2019), which
estimate the firm-level markups of Japanese companies, adopting the approach by Loecker
and Warzynski (2012) and Loecker et al. (2020). They find that there has been no significant
increase in various types of aggregate markups, including the overall manufacturing markup
and the aggregate markup among the top 10% of firms, over the specified period in Japan.
When these findings are considered collectively, it supports our conclusion that markups
have had a minimal influence on the observed stagnation in the MST.

25

1.2

1.2

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

0
1995

2000

2005

2010

2015

1995

(a) Relative Markup of Manufacturing Good

2000

2005

2010

2015

(b) Relative Price of Manufacturing Good

6
5
4
3
2
1
0
0

1

2

3

4

5

6

Figure 10: Cross-Country Evidence

4.4

Cross-Country Evidence

Finally, we present cross-country evidence to support our argument. If technological progresshas stagnated in Japan, a similar trend should be observed in other developed countries. Thisis because they are likely to share the same level of technology on the frontier. We find that
this is indeed the case.33
Figure 10 illustrates the growth rates of the MST for numerous developed countries.
The vertical axis represents the average growth rates of the MST up until 2005, while thehorizontal axis displays those since 2014. As evident from Figure 10, although the extent of
MST stagnation varies among countries, most developed countries have experienced MST
stagnation.
Considering the evidence provided in this section, we argue that our observation of MST
33

In Takahashi and Takayama (2023), we examine the implications of the technology stagnation of the
durable consumption good and the ICT investment good on the slowdown of growth across developed
countries.

26

stagnation in Japan is a robust finding.

5

Extension

In the baseline model in Section 2, we abstract from capital accumulation and assume that
the EIS is one. In this section, we relax these to see if the results from the baseline model
survive under more general settings. These extensions are significant because (1) technological progress specific to ICT equipment has also stagnated, potentially causing additional
inflationary pressure, and (2) numerous studies have found the EIS to be estimated at lessthan one.34
To maintain tractability in our analysis, we impose the following restrictions. The genericoutput producer is assumed to have a Cobb-Douglas production function that combines capital and labor inputs. Moreover, we only conduct the steady-state analysis on the impact of
the MST shock and additional technology stagnation specific to ICT equipment on aggregate
inflation and consumption. We demonstrate that these extensions either strengthen or do
not substantially alter our baseline results.

5.1

Introduction of the Extended ModelIn this economy, multiple investment goods exist, such as ICT equipment, transportationequipment, research and development (R&D) , and more. Let I denote the set of theseinvestment goods. The representative producer of the generic output combines these capitalstocks and labor. The technology is given by
Yt = A tYαθ,Kj,t j L1−α
t

with

X

θj = 1,

(23)

j∈I

j∈I

where Kj,t is capital stock j ∈ I installed at date t. The consumption-goods producers havethe same linear technology functions as in the baseline model. Similarly, the representative investment-good firms utilize linear technology functions to convert generic output toinvestment goods with Ij,t = Aj,t Mj,t . Thus, the relative price of investment good j is
pj,t ≡

Pj,t
= A−1
j,t ,
Pt

where Pj,t is the price of investment good j at year t. The technology progress Aj,t is referred
to as j-investment-good specific technology progress, orj-IST for short.
34

See Havranek (2015) for a meta-analysis.

27Extending the results by Greenwood et al. (1997), we obtain the formula for the impact
of the technology shocks, ĝA , ĝAj j∈I , on the growth rate of the output, ĝY :35
ĝY =

X αθj
1
ĝA +
ĝA .
1−α
1−α j
j∈I

(24)

The term αθj represents the output elasticity of capital stock j, and the term, 1/ (1 − α)corresponds to the capital deepening effect. Since there are multiple sources of technology
progress, output growth is a linear combination of these technology progress.
The instantaneous utility function of the representative consumer is generalized in thefollowing manner:
 γn γm 1−σ (Cn,t Cm,t ) h (1 − N )σ ̸= 1t
1−σ,(25)u (Cn,t , Cm,t ) =(γ ln C + γ ln C ) h (1 − N )
σ=1
n

n,t

m

m,t

t

where h (·) represents the utility from leisure and Nt is the number of hours worked. This
class of the utility functions still guarantee the existence of BGP. Given this instantaneous
utility function, the Euler equation becomesr − πi = ln β −1 + gCi + (σ − 1) (γn gCn + γm gCm ) .

(26)

Note that when the EIS is one, equation (26) boils down to the Euler equation of the baselinemodel in Section 3.
Equation (26) sheds light on the new effects resulting from the two extensions. To focus
on the implications of having multiple investment goods, we momentarily assume that the
EIS is one. Recall that investment goods affect the production of all consumption goods,(24). Put differently, the ISTs affect consumption growth through the capital accumulation
channel. Hence, if j-IST stagnates, consumption growth has to slow down through thischannel in the equilibrium. To deliver the slowdown in the equilibrium, an equilibrium force
lowers the real interest rate to encourage lower consumption growth (see equation (26) withσ = 1). When the nominal interest rate is pegged, this lower real interest rate is only
obtained by higher inflation. Note that this effect resembles the classic Fisher effect: thenominal interest rate and inflation co-move in the long-run. Because of the similarity, we
refer to this effect as the Fisher-like effect. The strength of the Fisher-like effect depends onthe extent to which j-IST depresses consumption, which depends on the output elasticity ofcapital stock j, αθj .
35

Gourio and Rognlie (2020) uses this formula to re-examine the impact of capital-embodied technology
progress on growth.

28

Next, let us consider the case in which the EIS is not unitary, σ ̸= 1. The change inmarginal utility with respect to Ci includes two additional terms. These terms correspondto the last term in equation (26), which is omitted in the above discussion. When the
EIS is less than one (i.e., σ > 1), the representative consumer prefers more consumption
smoothing. Consequently, the real interest rate must adjust more significantly to incentivize
the consumer to save more. Conversely, if the EIS is greater than one, the representative
consumer prefers less consumption smoothing, and a smaller change in the real interest rate
can substantially alter the consumer’s intertemporal consumption decision.
To quantify the impacts of these new effects on aggregate inflation and consumption, we
take the total derivative of equation (26) with respect to the MST shock ĝAm and j-ICT
shock ĝAj . The following equations are the generalization of Proposition 1:




αθICT
αθj
−ĝAj + (σ − 1)−ĝAj + γm (−ĝAm ) .
(27)
π̂∞ = γm (−ĝAm ) +| {z } 1 − α
1−α
|
{z
}
|
{z
}
(A)
(B)

(C)

αθj
ĝC∞ /L∞ = γm ĝAm +ĝ .
| {z } 1 − α Aj
| {z }
(D)

(28)

(E)

These two formulas delineate the influence of the extensions on aggregate inflation andconsumption. The first term (A) on the RHS of equations (27) and (28) represents thebaseline effect, operating through the relative price. The other terms (B) and (C) in equation(27) represent the new effects described above. The real consumption growth decreases dueto the direct effect of the MST shock (D) and through the capital deepening effect via the
j-investment good (E).

5.2

Quantification under the Extended ModelIn this subsection, we first demonstrate that technology progress specific to ICT equipment
has slowed down, while other ISTs have not (in Section 5.2.1). Subsequently, we quantify
the impacts of these two shocks on the manufacturing good and ICT equipment on inflationand consumption (in Section 5.2.2).
5.2.1

Technology Stagnation of ICT Equipment

Figure 11a displays the various ISTs measured by the inverse of their relative prices. It isevident from Figure 11a that ICT-specific technology had advanced significantly comparedto the other ISTs. Notably, ICT-specific technology progress stagnated since around 2010,
as the MST stagnated.
29

0

0

-0.5

-0.5

-1

-1

-1.5

-1.5

1995

2000

2005

2010

2015

1995

(a) Various IST, Aj,t = Pn,t /Pj,t

2000

2005

2010

2015

(b) Comparison of ICT-Specific Technology

Figure 11: ICT-Specific Technology Stagnations
Notes: To make Figure 11a easier to see, we do not depict IST of investment goods j for which the shareof investment in total investment is less than 2%. These investment goods are defense equipment; cultivated biological resources; and mineral exploration and evaluation. To construct the TFP estimate for the
ICT equipment from the sectoral TFP estimates by KLEMS, we aggregate the sectoral TFP by using anappropriate weight. See Appendix A.3 for a detailed explanation.

The stagnation of ICT technology can be confirmed in the data by KLEMS. In Figure
11b, we present our estimate of ICT-specific technology progress alongside the estimate of
KLEMS. Both measures indicate that the technology progress of the ICT investment-good
sector has significantly stalled. Based on these findings and the robustness exercises in
Section 4, we conclude that ICT-specific technology has stagnated, just like the MST. We
measure the size of the ICT-ST by the difference in the growth rate of MST until 2010 andsince 2014, with ĝAICT = −7.2%. 36
5.2.2

Quantification

We now quantify the impacts of ĝAm and ĝAICT using equations (27) and (28). To apply
these formulas, we need to specify the labor share parameter α and the rental cost share of
ICT, θICT . We set α to be the average labor share from KLEMS, and estimate θICT using
the methodology developed in Gourio and Rognlie (2020).
Our findings are summarized in Table 3. As mentioned earlier, the aggregate inflation
rate in our data increased by 1.20 percentage points since 2014. When σ = 1, the additional
Fisher-like effect (represented as the term (B) in equation (27)) induced by the ICT-ISTshock increases the inflation rate by 0.26 percentage points. Thus, the two shocks are
36

Moreover, we can show that the sectoral markup of the ICT investment good sector estimated by KLEMS
has been marginally declining since 1994. This fact is not surprising given the findings by Nakamura andOhashi (2019). For the sake of completeness, we draw the sectoral markup for the ICT good sector in Section
2 of the Online Appendix.

30

π̂∞

σ=1

σ=2

σ = 2/3ĝC∞ /L∞(A)

0.57% pts

0.57% pts

0.57% pts

(D)

−0.57% pts(A) + (B)

0.83% pts

0.83% pts

0.83% pts(D) + (E)

−0.83% pts(A) + (B) + (C)

0.83% pts

1.67% pts

0.56% pts

Table 3: Quantification of Technology Stagnation
Notes: See equation (27) for what (A), (B), and (C) in the first column represent, and equation (28) for
what (D) and (E) in the fourth column represent.

capable of accounting for a significant proportion of the inflation uptick in Japan. Whenσ = 2 (the consumer prefers more consumption smoothing), the term (C) provides anadditional inflationary pressure, and the model predicts that the shocks increase inflation
by 1.67 percentage points. These figures should not be taken at face value because these
additional Fisher-like effects in our extended model have not been empirically establishedyet. Therefore, we take the qualitative features of the extended model more seriously andtreat the quantitative features with caution.
When σ < 1, the additional Fisher-like effects are considerably mitigated. Nevertheless,even if we set σ to a conventional value used in the literature, say 2/3 following Bansal andYaron (2004), we can still explain a significant proportion of the observed rise in inflation.
When σ = 2/3, the shocks increase aggregate inflation by 0.56 percentage points, which
accounts for roughly 40% of the increase in inflation. Consequently, our result is robust in
this dimension as well.
With the additional shock ĝAICT , the extended model now better accounts for the growth
slowdown in Japan since 2014 compared to the baseline model. The growth rate of consumption per effective labor gCt /Lt declines by 1.43 percentage points in data. As shown in
Section 3.2, the MST stagnation can explain approximately 40% of the observed decline in
gC/L . Moreover, the extended model can account for roughly 60% of the observed decline due
to ICT-IST shock ĝAICT (represented as the term (E) in equation (27)). Thus, we conclude
that our baseline results hold true in this extended model.

6Conclusion

Japan emerged from long-lasting deflation during the 2010s, which has been widely perceived
as a much-desired success of various monetary policies by the BOJ. However, we argue that
this perception is challenged by a puzzle: the apparent success was accompanied by thestagnation of real consumption, not revitalization. This paper offers a resolution to this31

puzzle.
We propose that this puzzle can be elucidated by viewing the phenomenon as a manifestation of stagflation, resulting from the technology stagnation specific to the manufacturing
good sector. The technology stagnation increases the relative price of the manufacturing
good, which translates into a higher aggregate inflation when the nominal interest rate ispegged. Our quantification reveals that the model can account for approximately half of theobserved rise in inflation and 40% of the observed decline in real consumption growth.
An important lesson from our analysis is that the rise in the headline inflation rate inJapan might not be an informative signal regarding the Japanese economy. Even though formany years the Japanese economy has been waiting for inflation to go back to normal, thecause behind the rise in inflation needs to be carefully scrutinized. This is because inflationis, of course, affected by various factors including not-so-evident ones, such as technology
stagnation.

32

A

Data Appendix

A.1

Construction of Consumption Sequences

To construct consumption sequences, we utilize Supporting Table 11 of the flow tables in the
Annual Report 2018 of JSNA.37 This table comprises three excel files that provide nominal
consumption, real consumption, and deflators. In these excel files, consumption is classified
into four categories: durable goods, semi-durable goods, non-durable goods, and services.
Let C denote the set of these categories.
A.1.1

Real Consumption Growth

To construct the real consumption sequences of the non-manufacturing good, we first compute the growth rates of real consumption for semi-durable goods, non-durable goods, andservices, excluding both the imputed and actual rents from the consumption growth rate ofservices. We then aggregate these using weights proportional to their nominal expenditure.
A.1.2

Inflation

This subsection outlines how we construct the inflation rates of the manufacturing and nonmanufacturing goods, excluding impacts of the VAT hike. For explanation, we define thefollowing terms. Let P̃i,t denote the after-VAT price level of consumption i at year t, andPi,t denote its before-VAT price level. Note that Supporting Table 11 provides the value ofP̃i,t for each consumption category mentioned above. Our goal is to obtain Pi,t for each iand year t.
During our sample period, the Japanese government increased the VAT in 1997 and 2014
during our sample period. The increases became effective on April 1 of those years. The
VAT hikes were not necessarily applied uniformly to all categories of consumption. So, wemust take into account this fact to construct Pi,t . Motivated by the institutional details, we
assume that the VAT uniformly rose for consumption goods, except for services. With thisassumption, the following relation between Pi,t and P̃i,t for for i ̸= services holds: (1 + τ ) 1 + (1 + τ ) 3  P
t ∈ {1997, 2014}
t 4
i,t
t−1 4
,
(29)
P̃i,t =
(1 + τ ) P
otherwiseti,twhere τt is the VAT rate of the last month in year t. The term in the square brackets inequation (29) accounts for the fact that the VAT hike only came into effect in April for
37

These supporting tables are retrieved from this URL.

33

both instances of the hike. Taking the log difference of equation (29), we can compute theinflation rates by adjusting the VAT hike πi,t , except for services.
To construct the inflation of services, we use the aggregate inflation rate adjusted for
the VAT hikes by the Statistics Bureau of Japan. This adjusted inflation rate explicitly
takes into account the item-level institutional issues, such as non-taxability and transitional
measures, which are mostly applicable to services.38 We denote the difference between theaggregate inflation, including impacts of VAT hikes and the one excluding them, as ∆t . Then,the difference ∆t should satisfy the following equation:Xsi,t−1 π̃i,t −i∈CX

si,t−1 πi,t = ∆t .

(30)

i∈C

Since we already know the VAT-adjusted inflation rates except services, we can recover the
inflation rate of services by solving equation (30) in terms of πService,t :PPsi,t−1 πi,t − ∆ti∈{Service}/i∈C si,t−1 π̃i,t −.
πService,t =sService,tFinally, we aggregate the inflation rates of semi-durable goods, non-durable goods, andservices by using weights that are proportional to the nominal expenditure to construct the
inflation of the non-manufacturing good:
πn,t =

X
i̸=m

A.2

si,t−1πi,t .
k̸=m sk,t−1

PConstruction of Investment Sequences

To construct investment sequences, we use Supporting Table 14 of flow tables in Annual
Report 2018 of JSNA.39 We classify the investment goods into nine subcategories: otherbuildings and structures, transport equipment, information and communication technology(ICT) equipment, other machinery and equipment, defense equipment, cultivated biologicalresources, R&D, mineral exploration and evaluation, and computer software. Supporting Table 14 itself provides the sufficient information for constructing nominal and real investmentin the above subcategories.
38
The data is only available and explained in Japanese. See the website on this URL. The excel file that
contains the data can be retrieved from this URL.
39
The data can be retrieved from the same URL mentioned in Footnote 37.

34

A.3

KLEMS

We primarily use two excel files: Capital input and Growth accounting.40 Since the KLEMS
industry classification and the JSNA classification are different, it is necessary to tie them
together. In KLEMS’ data, there are 100 sectors. Let S denote the set of these sectors. We
˜ Ĩ ⊂ S, such that the sectors in C˜ produce durable consumption goods andselect subsets C,
the sectors in Ĩ produce the ICT investment goods. Set C˜ comprises fix sectors: (1) household
electric appliances; (2) miscellaneous electronic equipment; (3) image and audio equipment;(4) communication equipment; (5) electronic data processing machines, digital and analog
computer equipment, and accessories; and (6) motor vehicles. Set Ĩ comprises three sectors:(1) image and audio equipment; (2) communication equipment; and (3) electronic dataprocessing machines, digital and analog computer equipment, and accessories.
We construct the TFP for the manufacturing good, gAKLEMS, and the ICT equipment,m,t˜gAKLEMS, by aggregating the sectoral TFP of i ∈ C and j ∈ Ĩ. Let gAKLEMS
denote the growth
i,t
ICT,t
rate of sectoral TFP of sector i ∈ S. These TFP are given by
gAKLEMS
=m,t

X

ωi,t gAKLEMS,i,tgAKLEMS
=
m,t

X

i∈C˜

ϖj,t gAKLEMS
,
j,t

j∈Ĩ

where ωi,t is the share of household consumption expenditure for i ∈ C˜ in total household
consumption expenditure in set C˜ and ϖj,t is the share of gross fixed capital formation(GFCF) of good j ∈ Ĩ in the total GFCF in set Ĩ. The industry-by-industry IO table provides
information regarding how much of the goods produced by each sector n is purchased forfinal consumption of households and GFCF.41
We also construct the aggregated markup for the manufacturing good, µm,t , and ICT
investment good, µICT,t , in a similar manner. Let µi,t denote the level of markup of sectori ∈ S. We then aggregate these sectoral markup, µICT,t .
µm,t =

X

ωi,t µi,t ,µICT,t =

i∈C˜

A.4

X

ϖj,t µj,t .

j∈ĨInflation of the Manufacturing Good across Major Cities

In this section, we explain how to construct the data used in Section 3.2 in detail. We cover
49 major cities of Japan, which consist of 47 prefectural capital cities and 2 other importantcities designated by government ordinance before 2005. To obtain the regional inflation rates
40

All the data, except sectoral markup, can be retrieved from the website of the RIETI. The data on
sectoral markup is only available in Japanese and can be retrieved from this webpage.
41
The industry-by-industry IO tables are retrieved from this URL.

35

that are conceptually as close as possible to the national inflation rate of the manufacturing
good used in our analysis, we use the weighted averages of the inflation rates for “household
durable goods” and “recreational durable goods” reported in CPI by major city. The former
consists of home appliances and furniture and the latter primarily corresponds to computer
hardware and audio-visual equipment. As earlier, we aggregate these inflation rates by using
the weights proportional to the corresponding consumption expenditure.
We mainly use CPI and the family income and expenditure survey (FIES).42 CPI provides
information on the price indexes of these durable goods by major city indexed by a. However,the city-level indexes are not chain-liked annually and the weights are updated every fiveayears. Let P̃i,tbe the price index of i ∈ D ≡ {household durables, recreational durables}at date t of city a. FIES provides information regarding the corresponding consumption
expenditure, denoted by Vi,ta . Specifically, we use the average consumption expenditure forhouseholds of two or more persons. The after-VAT inflation rate of the manufacturing goodin city a is calculated in the following manner:
a
π̃m,t
=

Vi,at̄(t)

X
P
i∈D

a
π̃i,t
,
a
V
k∈D k,t̄(t)where t̄ (t) is the base year used in CPI for year t.
Further, we calculate the growth rates of real consumption of the manufacturing good bycity as the difference between their inflation rates and the growth rates of relevant consumer
spending:a ≡ gV a − g a ,
gCi,t
P̃i,t
t
P
a
, we use
where Vta = i∈D Vi,ta . To eliminate the effects of the VAT on the inflation rate π̃m,ta
the same method as that described in Section A.1.2. Let πm,t denote such an inflation rate
for city a at date t.

B

Non-Horizontal Supply Curve

In this section, we verify that our theoretical results in Section 3.2 hold true in a model
where the asset supply curve (or saving function) is not horizontal with respect to a realinterest rate. This investigation additionally offers insights regarding the results in Section
5. Although there are many ways to derive an upward sloping supply function, we choose aclassic overlapping generations model for an expositional reason. We focus on steady-state
analysis and abstract away from the nominal rigidity.
42

The data can be retrieved from this URL.

36

The supply side of the economy is almost identical to that in Section 2. Since we abstract
away from the nominal rigidity, the real wage relative to the price of the non-manufacturing
good corresponds to the TFP, Wt /Pn,t = At . As in Section 2, the relative price of the
manufacturing good corresponds to the inverse of the MST, A−1m,t .
In contrast to the representative consumer model in the main text, we consider consumers
who live for two periods. At date t, a new consumer is born and the generation t consumer
inelastically supplies labor (1 − ξ) L and ξL units of labor at dates t and t + 1, respectively.
Thus, the total labor supply at date t is always L. As in the benchmark model in Section(2), there are two consumption goods: manufacturing and non-manufacturing goods, andthe only asset traded is the government bond. At date t, the consumer born at date t solves
the following maximization problem:γi !1−σ
Q
t
X
c
i,t+k
i∈{n,m}
βt
max
1−σ
k=0,1
X
s.t.
Pi,t cti,t + bt = wt ξLi∈{n,m}X

Pi,t+1 cti,t+1 = Rt bt + wt+1 (1 − ξ) L.

i∈{n,m}The government sets its interest rate, and the net supply of bond is zero, bt = 0. Further,P
the good market clearing conditions are k=0,1 ct−ki,t = Ci,t .
It is easy to derive the equilibrium of this economy. The Cobb-Douglass demand function
implies that Pi,t cti,t = γi wt ξL and Pi,t+1 cti,t+1 = γi wt+1 (1 − ξ) L. Since the real wage is At
and the relative price of the manufacturing good is A−1
m,t , we obtainctn,t = γn ξAt L ctm,t = γm ξAm,t At L

(31)

ctn,t+1 = γn (1 − ξ) At+1 L ctm,t+1 = γm (1 − ξ) Am,t+1 At+1 L.

(32)Thus, the individual consumption growth rate, ln cti,t+1 /cti,t , is ln (1 − ξ) /ξ + gA for i = n
and ln (1 − ξ) /ξ + gA + gAm for i = m.
The asset supply curve scaled by the nominal GDP is given by11ξ − (1 − ξ) ḡA β − σ (Rt /Πn,t+1 )− σ ḡAγmm
bt
=
 σ−1
σ−1
1
Pt Y t1 + β − σ (R /Π
) σ ḡ γm σ
t

n,t+1

 σ−1
σ
,

(33)

Am

where Πn,t+1 is the inflation rate of the non-manufacturing good and ḡA and ḡAm are thegross growth rates of At and Am,t respectively. This saving function is an increasing function
if σ ≤ 1. When σ > 1, the function increases locally around the equilibrium interest rate.
37

The bond market clearing condition determines the real interest rate, Rt /Πn,t+1 .
Consider the case in which σ = 1. Then, the asset supply function (33) boils down tobtξβ − (1 − ξ) ḡA (Rt /Πn,t+1 )−1=,Pt Y t1+β(34)

which is an increasing function with respect to the real interest rate. Suppose that a negativetechnology shock occurs on the manufacturing good so that ḡA declines to ḡA′ . Note that thisshock does not influence the saving decision of the households when σ = 1. The market
clearing condition implies that Πn remains unchanged while the relative price of good mincreases. Consequently, the aggregate inflation rate increases. We obtain the same comparative static result mentioned in the main text when σ = 1. Thus, we verified that the resultsin Section 3.2 hold true in a model in which the asset supply curve is not horizontal.
Furthermore, equation (34) offers an intuitive perspective on the results from the extended
model in Section 5. Recall that when σ > 1 (the EIS is less than one), the MST technology
stagnation ĝAm < 0 becomes more inflationary. Conversely, if σ < 1, the opposite holds.
These results can be understood by analyzing the supply curve of the economy. If σ ̸= 1,
then the MST stagnation ĝAm shifts the asset supply curve. When σ > 1, the negative
shock shifts the supply curve to the right. This shift occurs because a rise in future pricedrives households, motivated by the desire to smooth out their consumption, to save more.
Consequently, the market-clearing real interest rate declines, thereby exerting inflationarypressures on the economy. When σ < 1, the substitution effect due to the rise in pricedominates and households are encouraged to increase today’s consumption. Consequently,
the shock shifts the supply curve to the left. In this case, the market-clearing real interest
rate rises and this rise leads to disinflation of the non-manufacturing good. Thus, the overall
effect of the shock on the aggregate inflation is mitigated.

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