DP2024-16

Insatiable Wealth Preference: Evidence
from Japanese Household Survey
Mika AKESAKA
Ryo MIKAMI
Yo s h i y a s u O N O

Revised May 23, 2024

April 17, 2024
Revised May 23, 2024

Insatiable Wealth Preference:
Evidence from Japanese Household Survey *Mika Akesaka†

Ryo Mikami‡

Yoshiyasu Ono §Kobe University

Shinshu University

Osaka University,
Osaka University of
Economics

Abstract
This study theoretically considers household behavior with wealth preference
and empirically investigates the validity of insatiable wealth preference usinga nationally representative survey. With wealth preference, the marginal rateof substitution of asset holdings for consumption depends on the nominalinterest rates of assets at each point in time. We focus on this property andfind that the marginal utility of holding financial assets remains strictly
positive as asset holdings increase and has a strictly positive lower bound,
implying the insatiability of wealth preference. This property plays a crucialrole in creating secular demand stagnation and expanding asset price bubbles.
JEL classification: D12, E21, E43, E71
Keywords: wealth preference, survey data, secular stagnation, bubbles* We thank Nobuyuki Hanaki, Naoko Hara, Charles Yuji Horioka, Miki Kohara, and seminar participantsat the 22nd Panel Survey Conference for their comments and suggestions. Any errors are our own. We
acknowledge financial supports from JSPS KAKENHI Grant (20H05631, 21H04397), and the Joint
Usage/Research Center at ISER (Osaka University).
† Corresponding author: Research Institute for Economics and Business, Kobe University, 2-1, Rokkodai,
Nada, Kobe, Hyogo 567-8501, JAPAN. Email:mika_akesaka@rieb.kobe-u.ac.jp‡ Faculty of Economics and Law, Shinshu University, 3-1-1, Asahi, Matsumoto, Nagano 390-8621,
JAPAN. Email: mikamiryomyself@gmail.com§ Institute of Social and Economic Research, Osaka University, 6-1, Mihogaoka, Ibaraki, Osaka 5670047, JAPAN. Email: ono@iser.osaka-u.ac.jp

1. Introduction
This study theoretically considers household behavior with wealth preference andempirically shows that wealth preference is insatiable. This property plays a crucial role increating critical malfunctions in advanced economies. Secular demand stagnation in which theparadoxes of toil, thrift, and flexibility appear, and expanding asset price bubbles along which
the transversality condition is valid (i.e., rational bubbles).
Under this property, the marginal utility of financial asset holdings slowly declines andapproaches a strictly positive level whereas the marginal utility of consumption decreases fasterthan that of asset holdings and approaches zero as consumption and asset holdings increase.
Therefore, consumption initially increases with asset holdings, and then increases less; it
eventually stops increasing, resulting in secular stagnation with aggregate demand shortages.
In this state, prices continue to decline, which expands the real value of financial assets, but
the marginal utility of asset holdings does not change; hence, consumption is not stimulated.
Higher productivity and more flexible price adjustments worsen deflation, which makes it moreadvantageous for households to reduce consumption and accumulate financial assets. Thisimplies the paradoxes of toil and flexibility, respectively. Greater wealth preference directly
decreases consumption, implying the paradox of thrift. Additionally, insatiable wealthpreference enables asset prices to continue expanding beyond the fundamental values
determined by dividends.

[Insert Figure 1 here][Insert Figure 2 here]

1Particularly, the relationship between household consumption and financial asset holdings
is observed in Japanese macroeconomic data. Figure 1 shows that household consumption grewsteadily in line with the growth of financial assets until the early 1990s. After that, while
financial assets continued to grow, household consumption stopped growing and neverrecovered, leading to prolonged economic stagnation. This nature of the Japanese economy isevident when compared to the U.S. economy, where consumption continues to grow asfinancial assets increase. firmly (Figure 2), and is often referred to as the “Japanese disease”. 1
Secular demand stagnation due to a strictly positive marginal utility of asset holdings was
first theoretically discussed by Ono (1994, 2001) and later extended by several studies. Recent
examples are Ono and Ishida (2014), Murota and Ono (2015), Michau (2018), Illing et al.
(2018), Hashimoto and Ono (2020), and Michaillat and Saez (2022) among others. With
insatiable wealth preference, ever-expanding equity prices (or rational bubbles) are supported
because they satisfy the transversality condition, as shown by Ono (1994, Chap. 11). 2 However,very few empirical researches examine the existence and insatiability of wealth preference.
Two exceptions are Ono et al. (2004) and Ono and Yamada (2018). The former examines theexistence of a strictly positive lower bound of the marginal utility of wealth by applying aparametric method to Japanese macroeconomic time-series data of consumption and financial
assets, and a non-parametric method to household data from the Tokyo metropolitan area. The
latter proves that status preference for wealth is such that households care more about thedifference of their asset holdings from the social average than about the ratio to the social
average, and find that such status preference makes the marginal utility of asset holdings

1 The US economy also experienced a similar downturn, but it was small and short. Inagaki et al. (2023)

apply a model with insatiable wealth preference to the Japanese and US data and analyze the Japanese
stagnation since the early 1990s and the US slowdown in output growth since 2008.

2 Michau et al. (2023) investigate the conditions for rational constant bubbles to appear under satiable

wealth preference.

2

constant and leads to secular demand stagnation. However, due to a lack of asset data, it uses
income data instead of asset data by assuming that income is closely related to asset holdings.
This study uses microdata from a nationally representative survey on Japanese household
consumption and wealth, and examines the explanatory power of wealth preference and theplausibility of the existence of a positive lower bound of the marginal utility of financial asset
holdings. 3
Several empirical studies focus on the effects of asset holdings on consumption behavior.
Most of them assume that consumption directly depends on income; thus, they focus on themarginal propensity to consume (MPC) with respect to income and discuss how the MPC
varies with the level of asset holdings. For example, Arrondel et al. (2019) and Fisher et al.
(2020) report that households with greater asset holdings have lower MPCs. 4 This finding is
consistent with our model although consumption does not depend on income in our model.
With wealth preference, consumption is directly related to asset holdings in such a way that theintertemporal marginal rate of substitution of consumption is equal to the benefit of holding
assets, which consists of the real rate of return and the marginal rate of substitution of asset
holdings for consumption. If wealth preference is insatiable, the MPC appears to decrease as
asset holdings increase because households with higher income tend to hold greater assets andconsumption increases much more slowly than asset holdings.
Other empirical studies focus on the marginal propensity to save (MPS) and find a positive
relationship between asset holdings and the MPS, implying that “the rich save more” (Dynan

3 Gechert

and Siebert (2022) carry out a simple laboratory experiment and conclude the possible
existence of wealth preferences.
4 Some studies focus on the MPC with respect to temporary and permanent income shocks due to different
kinds and levels of assets. Carroll et al. (2011) examine the effects of changes in real-estate and financialasset values on the marginal propensity of consumption while Carroll et al. (2014) compare the response of
consumption to a temporary income shock in rich and poor countries with different wealth levels. Kaplan etal. (2014) compared the impact of temporary income fluctuations on the MPC between hand-to-mouthhouseholds and wealthy households.

3

et al. 2004; Hendricks 2007; Hori et al 2016; Bozio et al. 2017; Gandelman 2017). Similar tostudies focusing on the MPC, they show that “the rich consume less.” Income is included as an
explanatory variable of the MPS, and assets are regarded as sources of income. This idea isshared with research that examines the impact of stock price changes on consumption, (Byrne
and Davis 2003; Christelis et al. 2015; Starr-McCluer 2002). 5
In contrast to previous studies, our study focuses on the direct relationship between
consumption and asset holdings at each point in time, which is obtained from the household
dynamic optimization behavior with wealth preference. Carroll (2000) also treats householdbehavior with wealth preference. He compares the plausibility of the life cycle, dynasty, andwealth preference models and concludes that the wealth preference model is the most plausible.
In his wealth preference model, he assumes that the elasticity of the marginal utility of
consumption is greater than that of asset holdings and finds that the richer individuals are, thelower their propensity to consume. While we share this idea, we further find that the marginalutility of holding assets remains strictly positive and show that this property explains typicalmalfunctions in advanced economies such as secular demand stagnation and explosive asset
price bubbles.
This study utilizes household-level micro data to examine the insatiability of wealthpreference. We use data from the Japan Household Panel Survey on Consumer Preferences andSatisfaction (JHPS-CPS) conducted by the Institute of Social and Economic Research (ISER)
at Osaka University, enabling us to observe the relationship between household financial assets

5 Other studies investigating the relationship between stock price fluctuations and consumption include

Mankiw and Zeldes (1991) and Koop (2008). Mankiw and Zeldes (1991) focus on the difference in
consumption behavior between shareholders and non-shareholders. Meanwhile, Koop (2008) applies a
Bayesian model to examine how consumption is related to asset holdings influenced by stock price changes,
and income.

4and consumption. Our results suggest that the marginal utility of wealth has a strictly positive
lower bound, aligning with our model’s implications.
The rest of the paper is organized as follows: Section 2 presents the model structure andobtains the conditions for secular demand stagnation and explosive asset price bubbles toappear. Section 3 empirically analyzes the plausibility and insatiability of wealth preference
using the survey data. Finally, Section 4 summarizes our results and concludes the study.

2. The Model
We present the model structure and summarize how secular demand stagnation andpersistently expanding asset price bubbles appear if the marginal utility of asset holdings isstrictly positive.

A. Households
A representative household has a labor endowment normalized to unity, but its actual labor
supply 𝑥𝑥 can be lower than unity𝑥𝑥 ≤ 1,

because unemployment may occur. Given the nominal wage 𝑊𝑊 and commodity price 𝑃𝑃, thehousehold supplies labor 𝑥𝑥, earns labor income 𝑊𝑊𝑊𝑊, receives government transfer 𝜏𝜏 (or pays

lump-sum tax if 𝜏𝜏 is negative), consumes 𝑐𝑐, saves 𝐴𝐴̇, and owns total assets 𝐴𝐴; 𝐴𝐴 consists ofmoney 𝑀𝑀, interest-bearing financial asset 𝐵𝐵 of which the nominal interest rate is 𝑅𝑅 𝑏𝑏 , and realestate 𝑙𝑙 of which the nominal price is 𝑄𝑄. Further, 𝑙𝑙 is allocated to its own housing ℎ and rent

housing supply 𝑙𝑙 − ℎ of which the nominal rate of return is 𝑅𝑅 𝑙𝑙 . Obviously, 𝑙𝑙 − ℎ is negative if

the household rents an accommodation. Then, the flow budget equation and the stock constraint
are as follows:5𝐴𝐴̇ = 𝑅𝑅 𝑏𝑏 𝐵𝐵 + 𝑅𝑅 𝑙𝑙 𝑄𝑄(𝑙𝑙 − ℎ) + 𝑊𝑊𝑊𝑊 − 𝑃𝑃𝑃𝑃 + 𝑃𝑃𝑃𝑃,

𝐴𝐴 = 𝑀𝑀 + 𝐵𝐵 + 𝑄𝑄𝑄𝑄,

𝑎𝑎̇ = 𝑅𝑅 𝑏𝑏 𝑏𝑏 + 𝑅𝑅 𝑙𝑙 𝑞𝑞(𝑙𝑙 − ℎ) + 𝑤𝑤𝑤𝑤 − 𝑐𝑐 − 𝜋𝜋𝜋𝜋 + 𝜏𝜏,

𝑎𝑎 = 𝑚𝑚 + 𝑏𝑏 + 𝑞𝑞𝑞𝑞,

which reduce to(1)where lower-case letters imply real values and 𝜋𝜋 is the inflation rate of 𝑃𝑃.

The household receives utility from real consumption 𝑐𝑐, real money balances 𝑚𝑚 for thetransaction motive, real financial asset holdings 𝑚𝑚 + 𝑏𝑏 for the wealth preference, and housingℎ. The household’s lifetime utility is as follows:∞∫0 𝑒𝑒 −𝜌𝜌𝜌𝜌 [𝑢𝑢(𝑐𝑐) + 𝑣𝑣(𝑚𝑚) + 𝛽𝛽(𝑚𝑚 + 𝑏𝑏) + 𝜓𝜓(ℎ)]𝑑𝑑𝑑𝑑,(2)

where the functions satisfy𝑢𝑢′ (𝑐𝑐) > 0, 𝑢𝑢′ (0) = ∞, 𝑢𝑢′ (∞) = 0, 𝑢𝑢′′ (𝑐𝑐) < 0,

𝑣𝑣 ′ (𝑚𝑚) > 0, 𝑣𝑣 ′ (0) = ∞, 𝑣𝑣 ′ (∞) = 0, 𝑣𝑣 ′′ (𝑚𝑚) < 0,𝛽𝛽 ′ (𝑚𝑚 + 𝑏𝑏) > 0, 𝛽𝛽 ′ (0) = ∞, 𝛽𝛽 ′ (∞) = 𝛽𝛽0 > 0,𝛽𝛽 ′′ (𝑚𝑚 + 𝑏𝑏) ≦ 0,𝜓𝜓′ (ℎ) > 0, 𝜓𝜓′ (0) = ∞, 𝜓𝜓′ (∞) = 0, 𝜓𝜓′′ (ℎ) < 0.

Note that 𝛽𝛽0 > 0 implies a strictly positive marginal utility of financial asset holdings.

The household maximizes the lifetime utility (2) subject to the two equations in (1). Given

the Hamiltonian 𝐻𝐻 of the maximization problem:

𝐻𝐻 = 𝑢𝑢(𝑐𝑐) + 𝑣𝑣(𝑚𝑚) + 𝛽𝛽(𝑚𝑚 + 𝑏𝑏) + 𝜓𝜓(ℎ) + 𝜉𝜉(𝑎𝑎 − 𝑚𝑚 − 𝑏𝑏 − 𝑞𝑞𝑞𝑞)+𝜆𝜆(𝑅𝑅 𝑏𝑏 𝑏𝑏 + 𝑅𝑅 𝑙𝑙 𝑞𝑞(𝑙𝑙 − ℎ) + 𝑤𝑤𝑤𝑤 − 𝑐𝑐 − 𝜋𝜋𝜋𝜋 + 𝑧𝑧),the first-order optimal conditions are as follows:𝑢𝑢′ (𝑐𝑐) = 𝜆𝜆,𝑣𝑣 ′ (𝑚𝑚) + 𝛽𝛽 ′ (𝑚𝑚 + 𝑏𝑏) = 𝜉𝜉,𝛽𝛽 ′ (𝑚𝑚 + 𝑏𝑏) + 𝜆𝜆𝑅𝑅 𝑏𝑏 = 𝜉𝜉,𝜓𝜓′ (ℎ) = 𝜆𝜆𝑅𝑅 𝑙𝑙 𝑞𝑞 = 𝜉𝜉𝜉𝜉,𝜆𝜆̇ = (𝜌𝜌 + 𝜋𝜋)𝜆𝜆 − 𝜉𝜉.
6They reduce to𝑐𝑐̇𝜌𝜌 + 𝜎𝜎 𝑐𝑐 + 𝜋𝜋 =𝑣𝑣 ′ (𝑚𝑚)𝛽𝛽 ′ (𝑚𝑚+𝑏𝑏)
𝛽𝛽 ′ (𝑚𝑚+𝑏𝑏)𝜓𝜓′ (ℎ)
𝑏𝑏
𝑙𝑙
+
=
𝑅𝑅
+
=
𝑅𝑅
=
,
′
′
′
𝑢𝑢 (𝑐𝑐)𝑢𝑢 (𝑐𝑐)𝑢𝑢 (𝑐𝑐)𝑞𝑞𝑢𝑢′ (𝑐𝑐)(3)where 𝜎𝜎 = −𝑢𝑢′′ (𝑐𝑐)𝑐𝑐/𝑢𝑢′(𝑐𝑐) > 0. The first equation shows that the nominal intertemporal
substitution rate of consumption equals the respective benefits of money, interest-bearing

assets, and real estate, consisting of each nominal rate of return and benefit of holding them.
The last term shows the marginal rate of substitution of housing payment for consumption
payment, where the real housing price 𝑞𝑞 implies the level of real consumption required to get
a unit of ℎ.

The transversality condition islim 𝜆𝜆𝜆𝜆exp(−𝜌𝜌𝜌𝜌) = 0.

𝑡𝑡→∞

(4)

B. Firms and Markets
The firm sector is competitive and has a linear technology:
𝑦𝑦 = 𝜃𝜃𝜃𝜃.

Hence, the real wage 𝑤𝑤 is invariant over time and satisfies𝑊𝑊𝑤𝑤 �= 𝑃𝑃 � = 𝜃𝜃,𝑊𝑊̇𝜋𝜋 = 𝑊𝑊.

(5)

The government expands nominal money 𝑀𝑀 at a time rate of 𝜇𝜇 and transfers it to households;
hence,

𝑀𝑀̇𝑀𝑀= 𝜇𝜇(> 0), 𝜏𝜏 = 𝜇𝜇𝜇𝜇.

The commodity, lending-borrowing, money, and real estate markets satisfy
commodity: 𝑐𝑐 = 𝜃𝜃𝜃𝜃,net lending: 𝑏𝑏 = 0 (⇒ 𝑎𝑎 = 𝑚𝑚),𝑀𝑀

money: 𝑚𝑚 = 𝑃𝑃 ,𝑚𝑚̇𝑚𝑚

= 𝜇𝜇 − 𝜋𝜋,7real estate: ℎ = 𝑙𝑙 = 𝑙𝑙,̅(6)

where the total supply of real estate 𝑙𝑙 is assumed to be constant. In the labor market, thenominal wage adjustment is perfect if full employment exists, but sluggish and depends on the
deflationary gap if unemployment occurs. Thus, we havelabor: 𝑊𝑊 perfectly adjusts if 𝑥𝑥 = 1,
𝑊𝑊̇𝑊𝑊

if 𝑥𝑥 < 1.

= 𝛼𝛼(𝑥𝑥 − 1)

(7)

C. Demand Stagnation
We show that insatiable wealth preference, 𝛽𝛽 ′ (∞) = 𝛽𝛽0 > 0 , yields secular demandstagnation. In the steady state with full employment, where 𝑐𝑐̇ /𝑐𝑐 = 0 and 𝑥𝑥 = 1, from (3) and(6), 𝑐𝑐 and 𝑚𝑚 satisfy
and 𝑞𝑞 satisfies(𝑐𝑐, 𝑚𝑚) = (𝜃𝜃, 𝑚𝑚 𝑓𝑓 ), where 𝜌𝜌 + 𝜇𝜇 =𝜌𝜌 + 𝜇𝜇 =𝑣𝑣 ′ �𝑚𝑚𝑓𝑓 �+𝛽𝛽 ′ �𝑚𝑚𝑓𝑓 �𝑢𝑢′ (𝜃𝜃)𝛽𝛽

0
�> 𝑢𝑢′ (𝜃𝜃)�,(8)𝜓𝜓′ (𝑙𝑙)̅
.
𝑞𝑞𝑢𝑢′ (𝜃𝜃)The left-hand side of the second equation in (8) represents the desire for present consumption
while the right-hand side represents the desire for accumulating assets when consumption takes
the full-employment level 𝜃𝜃. The full-employment steady state exists if and only if𝜌𝜌 + 𝜇𝜇 > 𝛽𝛽0 /𝑢𝑢′ (𝜃𝜃).

(9)

If not, 𝑚𝑚 𝑓𝑓 that satisfies (8) does not exist. In this case, the desire for present consumption islower than the desire for accumulating assets for any 𝑚𝑚; hence, consumption falls below 𝜃𝜃,leading to aggregate demand shortages.

If a steady state with stagnation is reached, demand shortages persist and deflation
continues. Real money 𝑚𝑚 continues to expand, resulting in 𝑣𝑣 ′ (𝑚𝑚) = 0 and 𝛽𝛽 ′ (𝑚𝑚) = 𝛽𝛽0, as is8

clear from the properties of 𝑣𝑣(.) and 𝛽𝛽(. ) given below Equation (2). Therefore, from (3), (6)and (7), the nominal interest rate of 𝑏𝑏 reaches zero (𝑅𝑅 𝑏𝑏 = 0) and 𝑐𝑐 satisfies
𝑐𝑐 𝑠𝑠

𝛽𝛽

𝑐𝑐 = 𝑐𝑐 𝑠𝑠 , where 𝜌𝜌 + 𝛼𝛼 � 𝜃𝜃 − 1� = 𝑢𝑢′ (𝑐𝑐0 𝑠𝑠 ),

𝑚𝑚̇

𝑐𝑐 𝑠𝑠

= 𝜇𝜇 − 𝛼𝛼 � 𝜃𝜃 − 1� > 0.
𝑚𝑚

(10)

𝛽𝛽

(11)

For the solution of 𝑐𝑐 𝑠𝑠 to exist between 0 and 𝜃𝜃, that is, 𝑐𝑐 𝑠𝑠 ∈ (0, 𝜃𝜃), and the transversality
condition (4) to be valid, we must have𝛽𝛽0𝛼𝛼 < 𝜌𝜌 < 𝑢𝑢′ (𝜃𝜃), 𝜇𝜇 < 𝑢𝑢′ (𝑐𝑐0𝑠𝑠 ),where the first inequality enables 𝑐𝑐 𝑠𝑠 (< 𝜃𝜃) to exist and the second makes 𝑚𝑚̇/𝑚𝑚(= 𝜇𝜇 − 𝜋𝜋) < 𝜌𝜌

implying that the transversality condition (4) is valid. If (9) is invalid, that is, the fullemployment steady state does not exist, and the second inequality of (11) is invalid, that is, thetransversality condition in the stagnation steady state is invalid, no dynamic equilibrium pathexists.
Thus, the conditions for each steady state to exist are as follows: 6

Proposition 1: The full-employment steady state and the stagnation steady state appear under
the following conditions:
𝛽𝛽

𝛽𝛽

0
− 𝜌𝜌 > 𝑢𝑢′ (𝑐𝑐0 𝑠𝑠 ) ,If 𝑢𝑢′ (𝜃𝜃)𝛽𝛽𝜇𝜇 > 𝑢𝑢′ (𝑐𝑐0 𝑠𝑠 ): the full-employment steady state;
𝛽𝛽0′
𝑢𝑢 (𝑐𝑐 𝑠𝑠 )𝛽𝛽0𝑢𝑢′ (𝜃𝜃)𝛽𝛽

𝛽𝛽

0≥ 𝜇𝜇 > 𝑢𝑢′ (𝜃𝜃)− 𝜌𝜌: the full-employment and stagnation steady states;− 𝜌𝜌 ≥ 𝜇𝜇: the stagnation steady state.
𝛽𝛽

0
− 𝜌𝜌,
If 𝑢𝑢′ (𝑐𝑐0 𝑠𝑠 ) ≥ 𝑢𝑢′ (𝜃𝜃)

6 These conditions are essentially the same as those obtained by Ono and Ishida (2014).

9

𝛽𝛽

0
𝜇𝜇 > 𝑢𝑢′ (𝜃𝜃)− 𝜌𝜌: the full-employment steady state;𝛽𝛽0′
𝑢𝑢 (𝜃𝜃)𝛽𝛽0

𝛽𝛽− 𝜌𝜌 ≥ 𝜇𝜇 ≥ 𝑢𝑢′ (𝑐𝑐0 𝑠𝑠 ): no dynamic equilibrium path;𝑢𝑢′ (𝑐𝑐 𝑠𝑠 )> 𝜇𝜇: the stagnation steady state.

Remark: If 𝛽𝛽0 = 0, full employment is always reached in steady state; thus, the positivity of
𝛽𝛽0 is critical for secular demand stagnation to arise.

In the stagnation steady state, national income is determined by consumption. This
causality is opposite to that in the conventional Keynesian consumption function: national
income determines consumption and a greater desire for saving leads to a lower MPC. Most
empirical studies share this causality and examine the relationship between the MPC (or MPS)
and asset holdings. In the present model, in contrast to the conventional view, strong wealthpreference is consistent with a high MPC. This is because strong wealth preference makes
consumption less than the full-employment level; hence, investment disappears, whichequalizes income to consumption and makes the MPC equal one.

D. Bubbles
With insatiable wealth preference, ever-expanding asset price paths are supported andsatisfy the transversality condition. To show this property, we change the definition of 𝑏𝑏 toequities of an asset that yields a constant quantity 𝑧𝑧 of the commodity. Then, the commodity
market equilibrium given by the first equation of (6) becomes

and the real rate of return on 𝑏𝑏 is

𝑐𝑐 = 𝜃𝜃𝜃𝜃 + 𝑧𝑧,
10

𝑟𝑟 𝑏𝑏 (= 𝑅𝑅 𝑏𝑏 − 𝜋𝜋) = (𝑧𝑧 + 𝑏𝑏̇)/𝑏𝑏.

Therefore, from the first equation in (3) where 𝑐𝑐̇ /𝑐𝑐 = 0, we find𝜌𝜌 −𝛽𝛽 ′ (𝑚𝑚+𝑏𝑏)
𝑣𝑣 ′ (𝑚𝑚)𝑧𝑧+𝑏𝑏̇=− 𝜋𝜋 = 𝑏𝑏 ,𝑢𝑢′ (𝑐𝑐)𝑢𝑢′ (𝑐𝑐)(12)where from (6) and (7), 𝜋𝜋 satisfies

𝜋𝜋 = 𝜇𝜇 under full employment,
𝑐𝑐 𝑠𝑠 −𝑧𝑧

𝜋𝜋 = 𝛼𝛼 � 𝜃𝜃 − 1� under stagnation.

(13)

From (12) and (13), we obtain the following proposition, of which the proof is set out inAppendix A.

Proposition 2: A stable asset price and expanding asset price bubbles appear under thefollowing conditions:If 𝛽𝛽0 = 0, full employment occurs in the steady state and only a stable asset price appears.
𝛽𝛽0If 𝜌𝜌 > 𝑢𝑢′ (𝜃𝜃+𝑧𝑧)> 0, full employment occurs in the steady state and both a stable asset priceand explosive asset price bubbles can appear.
𝛽𝛽0≥ 𝜌𝜌, aggregate demand stagnation occurs in the steady state and both a stable
If 𝑢𝑢′ (𝜃𝜃+𝑧𝑧)

asset price and explosive asset price bubbles can appear.

Remark: Only if 𝛽𝛽0 is strictly positive, explosive asset price bubbles appear.

E. Alternative Assumptions on Wealth Preference
As for the persistent positivity of the marginal utility of asset holdings, Murota and Ono(2011), Ono and Yamada (2018), and Michaillat and Saez (2022) assume a status preferencewith respect to asset holdings, 𝛽𝛽(𝑎𝑎 − 𝑎𝑎‾) , where 𝑎𝑎‾ represents the social average of asset
11

holdings 𝑎𝑎. Given that the representative household’s asset holdings 𝑎𝑎 is equal to the social
average 𝑎𝑎‾, the marginal utility of wealth remains positive:
𝛽𝛽 ′ (𝑎𝑎 − 𝑎𝑎‾) = 𝛽𝛽 ′ (0) > 0,

for any 𝑎𝑎(= 𝑎𝑎‾). Michau (2018) assumes that the utility of wealth depends on the household
assets minus government liabilities so that the net wealth holdings equal real capital. Therefore,

no matter how much the nominal price declines and the real value of financial asset holdings
increases, the household net wealth stays the same and the marginal utility of wealth stays
positive.
All these settings yield the property that the marginal utility of financial asset holdings
stays positive.

3. Empirical Analysis
In section 2 we have shown that secular demand stagnation and explosive asset pricebubbles can appear only if the marginal utility of financial assets has a strictly positive lower
bound (i.e., 𝛽𝛽0 > 0). The validity of this property is empirically examined in this section.

We modify the model to incorporate households with different sizes. With all the otherproperties the same as in Section 2, the representative household has 𝑛𝑛 household members,
and only the head of the household has a labor endowment, which is unity. The household head
determines household consumption, money, asset holdings, and housing by considering thesum of all members’ utility of consumption and housing. We assume that each member receives
utility from consumption and housing per capita while all assets are held by the household
head. 7

7 We discuss alternative assumptions on the effect of the household size on utility in Appendix B andmention the plausibility of the present setting.

12The lifetime utility function (2) of the household head is rewritten as follows:
∞

𝑐𝑐

ℎ

∫0 𝑒𝑒 −𝜌𝜌𝜌𝜌 �𝑛𝑛𝑛𝑛 �𝑛𝑛� + 𝑣𝑣(𝑚𝑚) + 𝛽𝛽(𝑚𝑚 + 𝑏𝑏) + 𝑛𝑛𝑛𝑛 �𝑛𝑛�� 𝑑𝑑𝑑𝑑,(14)

which is maximized subject to the flow budget equation and asset constraint in (1). The Ramsey
equation is as follows:𝑐𝑐̇𝜌𝜌 + 𝜎𝜎 𝑐𝑐 + 𝜋𝜋 =𝑣𝑣 ′ (𝑚𝑚)+′ 𝑐𝑐𝑢𝑢 � �
𝑛𝑛

𝛽𝛽 ′ (𝑚𝑚+𝑏𝑏)
𝑐𝑐𝑛𝑛

𝑢𝑢′ � �= 𝑅𝑅 𝑏𝑏 +𝛽𝛽 ′ (𝑚𝑚+𝑏𝑏)
𝑐𝑐𝑛𝑛

𝑢𝑢′ � �= 𝑅𝑅 𝑙𝑙 =ℎ𝑛𝑛𝑐𝑐𝑞𝑞𝑢𝑢′ � �𝑛𝑛𝜓𝜓′ � �.

During the present data period (2005-2019), 𝑅𝑅 𝑏𝑏 is zero and the housing rent is almost
unchanged. 8 Therefore, from the above equation, we have
𝛽𝛽 ′ (𝑚𝑚+𝑏𝑏)
𝑐𝑐𝑛𝑛

𝑢𝑢′ � �(= 𝑅𝑅 𝑙𝑙 − 𝑅𝑅 𝑏𝑏 ) = 𝑅𝑅 𝑙𝑙 = constant.

(15)

We assume specific functional forms of 𝑢𝑢(𝑐𝑐/𝑛𝑛) and 𝛽𝛽(𝑚𝑚 + 𝑏𝑏) as follows:𝑐𝑐𝑢𝑢 �𝑛𝑛� =𝑐𝑐 1−𝜎𝜎
−1
𝑛𝑛

� �

1−𝜎𝜎

Applying them to (15) gives,

𝛽𝛽(𝑚𝑚 + 𝑏𝑏) = 𝛽𝛽0 ∙ (𝑚𝑚 + 𝑏𝑏) + 𝛽𝛽1
𝑅𝑅 𝑙𝑙 =

which reduces to𝑐𝑐 −𝜎𝜎�𝑛𝑛�

𝛽𝛽0 +𝛽𝛽1 (𝑚𝑚+𝑏𝑏)−𝜔𝜔
𝑐𝑐 −𝜎𝜎𝑛𝑛� �(𝑚𝑚+𝑏𝑏)1−𝜔𝜔 −1
1−𝜔𝜔

.

,

𝛽𝛽

𝛽𝛽

= 𝐴𝐴 + 𝐵𝐵(𝑚𝑚 + 𝑏𝑏)−𝜔𝜔 ; 𝐴𝐴 = 𝑅𝑅0𝑙𝑙 , 𝐵𝐵 = 𝑅𝑅1𝑙𝑙 ,(16)

where (𝑚𝑚 + 𝑏𝑏)−𝜔𝜔 and (𝑐𝑐/𝑛𝑛)−𝜎𝜎 exhibit a linear relationship. If 𝐴𝐴 is positive, 𝛽𝛽0 > 0 andpersistent shortages of aggregate demand and explosive asset price bubbles can occur. We
validate this hypothesis using micro data of Japanese households.

8 According to the Housing and Land Survey of Japan, conducted by the Statistics Bureau of the Ministry ofInternal Affairs and Communications, the average housing rent in Japan was 60,467 yen in 2008, 59,456 yen in2013, and 60,863 yen in 2018; housing rents have changed little over the period. Simizu et al. (2010) also findthat the housing rent is stable in Japan and that the stickiness is three times greater than that of the United States.

13

A. Data
We use data from the Japan Household Panel Survey on Consumer Preferences andSatisfaction (hereinafter referred to as JHPS-CPS), conducted by the Institute of Social andEconomic Research (ISER) at Osaka University. The JHPS-CPS is an annual, nationally
representative panel survey of residents in Japan. 9 The survey is based on self-administeredpaper questionnaires that are distributed to and collected from participating households in
February each year during 2005–2013 and 2016–2019. 10 The sample consists of 27,842
households, with approximately 1,300 to 4,000 households reporting their household structuresand financial situations each year.
The key variables are assets and consumption. For the assets variable, we follow StarrMcCluer (2002), Koop (2008), and Christelis et al. (2015), who highlight the robust correlation
between financial assets and consumption among various asset types, and focus on financial
assets as the primary source of asset information. The JHPS-CPS asks the quantity of household
financial assets using ten specified categories:
1.

Less than JPY 2.5 million (JPY 2.5 million)

2.

JPY 2.5 million to less than JPY 5 million (JPY 3.75 million)

3.

JPY 5 million to less than JPY 7.5 million (JPY 6.25 million)

4.

JPY 7.5 million to less than JPY 10 million (JPY 8.25 million)

5.

JPY 10 million to less than JPY 15 million (JPY 12.5 million)

9 The sample is stratified according to the geographical area and the city size. All municipalities areclassified into 40 stratums: 10 geographical areas and 4 categories corresponding to the population size. The
number of sample subjects in each stratum is distributed in proportion to the resident population aged 20–
69 years. The unit of sampling spot in each stratum is the census unit and is selected by random systematic
sampling.
10 The JHPS-CPS formally began in 2005 and was conducted annually thereafter until 2013. After a halt,

the survey was resumed in 2016. During the survey period, new households were added to the sample in2006 and 2009. All respondents are given a cash voucher (JPY 1,500 (USD 15) in 2009－2013 and 2016－2019, JPY 1,000 (USD 10) in the other years) by completing the survey.

14

6.

JPY 15 million to less than JPY 20 million (JPY 17.5 million)

7.

JPY 20 million to less than JPY 30 million (JPY 25 million)

8.

JPY 30 million to less than JPY 50 million (JPY 45 million)

9.

JPY 50 million to less than JPY 100 million (JPY 75 million)

10. More than JPY 100 million.
The distribution of households across asset categories in our sample is as follows: 1.
26.34%, 2. 15.81%, 3. 10.13%, 4. 9.44%, 5. 10.26%, 6. 7.48%, 7. 8.79%, 8. 6.75%, 9. 3.95%,
10. 1.05%. We exclude households in the top category (1.05%) from our sample because weare unable to identify their range of asset holdings, which could affect the study’s accuracy.
For the other categories, we use the median value (in parentheses) as each household’s financial
assets.
For the consumption variable, we use household expenditure, including utility bills andservices and excluding durable consumer goods (e.g. cars, houses, and high-value electricalappliances), taxes, social insurance premiums, and mortgage payments. Following (15), we use
consumption divided by the household size.
Besides these key variables, we use household information such as the age and educationof the household head and the household structure. Table 1 presents the descriptive statistics.

[Insert Table 1 here]

B. Estimation Model
We verify the relationship between household financial assets and consumption given by(16). For simplicity, we assume that the curvature of the utility functions for consumption andassets are the same, that is, 𝜎𝜎 = 𝜔𝜔, in the main analysis. We consider 𝜎𝜎 = 0.3 as the standard
15

value, following Anderson and Mellor (2008), who measure the relative risk aversion using thelottery choice of Holt and Laury (2002). 11 Then, the empirical equation becomes(𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑛𝑛𝑖𝑖𝑖𝑖 )−0.3 = 𝐴𝐴 + 𝐵𝐵(𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑡𝑡𝑖𝑖𝑖𝑖 )−0.3 + 𝛾𝛾𝑋𝑋𝑖𝑖𝑖𝑖′ + 𝛿𝛿year𝑡𝑡 + 𝑢𝑢𝑖𝑖 ,(17)

where A and B are parameters, and 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑛𝑛𝑖𝑖𝑖𝑖 and 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑡𝑡𝑖𝑖𝑖𝑖 are household i’s

consumption per capita and financial asset holdings, respectively. 𝑋𝑋𝑖𝑖𝑖𝑖′ denotes dummy

variables representing household characteristics, such as the age and educational level of thehousehold head, the household structure, and the prefecture in which the household lives.
Additionally, we include year dummies to control for idiosyncratic shocks across years, which
capture price changes across years although the price index in Japan does not change muchduring the analysis period. We do not control for household fixed effects, because there arealmost no switches between the categories of asset holdings in our sample.
We estimate equation (17) using ordinary least squares and test whether 𝐴𝐴 is strictly

positive, that is, whether the marginal utility of wealth has a strictly positive lower bound. If

the hypothesis of 𝐴𝐴 ≤ 0 is rejected, we empirically validate a strictly positive lower bound of
the marginal utility of wealth among the sample households.

C. Results
Graphical Evidence:
We present graphical evidence of the positive relationship between consumption andfinancial asset holdings, represented by (17), and the existence of a positive lower bound of themarginal utility of wealth ( 𝐴𝐴 > 0 ). Figure 3 shows the relationship between

11 Anderson and Mellor (2008) report that the mode of risk aversion in their experiment is 0.15 < 𝜎𝜎 <0.41. We suppose 𝜎𝜎 = 0.3 as the standard value of the risk parameter.

16

(𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑡𝑡𝑖𝑖𝑖𝑖 )−0.3 and (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑛𝑛𝑖𝑖𝑖𝑖 )−0.3, where a box plot illustrates the median and

25 and 75 PCTLs of consumption with the 95% confidence interval bar for each asset level,
and the predicted line is based on a single regression. It shows that the two factors are positively
correlated and that the intercept of their prediction line is strictly greater than zero. This result
is consistent with our hypothesis.

[Insert Figure 3 here]

Main Results:
Table 2 presents the estimates based on Equation (17). We control only for the year-fixed
effect in column (1). Then, we add regional dummies in column (2) and household
characteristics in column (3) as additional control variables. Additionally, we report the p-valueof the one-tailed test of 𝐻𝐻0 : 𝐴𝐴 ≤ 0 at the bottom of each column.

The coefficient of (𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑡𝑡𝑖𝑖𝑖𝑖 )−0.3 is 0.545 in column (1), 0.371 in column (2),and 0.399 in column (3). These estimates are statistically significant at the 1% level. In
addition, the hypothesis of 𝐴𝐴 ≤ 0 is rejected at the 1% significance level in all models.
[Insert Table 2 here]

Robustness of a Positive Lower Bound:
We examine whether our result on the one-tailed test for 𝐴𝐴 > 0 is robust to different valuesof 𝜎𝜎 and 𝜔𝜔. Figure 4 illustrates the intercept estimates of the model shown in column (3) of
Table 2 and their 95% confidence intervals for several values of 𝜎𝜎 and 𝜔𝜔. The vertical axis
17

represents the intercept estimates, the horizontal axis represents 𝜔𝜔 ranging from 0.1 to 0.9, andthe dots with various symbols are plotted for different values of 𝜎𝜎 ranging from 0.2 to 0.6.

Figure 4 shows that intercept 𝐴𝐴 is significantly greater than zero for all combinations of 𝜎𝜎and 𝜔𝜔. We do not report results for 𝜎𝜎 < 0.2 because the estimate of the intercept increases as

𝜎𝜎 decreases so that we can obviously reject the hypothesis (𝐴𝐴 ≤ 0). This result shows that themarginal utility of wealth has a strictly positive lower bound in most situations; hence, fromthe two Remarks of Propositions 1 and 2, secular demand stagnation and expanding equity
price bubbles can appear.

[Insert Figure 4 here]

Confirmation of Model Fit:
We confirm our model fit by predicting consumption using financial assets and ourestimates of 𝐴𝐴 and 𝐵𝐵 in Equation (17).

In Figure 5, the lower panel shows the distribution of asset values, while the upper panel

shows the predicted value of consumption for each financial asset values and the 25th to 75th
percentile range bar for the raw value of consumption. Each predicted value is located aroundthe middle of the range for most asset values. The group with high assets is worse in predicting
the consumption level than the other groups; however, only a few households are part of thegroup, as shown in the lower panel of Figure 5. Thus, our model can depict the relationshipbetween financial asset holdings and consumption.

[Insert Figure 5 here]18

4. Conclusion
This study considers household behavior with wealth preference and empirically examines
whether the marginal utility of wealth holdings has a strictly positive lower bound. This
property is vital in theoretically explaining secular demand stagnation and expanding asset
price bubbles. We use household-level micro data from a nationally representative household
survey. Our results suggest that the marginal utility of wealth has a strictly positive lower
bound; therefore, secular demand stagnation and expanding asset price bubbles can occur.

Appendix A: Proof of Proposition 2
If full employment is reached and the asset price is stable in steady state (𝑏𝑏̇ = 0), from

(12) and (13) we have

𝑣𝑣 ′ (𝑚𝑚)
𝑧𝑧
−
𝜇𝜇
=
,
′
𝑏𝑏
𝑢𝑢 (𝜃𝜃+𝑧𝑧)𝜌𝜌 −𝛽𝛽 ′ (𝑚𝑚+𝑏𝑏)
𝑧𝑧
=
.
′
𝑏𝑏
𝑢𝑢 (𝜃𝜃+𝑧𝑧)(A1)

The first equation gives 𝑏𝑏 as a function of 𝑚𝑚, which satisfies
𝑏𝑏 = 𝑏𝑏(𝑚𝑚), 𝑏𝑏(0) = 0, 𝑏𝑏(𝑚𝑚� ) = ∞ where�)
𝑣𝑣 ′ (𝑚𝑚= 𝜇𝜇;𝑢𝑢′ (𝜃𝜃+𝑧𝑧)

𝑏𝑏 ′ (𝑚𝑚) > 0.

(A2)

We first consider the case where 𝜌𝜌 > 𝛽𝛽0 /𝑢𝑢′ (𝜃𝜃 + 𝑧𝑧) ≥ 0. By substituting 𝑏𝑏(𝑚𝑚) defined

above to the second equation in (A1), we find𝜌𝜌 −−∞ = 𝜌𝜌 −� +𝑏𝑏(𝑚𝑚� )�
𝛽𝛽 ′ �𝑚𝑚𝑢𝑢′ (𝜃𝜃+𝑧𝑧)

𝛽𝛽 ′ �0+𝑏𝑏(0)�
𝑢𝑢′ (𝜃𝜃+𝑧𝑧)𝑧𝑧< 𝑏𝑏(0) = ∞,

𝛽𝛽

𝑧𝑧

0
= 𝜌𝜌 − 𝑢𝑢′ (𝜃𝜃+𝑧𝑧)> 0 = 𝑏𝑏(𝑚𝑚�),

implying that 𝑚𝑚 and 𝑏𝑏(𝑚𝑚) have finite solutions in 0 < 𝑚𝑚 < 𝑚𝑚
� and 0 < 𝑏𝑏 < ∞, the latter ofwhich implies a stable asset price. If explosive bubbles (𝑏𝑏 → ∞) occur, from (12) and (13) we

have

𝑏𝑏̇

𝛽𝛽

0
= 𝜌𝜌 − 𝑢𝑢′ (𝜃𝜃+𝑧𝑧)
> 0.
𝑏𝑏

19

Therefore, 𝑏𝑏̇/𝑏𝑏 < 𝜌𝜌 and the transversality condition (4) is valid if 𝛽𝛽0 > 0. If 𝛽𝛽0 = 0, 𝑏𝑏̇/𝑏𝑏 = 𝜌𝜌and the transversality condition is invalid.

In sum, if 𝛽𝛽0 = 0, the full-employment steady state is reached and only a stable asset priceis feasible. If 𝜌𝜌 > 𝛽𝛽0 /𝑢𝑢′ (𝜃𝜃 + 𝑧𝑧) > 0, the full-employment steady state is reached and both astable asset price and explosive bubbles are feasible.

Next, we consider the case where 𝜌𝜌 ≤ 𝛽𝛽0 /𝑢𝑢′ (𝜃𝜃 + 𝑧𝑧). The full-employment steady statemust satisfy (13); hence,𝜌𝜌 −𝛽𝛽 ′ (𝑚𝑚+𝑏𝑏)
𝑧𝑧+𝑏𝑏̇=> 0.
′𝑏𝑏𝑢𝑢 (𝜃𝜃+𝑧𝑧)(A3)

However, from (A2), if 𝜌𝜌 ≤ 𝛽𝛽0 /𝑢𝑢′ (𝜃𝜃 + 𝑧𝑧), we have𝜌𝜌 −𝛽𝛽 ′ (𝑚𝑚+𝑏𝑏)
𝛽𝛽0< 𝜌𝜌 − 𝑢𝑢′ (𝜃𝜃+𝑧𝑧)≤ 0,
𝑢𝑢′ (𝜃𝜃+𝑧𝑧)

implying that (A3) never holds. Therefore, in this case the full-employment steady state does
not exist and the stagnation steady state is reached.
In the stagnation steady state, 𝑐𝑐 𝑠𝑠 < 𝜃𝜃 + 𝑧𝑧, deflation continues and 𝑚𝑚 expands to infinity,

leading to 𝛽𝛽 ′ (𝑚𝑚 + 𝑏𝑏) = 𝛽𝛽0 and 𝑣𝑣 ′ (𝑚𝑚) = 0. Therefore, from (12) and (13),𝛽𝛽𝑐𝑐 𝑠𝑠 −𝑧𝑧

0 < 𝜌𝜌 − 𝑢𝑢′ (𝑐𝑐0 𝑠𝑠 ) = − 𝛼𝛼 � 𝜃𝜃 − 1� =𝑧𝑧+𝑏𝑏̇
𝑏𝑏

< 𝜌𝜌.

(A4)

From (A4), if 𝑏𝑏 is stable (𝑏𝑏̇ = 0), 𝑏𝑏 has a positive solution. If 𝑏𝑏 is expanding (𝑏𝑏̇/𝑏𝑏 > 0), 𝑏𝑏̇/𝑏𝑏

is less than 𝜌𝜌; hence, the transversality condition is valid. Therefore, both a stable asset priceand explosive bubbles are feasible.

Appendix B: Household-Size Weight
We consider various household-size weights on consumption using the following utility
function:

20

𝑐𝑐

1−𝜎𝜎

� 𝛿𝛿 �
−1∞
max ∫0 𝑒𝑒 −𝜌𝜌𝜌𝜌 �𝑛𝑛 𝑛𝑛 1−𝜎𝜎 + 𝑣𝑣(𝑚𝑚) + 𝛽𝛽(𝑎𝑎)� 𝑑𝑑𝑑𝑑,

where 𝑐𝑐/𝑛𝑛𝛿𝛿 is the standardized consumption per capita. By applying this function to Equation(3) we obtain𝑛𝑛−�

1−𝛿𝛿(1−𝜎𝜎)�𝜎𝜎

𝑐𝑐 = 𝑛𝑛−�(1−𝛿𝛿)(1−𝜎𝜎)
�
𝜎𝜎

1

𝜎𝜎
𝑅𝑅 𝑙𝑙
�𝑛𝑛� = �𝑣𝑣′ (𝑚𝑚)+𝛽𝛽′ (𝑎𝑎)� ≡ Θ,

𝑐𝑐

where Θ is constant for given financial asset holdings and 𝑅𝑅 𝑙𝑙 . From this property we obtain
𝑐𝑐 = 𝑛𝑛

In the text we adopt 𝜎𝜎 = 0.3.

1−𝛿𝛿(1−𝜎𝜎)
𝜎𝜎

Θ,

𝑐𝑐

= 𝑛𝑛
𝑛𝑛

(1−𝛿𝛿)(1−𝜎𝜎)
𝜎𝜎

Θ.

(A5)

Many studies (e.g., Buhmann et al. 1988; Gottschalk and Smeeding 1997; Mani et al.

2013) adopt a square root of the household size as the equivalence scale (i.e., 𝛿𝛿 = 0.5). In thiscase, as the household size is doubled, household consumption 𝑐𝑐 is 4.5 times more and per

capita consumption 𝑐𝑐/𝑛𝑛 is 2.2 times more, which are both unrealistically too high. Moreover,if 𝛿𝛿 < 1, the power exponent of 𝑛𝑛 in the second equation of (A5) is positive, implying that 𝑐𝑐/𝑛𝑛
increases as 𝑛𝑛 is larger, which is unrealistic.

If 𝛿𝛿 = 1, 𝑐𝑐/𝑛𝑛 is unchanged regardless of the value of 𝜎𝜎 . As 𝛿𝛿 is larger, 𝑐𝑐/𝑛𝑛 sharply

decreases. For example, it becomes 0.85 times if 𝛿𝛿 = 1.1, and 0.72 times if 𝛿𝛿 = 1.2. Thus, we
assume 𝛿𝛿 = 1.

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Figure 2—Trends in relationship between financial assets andconsumption in the United States

20

Figure 1—Trends in relationship between financial assets andconsumption in Japan

Household consumption per capita
in 100 thousand JPY
5
10
15

1990s

2000s

2010s

1980s

0

1970s

0

20

40
60
80
100
Household net financial assets per capita
in 100 thousand JPY

120

Source: System of National Accounts in Japan.
Notes：This figure shows the macro trends of the relationship between household financial
assets per capita and consumption per capita, excluding imputed rent, in Japan. The sample
covers the period from 1970 to 2019, and the value of assets and consumption are shownwith different symbols for each decade. The values of assets and consumption are real values
based on 2015 values.

Source: U.S. Bureau of Economic Analysis.
Notes：This figure shows the macro trends of the relationship between household financial
assets per capita and consumption per capita, excluding imputed rent, in the United States.
The sample covers the period from 1970 to 2019, and the value of assets and consumption
are shown with different symbols for each decade. The values of assets and consumption are
real values based on 2017 values.

Figure 3—Relationship between (𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐧𝐧𝐢𝐢𝐢𝐢 )−𝟎𝟎.𝟑𝟑 and (𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐭𝐭 𝐢𝐢𝐢𝐢 )−𝟎𝟎.𝟑𝟑

Notes: This figure shows the relationship between (𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑡𝑡𝑖𝑖𝑖𝑖 )−0.3 and (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑛𝑛𝑖𝑖𝑖𝑖 )−0.3.
The box plot illustrates the median and 25 and 75 PCTLs of consumption with the 95% confidence
interval bar for each asset level, and the predicted line is based on a single regression.

Figure 4—Robustness check

Notes: This figure illustrates the intercept estimates from the model shown in column (3) of Table 2 and their 95%
confidence intervals for several different values of σ and ω. The vertical axis represents the intercept estimates, thehorizontal axis represents ω ranging from 0.1 to 0.9, and the dots with different symbols are plotted for different values of
σ ranging from 0.2 to 0.6.

Figure 5—Actual and predicted values of consumption

Notes: The top panel shows the predicted value of consumption for each financial asset value from our model as dots andthe 25th to 75th percentile range bar for the raw value of consumption. The bottom panel shows the distribution of financial
asset holdings in the sample.

Table 1—Descriptive statistics
Variables

Obs

Mean

Std. Dev.

Min

Max

Financial Asset

29,2721324.278

1715.548

125

7500

Consumption

29,272

6.985

5.018

1

130

House Owner

29,272

0.861

0.346

0

1

Single29,272

0.062

0.241

0

1

Couple29,272

0.217

0.412

0

1

Parents + Child(ren)29,272

0.446

0.497

0

1

Single parent + Child(ren)29,272

0.053

0.225

0

1

3 generations

29,272

0.131

0.338

0

1

3 generations including parent's sibling

29,272

0.008

0.087

0

1

Others29,272

0.083

0.276

0

1

20s

29,272

0.036

0.187

0

1

30s

29,272

0.115

0.319

0

1

40s

29,272

0.208

0.406

0

1

50s

29,272

0.250

0.433

0

1

60s

29,272

0.257

0.437

0

1

70s

29,272

0.134

0.340

0

1

Junior High School

29,272

0.125

0.331

0

1

High School

29,272

0.463

0.499

0

1

Vocational School, Collage

29,272

0.076

0.265

0

1

University

29,272

0.308

0.461

0

1

Master29,272

0.024

0.152

0

1

Doctor29,272

0.005

0.069

0

1

Types of Family

Age of Household head

Educational Background of Household Head：

Notes: Data are from the Japan Household Panel Survey on Consumer Preferences and Satisfaction (JHPS-CPS) in 2005–
2013 and 2016–2019 conducted by the Institute of Social and Economic Research (ISER) at Osaka University. The
definitions of financial asset and consumption variables are found in Section 3 (A).

Table 2—Main results(1)

Outcome: (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑛𝑛𝑖𝑖𝑖𝑖 )−0.3
(2)

(3)

0.545***

0.371***

0.399***(0.015)(0.016)(0.016)0.515***

0.514***

0.513***(0.004)(0.005)(0.008)

Mean

0.611

0.611

0.611

Observations

27842

27842

27842

✓

✓

✓

✓

✓

(𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑡𝑡𝑖𝑖𝑖𝑖 )−0.3
A (intercept)

Year Fixed EffectRegional Fixed EffectHousehold Characteristics
P-value (𝐻𝐻0 : A ≤ 0)

✓
0.000

0.000

0.000

Notes: This table reports the estimates based on Equation (17). Section 3 (A) provides the definitions of financial asset
and consumption variables. Column (1) reports the estimation results controlling only for year dummies. Column (2)reports the results with the region dummies added to the control variables in column (1). Column (3) reports the resultswith household characteristics added to the control variables in column (2). The p-value at the bottom of each column
reports the result of the one-tailed test of H0 : A ≤ 0. Robust standard errors are in parentheses. Significance levels: ***p<0.01, ** p<0.05, and * p<0.10.