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5Comparison of Various Fiscal Policies in the Face of Different

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Demographic Stages

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Naoyuki Yoshino
Keio University

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Keigo Kameda
Kwansei Gakuin University

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Hiroaki Miyamoto

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Hitotsubashi University

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Zhenkun Lu*
Kwansei Gakuin University

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April, 2024

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*

Corresponding author: School of Policy Studies, Kwansei Gakuin University
Gakuen-Uegahara, Sanda, Hyogo 669-1337, Japan, Email: gys53987@kwansei.ac.jp

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Abstract
This study examines the impact of aging on the effectiveness of various fiscal
expenditures, including government consumption, one-time governmenttransfers to households, public investment, and R&D spending, using a dynamic
stochastic general equilibrium model. Our findings reveal that (1) Agingenhances the effects of the transfer on augmenting GDP. (2) Regardless of aging,
R&D expenditure consistently stands out over all time spans, with younger
society benefiting more. (3) Public investment ranks second among 4 different
fiscal policies compare in the long run while younger society shows bigger
impact. (4) Government consumption has only a temporary effect and is theleast effective in boosting GDP in both young and old societies. (5) Multipliers
for public investment and R&D expenditure increase with the accumulation of
public capital and TFP. The multipliers of young society is larger than oldsociety because impact on consumption is much more effective.

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Keywords: Fiscal Policy Effectiveness, Aging Population, Japan, DSGE

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Model.
JEL Code: E62, H30, J1

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Acknowledgements
We thank Kazuki Hiraga for his valuable comments at the 2023 Spring
Conference of the Japanese Economic Association. Any errors or inaccuracies
that may exist are solely the responsibility of authors. This study is supportedby the Japan Society for the Promotion of Science (Grant-in-Aid for Scientific
Research # 19K21712, 21K01525, 22K01564 and Grant-in-Aid for JSPS
Fellows # 23KJ2120).

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1. Introduction

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Population aging presents a significant challenge for policymakers acrossboth developed and developing countries (Figure 1). Recent studies have thus
explored the link between population aging and the effectiveness of fiscal
spending. Honda and Miyamoto (2021) found that aging reduces the outputenhancing effects of fiscal expenditure in OECD countries during recessions.
Similarly, Basso and Rachedi (2021) identified larger fiscal multipliers in U.S.
states characterized by younger populations. Miyamoto and Yoshino (2022)
found that aging diminishes the impact of fiscal stimulus on private
consumption and employment.１
Despite these insights, there remains a significant gap in understanding how
aging influences the outcome of various fiscal measures. Moreover, theliterature has yet to fully explore the heterogeneity in the effects of different
fiscal expenditures. A critical oversight is the lack of detailed analysis regarding
in the underlying mechanisms through which population aging impacts thesefiscal measures
Addressing these gaps, this paper compares various fiscal policies facing
different stages of demography using a dynamic stochastic general equilibrium(DSGE) model that includes both workers and retirees, developed by Yoshino
and Miyamoto (2017).２ We offer three key expansions: First, we thoroughly
investigate how aging influences the macroeconomic effectiveness of fiscal
expenditures. Second, we compare a wide range of fiscal policies, including (i)government consumption aimed at stimulating aggregate demand, (ii) universal
government transfers to all generations, (iii) public investment in infrastructure,and (iv) R&D expenditure fostering technological progress. The first two
policies primarily aim to stimulate aggregate demand in the economy, while theIn the context of Japan, Bessho (2021) demonstrated higher fiscal multipliers in regionswith younger populations.
２
As Yoshino and Le (2022) shows, analysis of aging using an overlapping generations(OLG) model is possible, demonstrating the potential for a decline in the effectivenessof fiscal and monetary policies. However, akin to Yoshino and Miyamoto (2017),
introducing heterogeneous agents into a DSGE model, accommodating both workers
and the elderly simultaneously, allows for an analysis of policy in scenarios where theproportion of the elderly changes. Thus, we argue that the method utilized in this paper
is superior to OLG.
１

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latter two contribute to enhancing aggregate supply.
The results of our policy simulation are summarized as follows: Firstly, theGDP-enhancing effect of the three policies (namely, government consumption,
government investment and R&D expenditures), other than one-timegovernment transfer, decreases with aging. Aging implies an increase in theshare of policy-irrelevant, stable consumption among retirees in aggregate
consumption, thereby weakening the demand expansion effect of the threepolicies other than one-time transfers. Meanwhile, the output multiplier effectof the transfer gives a greater demand expansion effect with aging due to a larger
increase in the sum of retirees' consumption. Secondly, regardless of the degreeof aging, R&D expenditure consistently emerges as the most effective measureacross all time spans due to its considerable impact on aggregate supply. Public
investment ranks second in the long run, while government consumption takes
this position in the short run. The one-time transfer is the least effective in
expanding GDP in any time spans except for the very short term. Thirdly,
government consumption multipliers tend to decrease over time after policy
implementation, indicating stronger short-term stimuli but weaker long-term
effects. These time-dependent changes in fiscal multipliers become more
pronounced as aging progresses. Moreover, the rank of fiscal policies’ welfare
multiplier aligns with the output multiplier. Furthermore, demographic aging
significantly diminishes the welfare benefits from policies enhancing aggregate
supply, underscoring the need for nuanced policy considerations in the face ofshifting demographic structures.
The paper proceeds as follows: Section 2 extends the New Keynesianmodel with retired workers. Section 3 calibrates the model. Section 4 examines
fiscal policies' impacts. Section 5 compares various fiscal policies in face ofdifferent demographic stages. Section 6 presents conclusions.

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2. The Model

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Our model consists of four sectors: households, firms, government, and

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central bank. Households are conceptualized as a continuum distributed overthe interval [0,1] . Within this framework, a proportion 𝜙 of households ischaracterized as workers, while the rest represents retirees. In addition toheterogeneous households, our model incorporates monopolistic competitionand price stickiness among firms, following Calvo (1983). The government
operates under a budget constraint, collecting revenue through lump-sum taxes
and influencing the economy through various fiscal spendings. The central bankbalances inflation and economic growth stability by controlling the nominalinterest rate.
As our model's household and firm settings are similar to those of Yoshino
and Miyamoto (2017), we focus on describing the main modifications here. Bychanging elderly ratio we can analyze the impact of various fiscal policies inyoung economy.

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2.1 Household's Problem
We begin with the worker's problem. In the standard New Keynesian model,
government consumption is wasteful expenditure, crowding out private
consumption through a negative wealth effect. However, many empiricalstudies on macro-data in Japan have ascertained that an increase in government
consumption positively influences private consumption (see, for instance,
Kameda, 2014; Morita, 2015). To better reconcile with this finding, Yoshino andMiyamoto (2017) introduces imperfect substitutability between private andgovernment consumption in households’ utility function. Consequently, theexpected lifetime utility function of a worker is given by

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(1)
where β∈ (0,1) is subjective discount factor, 𝑐𝑤,𝑡 is one worker's consumption,
𝑔𝑡 is government consumption of such services as hospital service, free public
transportation, etc., and ℎ𝑤,𝑡 is work hours. The parameter 1/σ is intertemporalelasticity of substitution, and 1/μ is the Frisch elasticity of labor supply. The
parameter ζ is the elasticity of substitution between private and government
consumption, and the share parameter ω determines how much government
consumption affects utility.

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The budget constraint of a worker is as follows:

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(2)

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where 𝑤𝑡 is real wages, 𝑟𝑡 is the real interest rate, 𝑅𝑡 is the gross nominalinterest rate, 𝑑𝑤,𝑡 is the dividend that the worker receives from the firm sector,
𝜏𝑤,𝑡 is the lump-sum tax, 𝑇𝑅𝑤,𝑡 is the one-time transfer received by workers,

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and 𝜋𝑡 ≡ 𝑃𝑡 /𝑃𝑡−1 is the gross inflation rate.
The accumulation of one worker’s capital stock is given by

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(3)

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where δ is the depreciation rate and 𝑖𝑤,𝑡 is investment of one worker.
The worker chooses consumption 𝑐𝑤,𝑡 , capital stock 𝑘𝑤,𝑡 , and government
bonds 𝑏𝑤,𝑡 to maximize the above expected lifetime utility subject to the budget

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constraint and capital accumulation equation. The first-order conditions are as
follows:

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(4)

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(5)

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(6)

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(7)

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where 𝜆𝑡 is the Lagrange multiplier on the budget constraint, which also
represents the worker’s marginal utility of income.

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The remaining measure of 1 − ϕ households is retired. The lifetime utility
function of a retiree is given by

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(8)

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where 𝑐𝑟,𝑡 is one retiree's consumption.

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Following Yoshino and Miyamoto (2017), retirees are not confronted withthe trade-off between saving and consumption. Nevertheless, considering the

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uniformity of pension disbursements over time and anchored in the principle ofconsumption smoothing, it follows logically that a retiree's optimal
consumption mirrors the pension they receive. Thus, the consumption of one
retiree 𝑐𝑟,𝑡 is

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(9)

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where 𝑠 × 𝑤
̅ is the pension related to the steady state value of real wages.
Moreover, 𝑇𝑅𝑟,𝑡 is the one-time transfer received by retirees.

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2.2 Firm's Problem
As we explained earlier, there are two types of firms: a perfectly competitive
final good firm and monopolistic competitive intermediate goods firms indexedby j∈ [0,1]. No corporate tax is considered for simplicity.

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The final good 𝑌𝑡 is produced by combining a continuum of differentiatedintermediate goods 𝑦𝑗,𝑡 . The production function is given by

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(10)

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where ε governs the degree of substitution between different inputs.
The final good producer is perfectly competitive and maximizes real profits
subject to (10). Thus, the problem of the final good producer is

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(11)

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This yields the demand for intermediate goods:

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(12)

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Substituting (12) into (10), we have the following relationship between theaggregate price level and the prices of intermediate goods:

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(13)

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The production function of intermediate goods firm j is given by

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(14)

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where 𝑘𝑗,𝑡−1, 𝑘𝑔,𝑡 and ℎ𝑗,𝑡 represent private capital, aggregate public capital and24
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labor services hired by firm j, and 𝐴𝑡 denotes the TFP. Public capital is treatedas exogenous for simplicity.
Cost minimization implies

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(15)

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This equation implies that the capital-labor ratio is equalized acrossintermediate goods producers. Then, the marginal costs of firms are given by

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(16)

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We assume that intermediate goods firms are subject to price setting frictions
à la Calvo (1983). Thus, an intermediate goods firm can set its price optimallywith probability 1–ξ, and with probability ξ, it must keep its price unchanged
relative to what it was in the previous period:
(17)

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A firm optimizing its price maximizes
(18)

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subject to the demand function
(19)

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and where 𝑃𝑡∗ is the optimal nominal price.
The profit maximization problem yields

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(20)

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Finally, combine with Eq. (13), the law of motion for the aggregate price levelis given by

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(21)

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2.3 Aggregation of the economy
The aggregate level of any consumer-specific variables 𝑥𝑖,𝑡 where 𝑖 ∈ {𝑤, 𝑟}
1

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is given by 𝑥𝑡 = ∫0 𝑥𝑖,𝑡 𝑑𝑖 = 𝜙𝑥𝑤,𝑡 + (1 − 𝜙)𝑥𝑟,𝑡 , as households in each of the23

two groups are identical. Hence, aggregate consumption 𝑐𝑡 is given by
(22)

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Since only workers provide labor services and retirees keep constant real2

deposits (capital stock), the aggregate hours of worker ℎ𝑡 , aggregate capital
supply 𝑘𝑡 , and aggregate investment 𝑖𝑡 are given by
(23)
(24)
(25)

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We assume that the one-time transfer payments for retirees and workers are
identical. Consequently, the aggregated transfer payments can be expressed as:

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(26)

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Similarly, only workers hold financial assets, receive dividends from firms,
and pay the lump-sum tax. Thus, we have
(27)
(28)
(29)

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In this paper, policy effects in different aging economy will be compared

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by changing the value of 𝜙 in Section 5.

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2.4 Fiscal and Monetary Authorities

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The government purchases goods for consumption 𝑔𝑡 , public investment
purpose 𝑖𝑔,𝑡 , R&D expenditure for technology 𝑅𝐷𝑡 , social security benefits22(1 − 𝜙)𝑠𝑤
̅, and one-time transfer 𝑇𝑅𝑡 . It finances them by levying the lump-

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sum tax and issuing government bonds. Hence, the government budget
constraint in real terms is given by

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(30)

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The accumulation of public capital follows:
(31)

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Public investment 𝑖𝑔,𝑡 follows a stochastic process:

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(32)

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Government consumption 𝑔𝑡 follows a stochastic process:
(33)

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Similarly, the one-time transfer follows:

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(34)

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For representing the effect of R&D expenditure 𝑅𝐷𝑡 , we specify that the
TFP follows the stochastic process below３.

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(35)

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Moreover, the R&D expenditure shock takes the following form:

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(36)

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where 𝜌𝑅𝐷 is the persistency of R&D expenditure shock.
Furthermore, we allow for debt financing but assume a tax rule exists tokeep the level of real debt constant in the long run. Thus, the tax rule is

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(37)

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where ψ is the feedback parameter from debt to taxes. The monetary policy
follows a Taylor rule,

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(38)

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In the second term of equation (33), we adjust the ratio of R&D expenditure
to GDP by subtracting its steady-state value, ensuring that TFP eventuallyconverges to its steady-state level. This adjustment is crucial for ensuring thatthe model possesses a well-defined steady state without growth trend, following
Minford and Meenagh (2019).
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where any variable without a time subscript denotes the corresponding steady-2
4state value of the variable, 𝜑𝜋 Indicates how strongly the monetary authority
responds to deviations of inflation from target, 𝜑𝑌 is the response to the output
gap, and 𝜐𝑡 follows a stochastic process:

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(39)

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2.5 Market Clearing Conditions
The labor market is in equilibrium when the labor demand by the intermediate1

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goods firms ℎ𝑡 ≡ ∫0 ℎ𝑗,𝑡 𝑑𝑗 is equal to the labor services supplied by workers.

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Similarly, the capital rental market is in equilibrium when the demand for capital11

by the intermediate goods firms 𝑘𝑡 ≡ ∫0 𝑘𝑗,𝑡 𝑑𝑗 equals to the capital supply. The

1216monetary policy rule determines the nominal interest rate. In order to maintainmoney market equilibrium, the money supply adjusts endogenously to meet themoney demand at those interest rates. The final good market is in equilibrium
when the supply by the final good firms (Eq. 10) equals the demand by
consumers and the government:

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(40)

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3. Calibration for quarterly macroeconomic data

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Calibrating the model, we utilize Japanese data, which reflects the mostpronounced aging trends worldwide, as summarized in Table 1. The model

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period is set to one quarter, with a subjective discount factor of 𝛽 = 0.99 ,implying a 4% per year steady-state real interest rate.
Following existing studies, we calibrate parameters in the consumer utility26function. We set the risk aversion parameter 𝜎 = 1.0 following the estimation

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of Sugo and Ueda (2008). In addition, 𝜇 is set at 2.0 indicating a Frisch elasticity
of 1/𝜇 = 0.5, in line with micro evidence (Kuroda and Yamamoto, 2008). We
set the share parameter of public and private goods 𝜔 = 0.6 and elasticity of
substitution 𝜁 = 0.4 based on Hamori and Asako (1999) and Brückner and

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Pappa (2012).
Turning to the production function, we target capital share with α=1/3 andnormalize the steady state of technology level to 𝐴̅ = 1. Based on the estimationof Kameda et al. (2022), we set the elasticity of output with respect to public
capital 𝛼𝑔 = 0.2 . We set the deprecation rate 𝛿 = 0.028 following EstebanPretel et al. (2010).
Next, we calibrate nominal rigidity parameters based on existing studies.

9Specifically, demand elasticity is set to ϵ = 11, implying a steady-state markup
of 10%. Considering estimates from Iiboshi et al. (2006), Sugo and Ueda (2008),

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Ichiue et al. (2013), and Kuo and Miyamoto (2016), we set the Calvo parameter11

to 𝜉 = 0.8 , indicating an average contract duration of approximately fivequarters.

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We determine the fraction of workers ϕ based on the ratio of the population
aged 20–64 to those aged 20 or older, setting ϕ = 0.85 according to the
National Institute of Population and Social Security Research.
As for policy parameters, to maintain comparability with existing studies(Clarida et al. 1998; Fujiwara et al. 2007; Fujiwara et al. 2008) we set 𝜑𝜋 = 1.5
and 𝜑𝑌 = 0.1 for the Taylor rule.
Based on relevant surveys, Explanation of the Statistical Survey of Actual
Status for Salary in the Private Sector conducted by the National Tax Agency,
and the Annual Report on the Public Pension System conducted by the Ministryof Health, Labour and Welfare, we set the ratio of average pensions to averagesalary 𝑠 to 0.4. Additionally, we establish steady-state values for thegovernment spending to GDP ratio (𝑔̅ /𝑌̅ = 0.16), one-time transfer to GDP̅̅̅̅ /𝑌̅ = 0.03), public investment to GDP ratio (𝑖̅𝑔 /𝑌̅ = 0.06) and debt toratio (𝑇𝑅29

GDP ratio (𝑏̅/𝑌̅ = 1.7), following Yoshino and Miyamoto (2017). The steadystate value for R&D expenditure to GDP ratio ̅̅̅̅𝑅𝐷/𝑌̅ is set to 0.04 based on dataof Chun et al. (2012). Following Kato and Miyamoto (2013), we set government
spending autoregressive parameters 𝜌𝑔 = 𝜌𝑅𝐷 = 𝜌𝑡𝑟 = 0.9, the same as each30

other for comparison. Lastly, following Gali et al. (2007), we consider a3133

moderately persistent monetary shock and set 𝜌𝜐 = 0.5.
Furthermore, we calibrate the persistency parameter of TFP, 𝜌𝑎 , and theelasticity of TFP with respect to R&D expenditure 𝜌𝑎𝑔 through an empirical34

study for Japan as follows. Chun et al. (2012) estimates the relationship between

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the growth rate of TFP and R&D expenditure as follows:23
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where 𝛽1 and 𝛽2 is estimated as 0.61 and －0.13, respectively. We can rewrite this regression equation as follows:5
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Therefore, we can calibrate the values of 𝜌𝑎 and 𝜌𝑎𝑔 to match the stochastic
process of TFP in Eq. (33) with this regression equation.

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Overall, our calibration is based on existing studies and statistical data, andwe believe it provides a reasonable representation of the Japanese economy.
Finally, drawing on the approach used by Yoshino and Miyamoto (2017),

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we set the labor participation rates 𝜙 at 0.85 and 0.55 respectively, to simulate
the effects on fiscal policy. This method allows for a nuanced understanding of
how changes in population structure can influence macroeconomic dynamics

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after the implication of fiscal policies. With a labor participation rate 𝜙 = 0.85,

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we set the debt-to-taxes feedback parameter 𝜓 to 0.1 following Mayer et al.
(2010). To maintain consistent tax revenues across different population

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structures, we adjust 𝜓 to 0.067 when 𝜙 = 0.55. This change only affects the
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dynamics of lump-sum taxes and national debt, with no impact on other20
variables.
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Table 1: Parameter values (quarterly basis)
Parameter Description
Value
Source/Target
Discount factor
0.99
Data
𝛽
Relative risk aversion parameter
1.0
Sugo and Ueda (2008)𝜎
Kuroda and Yamamoto
The inverse of Frisch elasticity
2.0𝜇(2008)
Share parameter of government𝜔
0.6
Hamori and Asako (1999)
consumption
Elasticity of utility function
0.4
Brückner and Pappa (2012)𝜁
Capital share
1/3
Data
𝛼
Elasticity of output with respect to𝛼𝑔
0.2
Kameda et al. (2022)
public capital
Steadystateofaggregate 1.0
Normalization
𝐴̅
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𝛿

productivity
Depreciation rate

0.028

𝜖

Elasticity of demand

11

𝜉
𝜙
𝜑𝑦
𝜑𝜋
𝜓

Calvo parameter
Fraction of workers
Taylor rule coefficient for output
Taylor rule coefficient for inflation
Feedback parameter in the tax rule

0.8
0.85
0.1
1.5
0.1 and 0.067𝑠Social security benefits to wage ratio 0.4𝑔̅ /𝑌̅

Government spending to GDP ratio

0.16

̅̅̅̅/𝑌̅𝑇𝑅

One-time transfer to GDP ratio

0.03

𝑖̅𝑔 /𝑌̅

Public investment to GDP ratio

0.06

𝑏̅/𝑌̅

Debt to GDP ratio

1.7

̅̅̅̅
𝑅𝐷/𝑌̅

0.06
0.9

Kato and Miyamoto (2013)

0.5
0.9

Gali et al. (2007)
Kato and Miyamoto (2013)

0.9

Kato and Miyamoto (2013)

0.87

Chun et al. (2012)𝜌𝑎𝑔

R&D expenditure to GDP ratio
Persistency of gov. consumption
shock
Persistency of monetary policy shock
Persistency of one-time transfer
Persistency of gov. R&D expenditureshock
Persistency of TFPElasticity of TFP with respect to
R&D expenditure

Esteban-Pretel et al. (2010)
10% steady-state markup
rate
Kuo and Miyamoto (2016)
Data
Fujiwara et al. (2008)
Fujiwara et al. (2008)
Mayer et al. (2010)
Annual Report on the Public
Pension System
Yoshino and Miyamoto(2017)
Yoshino and Miyamoto(2017)
Yoshino and Miyamoto(2017)
Yoshino and Miyamoto(2017)
Chun et al. (2012)

0.61

Chun et al. (2012)

𝜙Labor participant ratio

0.85 and 0.55

Yoshino(2017)

𝜌𝑔
𝜌𝜈
𝜌𝑡𝑟
𝜌𝑅𝐷
𝜌𝑎

and

Miyamoto

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4. Quantitative Analysis

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This section will consider how aging change the macroeconomic effects ofthe four types of government fiscal policies, i.e., government consumption on
public goods, 𝑔𝑡 , universal one-time government transfers to all generations,
𝑇𝑅𝑡 , public investment in infrastructure 𝑖𝑔,𝑡 , and the R&D expenditureaugmenting TFP, 𝑅𝐷𝑡 .
In the steady state, the ratios of the four fiscal expenditures to GDP vary, as

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shown in Table 1. When applying a 1% policy shock to each, the actual increasein expenditure differs for each type. For example, a 1% shock in government
consumption leads to a 0.16% rise in the GDP's steady state value. In contrast,
a 1% one-time transfer shock results in only a 0.03% rise. So, it's not accurate
to compare these policies by just using a 1% shock. To make a fair comparison,
we adjust the shock size so that the initial increase in each expenditure type isequal to 0.01% of the GDP's steady-state value.
Before the comparison, we show the impulse responses to a 0.01% GDP
increase in government consumption, assuming no complement effects withprivate consumption in Figure 2 as a benchmark.４ These responses, as expected,
closely resemble the outcomes in the standard Real Business Cycle model. The
anticipated future tax burden on workers triggers a negative wealth effect,leading to a reduction in their consumption. This effect, in turn, raises labor
supply and savings. However, the rise in government consumption outweighs
the decrease in private consumption, thereby boosting aggregate demand. In thecapital market, the additional national debt absorbs households' savings,
diminishing the supply of productive capital. Despite this, the expansion of
aggregate demand increases capital demand, overwhelming the supply.
Consequently, the real interest rate rises, and private investment is crowded out.

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In the labor market, the increase in labor supply exceeds the heightened labordemand, causing a decline in real wages. In a parameter setting reflecting theJapanese economy, the increased real interest rate and decreased real wage leadto a rise in the marginal cost of intermediate goods for firms, resulting in an
increase in the inflation rate. Furthermore, the central bank raises the nominalinterest rate through the Taylor rule.
Following the initial shock, the increment of government consumption
declines. However, the accumulation of debt continued, leading to a sustained
rise in real interest rate. Consequently, the marginal costs and inflation rates also
increases, along with nominal interest rates. Also, this increase in real interest
rate decreases the labor supply through factor substitution, which makes wage

31

recovers to its steady state.

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In this case, we set the share parameter, 𝜔, for private consumption in the utility function
to 1. Consequently, government consumption does not augment the marginal utility ofprivate consumption and becomes a kind of 'wasteful expenditure'.
４

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Let us now examine the effects of aging on this fiscal spending, comparing

2

macroeconomic responses under two different demographic structures, 𝜙 =0.85 and 0.55. Given the complexity of causal mechanisms involved, wecategorize these effects into two components: the demand-side aging effect andthe supply-side aging effect.
On the demand-side, aging works to weaken the policy effects. Aggregate
consumption consists of the weighted sum of workers’ and retirees’
consumption. An increase in government expenditure decreases workers’
consumption through the negative wealth effects. Meanwhile, aging means a

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decrease in the share of workers in total population. Under our parametersettings, this decreased share effects overwhelms the negative wealth effects.
Therefore, aging reduces the increase in aggregate consumption thatgovernment aims to expand. We call this mitigation effect of aging “the demandside aging effect.” Note that retirees are characterized by their Rule-of-Thumbbehavior but shielded from the volatility of labor income due to their stablepension incomes. ５
On the other hand, aging concentrates the tax burden on a smaller amountof workers. Therefore, when the government increases fiscal expenditure in the
aging economy, the resultant reduction in workers' lifetime income amplifies
the increase in factor supply: labor supply and saving. We refer to this factorincreasing effects as “the supply-side aging effect.”
Based on these two-side effects, let us consider the total aging effect. Whenthe government expands their consumption in an aging economy (𝜙 = 0.55),
aging works to mitigate the policy effect through the demand-side aging effects,
resulting in a smaller decrease in aggregate consumption. As evident, this leads
to a greater increase in aggregate demand, and subsequently, in labor and capital

５This setting is different from Gali et al. (2007), which also introduced a segment ofhouseholds—those adhering to the Rule-of-Thumb consumption behavior—into theirmodel. These households do not save and thus their consumption is equal to their labor
income. Gali et al. (2007) reported that an increase in government consumption not only
elevates the labor income of these Rule-of-Thumb households but also intensifies the
positive repercussions on aggregate consumption and output.

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demand. On the other hand, the supply-side effects are amplified by aging,
resulting in a greater increase in factor supply. In the labor market, the supply
overwhelms the demand; therefore, the real wage is lower than in the case of
𝜙 = 0.85. In contrast, real interest rates become higher in the capital market.
Under our parameter setting, the changes in factor prices does not change themarginal cost of intermediate good for firms, thereby have a little influence in
the inflation rate and nominal interest rate

8
9

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Figure 2: Impulse responses to a 0.01% increase of GDP in government
consumption without complimentary effect(Basis point deviation from steady state values)

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Note: Impulse responses reflect basis point deviations from steady-state values.
Red lines labeled “ϕ=0.85” show responses from the model with higher labor
participation, while blue lines labeled “ϕ=0.55” show responses from the model

18

with lower labor participation.

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4.1 Case 1: Effects of an increase in government consumption withcomplimentary effect on private consumption

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Figure 3 shows the impulse responses to a 0.01% GDP increase ingovernment consumption that has the complement effects as shown in Eq. (4).
In this case, since the government consumption raises the marginal utility of
consumption of workers, it bolsters aggregate consumption to large extent.
Therefore, aggregate demand increases more than in the benchmark case,leading to higher demand of labor and capital. However, to compensate theincreased consumption, workers supply both factors more than in thebenchmark case, causing a greater drop in real factor prices. Similar to thebenchmark case, changes in factor prices result in a rise in the marginal costs
under our parameter settings, causing an increase in the inflation rate.
After this initial shock, government consumption declines gradually. As aresult, the marginal utility of private consumption drops down, resulting in a
decline in private consumption and the factor supply of workers. As a result,real wages slightly recover, real interest rates rise, and so do nominal interest
rates and inflation rates.
As seen in the benchmark case, in the aging economy with ϕ=0.55, the tax
burden concentrates on a smaller number of workers, leading to a greater
reduction in their consumption. However, since the effect of government
consumption on increasing the marginal utility of consumption is stronger when30

consumption levels are lower, per capita consumption of workers in the aging
economy increases more than in the younger economy with ϕ=0.85, in contrast
with the benchmark case. This, in turn, through equations (4) and (5), moderates
the increase in labor supply in the aging economy and consequently results in amoderate decrease in wages.
Having said that, since there are more workers in the younger economy,
aggregate consumption increases more than in the aging economy. Therefore,
the impact on output at the initial stage becomes more significant in the younger
economy. However, this expansion of consumption through equations (4) and(5), implies a decrease in savings, and the resulting decrease in capital
accumulation shrinks production. Thus, the long-term policy effects are smaller31

in the younger economy.

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Figure 3: Impulse responses to a 0.01% increase of GDP in government.
consumption (Basis point deviation from steady state values)

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5
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8

Note: Impulse responses reflect basis point deviations from steady-state values.
Red lines labeled “ϕ=0.85” show responses from the model with higher labor
participation (i.e. younger economy), while blue lines labeled “ϕ=0.55” show
responses from the model with lower labor participation (i.e. aging economy).

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4.2 Case 2: Effects of an increase in one-time transfer to all generations
Figure 4 shows the impulse responses to a 0.01% increase of GDP in onetime government transfer to all generations. Increased transfers can beinterpreted as a combination of increased taxes on workers and increased
income to retirees and workers, given that this transfer is financed exclusively
by future lump-sum taxes collected from workers. Note that the fact that thecomplemental effects of government consumption don’t work for one-timetransfer.
The mechanism of one-time transfer operates as follows: On one hand, thenegative wealth effect from tax hikes leads to a decline in consumption ofworkers. Meanwhile, retirees consume all of the transfers from the government
due to their rule-of-thumb behavior. As a result, aggregate consumption

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increases. The same factor price mechanism explained in the benchmark case,which increases real interest rates and decreases real wages, is at play here as
well, resulting in a decline in a decrease in inflation rates and nominal interest
rates６.
In examining the impact of aging on the effectiveness of a one-time transfer
policy under ϕ=0.55, a crucial observation is that retirees deplete the entire
transfer amount. Consequently, despite the presence of the demand-side aging
effect, aggregate consumption experiences a more pronounced increase in an
aging economy with ϕ=0.55. The supply-side aging effect leads to a marked
increase in their factor supply, subsequently resulting in a notable decrease inreal wages in the aging economy. Because the effects of real wages on themarginal cost of intermediate goods surpass those of real interest rates in theinitial period, the marginal costs and inflation rates become negative initially,
then increases along with a rise in the factor prices.
Overall, contrasting with the benchmark case, population aging enhances thedemand-side effect of transfer payments, leading to a greater increase in the
inflation rate.

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The dynamics of the labor and capital markets are analogous to the case of government
consumption in Section 4.1, and therefore, will not be elaborated further.
６

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Figure 4: Impulse responses to a 0.01% increase of GDP in one-time transfer.
(Basis point deviation from steady state values)

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6
7

Note: Impulse responses reflect basis point deviations from steady-state values.
Red lines labeled “ϕ=0.85” show responses from the model with higher labor
participation, while blue lines labeled “ϕ=0.55” show responses from the modelwith lower labor participation.

89

4.3 Case 3: Effects of an increase in public investment

10

Figure 5 depicts the impulse responses to a 0.01% increase in GDP
resulting from public investment. On the demand side, public investment works
similarly to the benchmark ones. Therefore, the aggregate demand increases.
Meanwhile, this policy enhances the productivity of intermediate goodfirms, leading to higher future income rise for workers. Therefore, the increasein factor supply from workers is less than that in the benchmark case.
Simultaneously, the increased productivity moderates the factor demandcompared to the benchmark. As a result, in the initial period, real wages arealmost invariant and real interest rates increase more in contrast to thebenchmark case. The mixed effects of this invariant wage and the increased real

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interest rates initially drive up the marginal costs and inflation rates.
Following these initial shocks, public investment starts generating positive
externalities in the productivity of intermediate goods, causing their marginal
cost to decrease as public capital accumulates. This downward trend leads to a
gradual decrease in inflation. The nominal inflation rate reflects these responses
through the Taylor rule. In addition, the accumulation of public capital results
in an increase in output, which subsequently causes both consumption andinvestment to respond positively in the medium term.
In an aging economy with ϕ=0.55, the increase in output after public
investment becomes lower, but the impact is quantitatively insignificant, asshown on the vertical scale. Qualitatively, the influence of aging manifests asfollows:
On the demand side, the additional income generated by public investment
concentrates on a smaller proportion of workers, and this, in turn, increases
consumption per worker. However, the demand-side aging effect works, so a

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comparatively lower aggregate consumption is observed in an aging economy.
Meanwhile, because of this increased income per worker, the supply-side
aging effects is weakened in the aging economy. Consequently, real wage
decreases in lesser extent and real interest rates increases slightly more. These
make the marginal cost and inflation rate raised up in the same manner so far.
Overall, policy effects are weakened in an aging economy akin to thebenchmark. However, effects of a lowered factor supply support factor prices,
so inflation rates and nominal interest rates are higher under aging.

9

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Figure 5: Impulse responses to a 0.01% increase of GDP in public investment.
(Basis point deviations from steady state values)

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Note: Impulse responses reflect basis point deviations from steady-state values.
Red lines labeled “ϕ=0.85” show responses from the model with higher labor
participation, while blue lines labeled “ϕ=0.55” show responses from the modelwith lower labor participation.

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4.4 Case 4: Effects of an increase in R&D expenditure
Figure 6 illustrates the impulse responses to a 0.01% rise in R&D
expenditure as a percentage of GDP. Its effects differ entirely from the public

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investment case. The large increase in TFP resulting from government R&D
expenditure enhances the lifetime income of workers. Consequently, despite theincreased tax burden, there is a decrease in labor supply in the initial period.
After this initial shock, output remains much higher than that of thebenchmark case due to the elevated TFP. This output expansion triggers
deflation. Specifically, the improved TFP enhances the marginal productivity ofcapital and labor for intermediate goods firms, leading to a decrease in demands
for both factors. Therefore, despite the decreased labor supply, real wage
gradually decreases in the medium term as R&D expenses accumulate.
Meanwhile, the decrease in capital demand surpasses an increase in public debt,
even considering a reduction in saving, resulting in an immediate decline in realinterest rates. These two factors depress the marginal cost of intermediate firms,
causing a decline in inflation rate. This deflationary impact results in a decline
in nominal interest rates through the Taylor rule.
Although the demand effects continue, and the cumulative R&D
expenditure enhances TFP, these effects will eventually dissipate. In particular,
TFP depreciation is relatively rapid, so the peak of the TFP level is at the eighth
period. After that, the TFP level declines, causing the marginal cost increase.
This is the reason why responses of the output and the marginal costs exhibit a
hump-shaped pattern.
Similar to public investment, the quantitative impact of aging on R&D
expenditure is insignificant.７
Since the demand side aging effect is similar to the case of public
investment, we observe the lower response of aggregate consumption in an
aging economy. On the supply side, workers decrease their labor supply morein an aging economy because of a higher increase in their lifetime income percapita. This leads to an amplification in the rise of real wages. In the capital
market, the amplified increase in income elevates worker savings, resulting in aslightly lower real interest rate compared to the case with 𝜙 = 0.85. However,changes in factor prices are minimal, resulting in similarly minimal impacts on
the marginal cost, inflation rate, and nominal interest rate.
Overall, the substantial impact of R&D expenditure on output
We summarize a difference in aging affects among four types of fiscal spendings in thenext section.
７

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enhancement diminishes the relative significance of changes brought about by
demographic shifts. The dominant role of R&D investment in driving economic
growth effectively overshadows the effects of population aging.

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6

Figure 6: Impulse responses to a 0.01% increase of GDP in R&D expenditure.

7(Basis point deviations from steady state values)

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Note: Impulse responses reflect basis point deviations from steady-state values.
Red lines labeled “ϕ=0.85” show responses from the model with higher labor
participation, while blue lines labeled “ϕ=0.55” show responses from the modelwith lower labor participation.

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4.5 Summary of Policy Comparison
The results of our policy simulation are summarized as follows: Firstly, thethe effectiveness of three policies (namely, government consumption, one-timegovernment transfer and public investment) in enhancing GDP-- excluding onetime government transfer-- diminishes with the aging population. This decline
is attributed to an increase in the share of policy-irrelevant, stable consumption
among retirees in aggregate consumption, which, in turn, weakens demand
expansion effect of these three policies. Meanwhile, the transfer exhibits agreater demand expansion effect with aging due to a larger increase in retirees'
consumption. On the other hand, because aging concentrates the tax burden andincome fluctuations on smaller workers, their savings and labor supply increase,
thereby strengthening the policy effect on the supply side. In DSGE models, as
policy-induced changes in GDP are generally determined by demand-side
policies, they dictate policy effects. Therefore, aging fundamentally weakens
the GDP-enhancing effects of policies other than one-time transfers andstrengthens the GDP-enhancing effect of one-time transfers. Note that supplyside policy effects significantly influence factor prices and inflation rates.
Secondly, regardless of the degree of aging, R&D expenditure consistently
emerges as the most effective measure across all time spans. Public investment24

is identified as the second most effective in the long run, while government
consumption takes this position in the short run. The one-time transfer is theleast effective in boosting GDP in any time span except for the very short term.
If R&D expenditure such as robots which will assist participation of elderly
workers into labor force will have bigger impact on the economy since it will25

increase the value of Ф.

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5.

Impact of Aging Population on Fiscal Multipliers andWelfares30
32

5-1. Comparison of Fiscal Multipliers by changes indemography

33

To compare the effects of four fiscal spending types and to analyze the

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4

impact of supply-side and demand-side aging effects on the multipliers further,
we refer to Mountford and Uhlig (2009) to compute present value output
multipliers under varying demographic structures. These output multipliers arecalculated as follows:

56where ∆𝑌𝑗 |𝜙 and ∆𝐺𝑗 |𝜙 represent the deviations of output and various fiscal

7

expenditures from their steady states in period 𝑗 after policy implementation,
under the labor participation rate 𝜙.
Figure 7 and Table 2 illustrates the short- and long-term fiscal multipliers
under different labor participation rates.
A systematic comparison within the same panel reveals the relative
effectiveness of various fiscal policies.Notably, the multiplier for R&D
expenditure outperforms those of other fiscal measures across all demographic
structures and throughout policy implementation timeline, establishing it as themost effective fiscal policy. Moreover, even in an economy with large amountof rule-of-thumb retirees, one-time transfer remains the least effective fiscal
expenditure policy. Furthermore, although the short-term multiplier effect ofpublic investment policies is lower than that of government consumption, its

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long-term impact is noteworthy.
Observing the shift of the same policy multipliers across different panels
enables a comparison of policy effectiveness over time. Under any demographic
structure, the multiplier for government consumption generally decreases withthe periods after policy implementation 𝑘 , suggesting a higher short-term
economic stimulus but weaker long-term effects. The one-time transfer
multiplier remains relatively stable over time. Lastly, the multipliers for public
investment and R&D expenditure, dependent on the accumulation of public
capital and TFP, increase with the duration of policy implementation 𝑘.
Finally, comparing fiscal multipliers within the same panel allows us toobserve changes in policy effectiveness across different population structures.
In the short term (k=5), the demand side aging effect predominates, reducing
the multipliers for government consumption, public investment, and R&D
expenditure with aging, while increasing the multiplier for one-time transfers.
In the long term (k=20), the supply side aging effect becomes apparent, while

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the multiplier for government consumption is weakened.
In conclusion, facing population aging, governments should prioritize R&D
expenditures to foster TFP accumulation, in line with the principle of wise
spending. If there are significant barriers to this policy implementation, public
investment emerges as a viable alternative. Lastly, even in the event of a
substantial economic downturn, governments should not consider one-timetransfers as a key component of their policy package.

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Figure 7: Present value fiscal multipliers of four fiscal expenditures under
different demographic structures

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Table 2: Output multiplier comparation
GovernPeriodment
after policy
implication consump
tion
Young
Population(𝝓 = 𝟎. 𝟖𝟓)
Old
Population(𝝓 = 𝟎. 𝟓𝟓)

short-term(𝑘 = 5)long-term(𝑘 = 20)
short-term(𝑘 = 5)long-term(𝑘 = 20)

Onetimetransfer

PublicR&D
Investme expendit
nt
ure

0.366

0.024

0.203

0.979

0.171

0.011

0.589

2.359

0.342

0.094

0.170

0.830

0.247

0.068

0.509

2.149

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5-2. Welfare Comparison

2

Although the output multiplier is often regarded as an essential tool for assessing the3effects of fiscal policies, it is also crucial to measure these policies’ efficacy in enhancing

4social welfare. In the following, we construct a "welfare multiplier" for fiscal expenditures,

5comparing the impact of different policies on social welfare under various population

6

structures. We construct a national welfare function utilizing the utility functions of workers

7

and retirees as follows:

89where 𝑊𝑒𝑙𝑓𝑎𝑟𝑒𝑤,𝑡 and 𝑊𝑒𝑙𝑓𝑎𝑟𝑒𝑟,𝑡 represent the welfare of workers and retirees, as below.

10

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Similar to the output multiplier, we define the welfare multiplier as follows:

12
13

Figure 8 and Table 3 show the short- and long-term welfare multipliers under different

14
15

population structures. Overall, we find that:

16Firstly, by comparing the welfare multipliers of different periods and population

17

structures, we find that R&D expenditure has the highest welfare enhancement effect18

among all policies since R&D shows not only short-run but also long-run impacts on supply

19

side.

20

Secondly, the lower the proportion of the elderly population in society, the higher the21

welfare multiplier of output-promoting policies (public investment, R&D spending). This22

is primarily because output-promoting policies increase the productivity of workers. As

23

output per labor unit rises, a higher proportion of workers significantly increases the24national welfare improvement.

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Finally, similar to the output multiplier, the long-term welfare multiplier of output-

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promoting policies exceeds that of the short-term, whereas it is the opposite for demand-27

stimulating policies. This is mainly because the production-enhancing effect of output-

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promoting policies is more pronounced in the long term, fostering consumption. Moreover,29

in the long term, output-promoting policies reduce workers' labor hours through positive

30

wealth effects. Both factors increase the long-term welfare enhancement effect of output-

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promoting policies.

2
3

4
5

Figure 8: Present value welfare multipliers of four fiscal expenditures under
different demographic structures

6
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Table 3: Welfare multiplier comparation
GovernPeriodment
after policy
implication consump
tion
Young
Population(𝝓 = 𝟎. 𝟖𝟓)
Old
Population(𝝓 = 𝟎. 𝟓𝟓)

short-term(𝑘 = 5)long-term(𝑘 = 20)
short-term(𝑘 = 5)long-term(𝑘 = 20)

Onetimetransfer

PublicR&D
Investme expendit
nt
ure

3.754

-1.5485.102

24.281-1.300-4.02010.75136.478

3.990

0.627

2.501

11.490

0.541

0.008

5.530

16.9648
9
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6. Conclusion

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This study examined the channels through which demographic changes
influence the effectiveness of fiscal policies, utilizing four policy tools: (i)government consumption, (ii) one-time government transfers, (iii) public

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investment, and (iv) R&D expenditures.
The findings of our policy simulation are summarized as follows: Firstly,
the impact of government consumption, public investment, and R&D
expenditure on augmenting GDP diminishes with an aging population. An
increase in the share of stable retirees' consumption weakens themacroeconomic response derived from these fiscal expansions. Meanwhile, theeffectiveness of the universal one-time government transfer to all generations
intensifies with aging. Although aging contributes to increasing savings andlabor supply among workers, the demand-side effects overwhelm these effects.
Secondly, regardless of the aging level, R&D expenditure consistently
emerges as the preeminent measure across all time spans. Public investment
takes a secondary position in the long run, while government consumption
assumes this role in the short term. The transfer is the least effective in
expanding GDP across any temporal scope without a relatively short-term
perspective.
Thirdly, government consumption multipliers tend to diminish after policy
implementation, indicating heightened short-term efficacy but attenuated longterm effects. Multipliers for the transfers persist at a low magnitude, whereas
those associated with public investment and R&D expenditure exhibit an
upward trajectory contingent upon the accumulation of public capital and TFP.
These tendencies become noticeably pronounced with the progression of aging.
Much remains for further research. To delve deeper into the channels
through which aging impacts the effectiveness of fiscal policy, this study
employed a relatively simplified market structure model akin to Yoshino andMiyamoto (2017). However, given the substantial social security pressures
induced by aging and their profound implications for public finances,incorporating the financial risks of public debt becomes crucial in future
research. Kameda (2014) highlighted that persistent increases in national debt
could lead to a rise in long-term interest rates, weakening its effectivenessthrough the crowding-out effect.
For a more comprehensive understanding of this process, future models
should incorporate financial frictions like Fernández-Villaverde (2010) andAshihara and Kameda (2018). These models would specifically analyze how
expectations of rising national debt due to aging affect the lending behaviors of

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the financial sector and how these changes further influence the effectivenessof fiscal policy. This allows for a more detailed analysis of the overarching
impacts of aging on the efficacy of fiscal policy.

45

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33

1

Figure 1: Share of population aged 65 and older.

2
3

Source: United Nations

4

34

1
2

3
4

Source: https://honkawa2.sakura.ne.jp/5090.html and Cabinet Office, National

5

Accounts of Japan (SNA)

635

Forecast (2020)(10 of Thousands)
14000

(%)
80.0
70.0

12000

60.0

10000

50.0
8000
40.0
6000
30.0
4000

20.0

2000

10.0

0

0.0
1950

1
2
3

1960

1970

1980

Age 14 and lessWorking Population Ratio (15–64)

1990

2000

2010

Age 15–64
Aged Population Ratio

2020

2030

Figure 2: Population Aging of Japan
Source: Ministry of Internal Affairs and Communication

4
5

36

2040

2050

Age 65 and over

2060

1

Figure 3: Social expenditure in health and elderly care (1980－2019)

(%)
20.00
16.00
12.00
8.00
4.00
0.00
1980

1985

1990

1995

2000

2005

2010

2015

2

Social Expenditure in Old age (in percentage of GDP)
Social Expenditure in Health (in percentage of GDP)
Social Expenditure in Old age and Health (in percentage of GDP)

3

Source: National Institute of Population and Social Security Research

4
5

37

1

Figure 4: Japan's Government Expenditures and Tax Revenues (Unit:

2

Trillion Yen)

3
4

Source: Ministry of Finance

5

6

38

1
2

Figure 5: R&D expenditure of Japanese government (1980－2019)
Source:
(%)
0.9
0.8
0.7
0.6

0.5
0.4
0.3
0.2

0.1
0
1983
3
4

1993

2003

2013

R&D expnditure of government (in percentage of GDP)
National Institute of Science and Technology Policy (NISTEP)

5
6
7
8

39