ISSN (Print) 0473-453X

Discussion Paper No. 1255

ISSN (Online) 2435-0982

ON THE UNDESIRABLE REPERCUSSIONSOF GENDER NORMS
IN AN ENDOGENOUS GROWTH MODEL

Ryo Sakamoto
Katsunori Minami

September 2024

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, JapanOn the Undesirable Repercussions of Gender
Norms in an Endogenous Growth Model
Ryo Sakamoto∗Katsunori Minami†

Sustainable growth has emerged as a critical policy challenge worldwide. We investigate the influence of conventional gender norms on fertility and economic growth
to explain the phenomena recently observed across high-income countries. To thisend, we construct an overlapping generations model with endogenous fertility andlabor supply, incorporating gender norms and R&D activities. We demonstrate thatconventional gender norms can impede fertility and economic growth. Specifically,
when gender norms are sufficiently conservative, income growth stagnates and population erosion eventually occurs. Conversely, when gender norms are sufficiently lessconservative, the economy follows a sustained growth path characterized by simultaneous growth in both population and income per capita. Our results underscore theneed to address and correct gender norms to achieve sustainable growth and improvewelfare.

Keywords: Gender norms, economic growth, fertility, domestic production
JEL classifications J13, J16, O40∗ Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka 567-0047,

Japan. Email: r.sk2015.g@gmail.com† Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka 560-0043,
Japan. JSPS Research Fellow. Email: minami@iser.osaka-u.ac.jp1

1

Introduction

Sustainable growth has emerged as a critical policy challenge worldwide. Nevertheless,several of the important objectives articulated in the UN Sustainable Development Goals
related to economic growth and gender equality remain unmet. Additionally, several
developed countries, including Italy and Japan, are facing rapid population declines,
which makes it difficult to maintain the social security system and address the problemof labor shortages. Therefore, ongoing discourse is necessary to identify and analyze theelements that both facilitate and hamper sustainable growth.
Among the elements considered to be potentially important, we focus on how thevalues or culture related to gender roles within and outside households (hereafter referred
to as gender norms) have repercussions on sustainable growth. Specifically, our study
is closely related to the idea proposed by Feyrer et al. (2008), who argued that there are“three distinct phases in women’s status generated by the gradual increase in women’s
workforce opportunities.”1 The authors’ important suggestion is that gender norms are
relatively persistent over time and change more slowly than women’s actual labor market
opportunities. Consequently, in the intermediate phase, despite the improved status of
women in the labor market, they are still likely to bear a greater burden of houseworkand childcare than men, impeding the compatibility of career and family for womenand decreasing fertility (Doepke et al., 2023). However, in the final phase when lessconventional gender norms prevail, the increased involvement of men in housework andchildcare not only supports women’s labor market participation, but also enhances fertility.
Based on this idea, we theoretically investigate the influence of gender norms on fertility and income per capita. In particular, we focus on the differences across high-income
countries because although women’s labor market opportunities have improved in the de1In the first phase, “women earn low wages relative to men and are expected to shoulder all of the childcare at home.” In the intermediate phase, “women have improved (but not equal) labor market opportunities
but their household status lags. Women in this stage are still expected to do the majority of child care andhousehold production.” In the final phase, “women’s labor market opportunities begin to equal those ofmen. In addition, the increased household bargaining power that comes from more equal wages results inmuch higher (if not gender-equal) male participation in household production.”2

veloped world, significant heterogeneity persists in the conservativeness of gender norms.
Before conducting the theoretical analysis, an examination of country-level data over the
past 40 years reveals several notable trends and relationships between the variables. First,
total fertility rates have remained relatively constant over time and appear to be converging. However, while the total fertility rates of some countries are close to the replacementlevel, others display significantly lower rates. Second, although GDP per capita has growncontinuously in many countries during this period, its diverges across countries and positively correlates with total fertility rates. Finally, both total fertility rates and GDP per
capita are lower in countries with more conventional gender norms than in those with lessconventional ones. Taken together, the heterogeneity in the conservativeness of gendernorms may account for international differences in fertility rates and economic growth.
To explain these phenomena, we construct an overlapping generations model withendogenous fertility and labor supply. Additionally, we explicitly incorporate gendernorms by assuming that women bear greater responsibility for housework and childcare
than men do within the framework of R&D-based growth. We demonstrate that moreconventional gender norms decrease fertility and income per capita. The underlying
mechanism operates as follows: fertility (i.e., the number of children) is modeled througha home production function that features complementarities between women’s and men’shome production time inputs as well as between time and monetary inputs. Although thiscomplementarity uniquely determines the efficient input ratio, conventional gender norms
prevent households from adopting this ratio. This inefficiency increases the cost of having
and raising children, thereby decreasing the population and labor force in subsequent
periods. The reduced labor force diminishes the number of researchers in the R&D
sector, impeding R&D activities and consequently lowering the economic growth rate. If
the degree of conservativeness exceeds a threshold, the economy displays a population
decline and a transitory increase in income per capita, followed by stagnation in income
growth and eventual population erosion. Conversely, if the degree of conservativenessis below this threshold, the economy follows a sustained growth path characterized by3

simultaneous growth in both population and income per capita.
Our study builds on and contributes to two strands of the literature. The first strand explores the influence of social norms on household behavior. The rationale for investigatingsocial norms stems from the observation that certain aspects of household behavior cannot
be adequately explained by conventional economic theory, which endeavors to describe
household decisions based solely on financial incentives. To address this issue, Akerlof
and Kranton (2000) introduced notions of identity from sociology and social psychology
to economics, with their framework since extensively used to understand the relationships
between social norms and household behavior (Fernández et al., 2004; Feyrer et al., 2008;
Gimenez-Nadal et al., 2012; Bertrand et al., 2015; Hwang, 2016; Goussé et al., 2017;
Bursztyn et al., 2020; Bertrand et al., 2021; Jessen et al., 2024; Sakamoto and Kohara,2024). For instance, Fernández et al. (2004) developed a model that accounted for a
man’s preference for his wife’s labor force participation to explain why the wives of men
whose mothers worked were significantly more likely to work. Furthermore, Sakamoto
and Kohara (2024) introduced gender norms as a time constraint in the household problem,
demonstrating that conventional gender norms not only affect resource allocation withinhouseholds, but also reduce household welfare. While previous research has predominantly focused on the influence of social norms on household behavior, our study extends
this analysis to present the macroeconomic consequences of gender norms, highlighting
their negative repercussions on fertility rates and economic growth.
Second, our study contributes to the literature on the causes and consequences of
economic development. Specifically, numerous studies demonstrate the interplay between
economic growth and fertility (or demographic transition) by focusing on the quantity–
quality trade-off of children (Becker and Barro, 1988; Barro and Becker, 1989; Becker
et al., 1990), technological progress (Galor and Weil, 1996, 2000), inequality (De La Croix
and Doepke, 2003), and child labor (Hazan and Berdugo, 2002; Doepke, 2004).2 Recently,
2Other crucial elements include life expectancy (Castelló-Climent and Doménech, 2008; Futagami andKonishi, 2019), variety expansion (Maruyama and Yamamoto, 2010), delay in childbearing (Dioikitopoulos
and Varvarigos, 2023), and childcare policies (Day, 2016).

4

Jones (2022) addressed the demographic transition and economic growth in contemporary
times, noting that the assumption typically employed in the semi-endogenous growth
literature—–constant or growing population—–is no longer valid. The author argued thatwith negative population growth rates, both endogenous and semi-endogenous growthmodels yield empty planet outcomes, wherein knowledge and living standards stagnate fora population that gradually erodes. Furthermore, recent research demonstrates that various
aspects of women’s empowerment either promote or interact with economic development(Bloom et al., 2009; Doepke and Tertilt, 2009; Fernández and Fogli, 2009; De la Croix
and Vander Donckt, 2010; Fernández, 2014; Anderson and Kohler, 2015; Doepke andTertilt, 2019). Our study complements this literature by showing that the recent positive
correlation between fertility rates and income per capita across high-income countries
can be attributed to international differences in the conservativeness of gender norms.
Most importantly, our model underscores the need to address and correct gender norms
promptly; failure to do so risks economies with conventional gender norms succumbing
to the empty planet scenario.
The remainder of this paper is organized as follows. Section 2 provides suggestive
evidence for the relationships among gender norms, fertility rates, and income per capita.
Section 3 introduces a theoretical model for exploring the influence of gender norms on
fertility and economic growth. Section 4 presents a dynamic analysis that explains andinterprets the observed phenomena. Section 5 concludes.

2

Macroeconomic Evidence among High-income Countries

Before proceeding with our theoretical analysis, we briefly provide suggestive evidence
for the relationships among gender norms, fertility, and income.

5

2.1

Selection of Countries and Periods

We use country-level data on high-income countries (as classified by the World Bank) inEurope, Asia, and North America. As in Bertrand et al. (2021), we exclude very small
countries (those with populations smaller than four million in 2015). In addition, we
exclude countries for which fertility data are unavailable. Our final sample consists ofthe following 24 developed countries: Austria, Belgium, Canada, the Czech Republic,
Denmark, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Japan, Korea, theNetherlands, Norway, Poland, Portugal, Slovakia, Spain, Sweden, Switzerland, the United
Kingdom, and the United States. To examine the long-term trends and relationships
between the variables, we use data from 1980 to 2019.

2.2

Data

The variables of interest are gender norms, fertility, and income. For the first variable,
following Bertrand et al. (2021), we use the 1990–1994 and 2010–2014 waves of theIntegrated Values Survey, a harmonized dataset that covers both the European Values
Study and the World Values Survey. This dataset includes participants’ responses tovarious gender-related questions asked across a set of countries. In particular, we use
participants’ responses (agree, disagree, or neither) to the following question: “When jobs
are scarce, men have more right to a job than women.” We use this question because
it covers the broadest range of countries and survey periods. Although it asks about thevalues of gender roles outside the home, combined with time constraints, it may also reflect
the values of gender roles within households (i.e., the division of housework and childcare
between couples). Using the answers given by respondents aged 18 years or older for eachcountry, we create a variable that indicates the ratio of respondents who answer “agree.”A higher value of this variable implies more conventional and conservative gender norms.
Although this question clearly measures the conservativeness of gender norms, itdoes not directly capture the values of gender roles outside and within households. In

6our theoretical model presented below, we introduce gender norms as “Women should
be more responsible for housework and childcare than men.” Hence, there is a slightdivergence between the theory and data. To address this issue, we also use the 2002 and2012 waves of the International Social Survey Programme as in Feyrer et al. (2008). We
focus on participants’ responses to the following question: “A man’s job is to earn money;
a woman’s job is to look after the home and family.” Respondents must answer agreestrongly, agree, neither agree nor disagree, disagree, or disagree strongly. We create avariable that indicates the ratio of respondents who answer “agree strongly” or “agree,”which measures conventional gender norms.
For the second variable, we use the total fertility rate between 1980 and 2019 fromthe OECD Family Database. Conceptually, the total fertility rate indicates the numberof children that would be born to a woman if she were to live until the end of herchildbearing years and bear children in accordance with the age-specific fertility rates
currently observed. Finally, our income measure is GDP per capita, based on World Bank
data. This measure is adjusted to current US dollars to ensure that the figures in different
countries and periods are comparable.

2.3

Trends in Fertility and Income

First, we examine fertility and income across countries and over time. Figure 1 illustrates
the trends in the total fertility rate for nine countries (Denmark, France, Germany, Italy,
Japan, Korea, Spain, Sweden, and the United States) from 1980 to 2019. Over recent
years, their total fertility rates are almost constant and typically below the replacementlevel of 2.1. Hence, these countries seem to have completed their demographic transition.
As the literature suggests (Bongaarts, 2002; Adsera, 2004), fertility rates behave differently across countries. In particular, when focusing on 2010, these nine countries can
be classified into countries with a total fertility rate of approximately 2 (i.e., Denmark,France, Sweden, and the United States) and those with a total fertility rate below 1.5 (i.e.,
Germany, Italy, Japan, Korea, and Spain). This is a well-known pattern in the literature.
7

Notes. The vertical and horizontal axes indicate the total fertility rate and year, respectively. The source is the OECD Family
Database.

Fig. 1 Trends in the total fertility rate across countries
The United States, Nordic countries, and Western European countries are typically characterized by high fertility rates, whereas Eastern and Southern European countries and East
Asian countries tend to have lower fertility rates (Feyrer et al., 2008; Chatterjee and Vogl,
2018; Delventhal et al., 2021). In the past 10 years, however, the rates of the countries inthe second group have diverged. While the total fertility rate has increased in Germany, it
has remained relatively constant in Italy, Japan, and Spain, while Korea has experienced
a drastic decline. Hence, the important question is “What generates these differences intotal fertility rates across countries?”
Before answering this question, we also explore the trends in GDP per capita inthe same countries between 1980 and 2019. Unlike the total fertility rate, GDP per
capita has continued to increase over the past 40 years, excluding in Japan where it
has remained almost constant since 1995. However, the income growth rates differ
across countries. Specifically, the United States, Nordic countries, and Western European
countries have higher growth rates than Eastern and Southern European and East Asian
countries. Interestingly, income growth rates are positively associated with total fertility
8Notes. The vertical and horizontal axes indicate GDP per capita and year, respectively. The source is World Bank data.

Fig. 2 Trends in GDP per capita across countries
rates.
The positive relationship between fertility and income has been widely acknowledged inrecent years. For instance, Ahn and Mira (2002) argued that fertility rates were negatively
associated with income per capita until the mid-1980s, but that this relationship became
positive toward the end of that decade. We confirm their findings using more recent data.
Figure 3 shows the relationship between the total fertility rate and GDP per capita in
1980 and 2010. Concurring with the findings of Ahn and Mira (2002), the relationshipis negative in 1980; the correlation coefficient is −0.664, statistically significant at the
1% level (see the upper panel). This negative relationship disappears by 1990 (data notshown); the correlation coefficient becomes −0.001, statistically insignificant. However, apositive and statistically significant relationship begins to be observed when the data from2000 are used. As shown in the lower panel, a clear positive relationship is observed in
2010, with a correlation coefficient of 0.588, statistically significant at the 1% level. This
positive relationship remains in 2019, the most recent year of our analysis. In summary,when focusing on the past (at least) 20 years, there has been a stable positive relationship9between the total fertility rate and GDP per capita.

2.4

Relationships among Gender Norms, Fertility, and Income

Among the sources that may generate this positive relationship between fertility and income
per capita, we focus on international differences in gender norms. In a modern economy,
gender norms are likely to play an important role in determining fertility because they
influence the division of labor between genders outside and within households (Fernández
et al., 2004; Hwang, 2016; Bertrand et al., 2021; Sakamoto and Kohara, 2024). Moreover,gender norms may also influence income per capita (or, equivalently, economic growth)because population growth rates and income growth rates interact in various ways (Becker
et al., 1990; Galor and Weil, 1996, 2000; Hazan and Berdugo, 2002; De La Croix andDoepke, 2003; Prettner, 2013; Jones, 2022; Cervellati et al., 2023).
Figure 4 illustrates the relationships among gender norms, fertility, and income percapita. Although all the analyses are correlational, we use lagged variables to mitigate theconcern about reverse causality; that is, the norm measure is drawn from the 1990–1994
wave of the Integrated Values Survey, whereas we use the fertility and income measuresin 2010. The upper panel indicates that more conventional gender norms are negatively
associated with the total fertility rate. The correction coefficient is −0.625, statisticallysignificant at the 1% level. Additionally, the lower panel confirms the negative relationshipbetween conventional gender norms and GDP per capita. The correlation coefficient is−0.625, significant at the 1% level. Similar results are obtained when using the fertility
and income measures in 1990 and 2000. Furthermore, the results remain consistent if we
instead use the norm measure from the 2002–2012 wave of the International Social Survey
Programme and combine it with the fertility and income measures in 2019. Therefore, aseries of observations provides suggestive evidence that conventional gender norms havelong-term negative repercussions on both fertility and income per capita. The theoreticalmodel presented in the next section attempts to clarify the underlying mechanisms.

10Notes. The upper and lower panels illustrate the relationship between the total fertility rate and GDP per capita in 1990 and 2010,
respectively. For each panel, the vertical and horizontal axes indicate the total fertility rate and GDP per capita, respectively. The
regression lines are also depicted. The fertility measure is from the OECD Family Database, while the income measure is from WorldBank data.

Fig. 3 Relationship between fertility and income per capita in 1980 and 201011

Notes. The upper panel illustrates the relationship between gender norms in 1990 and the total fertility rate in 2010. The lower panel
shows the relationship between gender norms in 1990 and GDP per capita in 2010. The regression lines are depicted. The norm
measure is from Bertrand et al. (2021) (see Table 4 in the authors’ online appendix), the fertility measure is from the OECD Family
Database, and the income measure is from World Bank data.

Fig. 4 Relationships among gender norms, fertility and income per capita

12

3

Model

3.1

Structure

Following Galor and Weil (1996), we consider a three-period overlapping generations
model with two genders, men and women. Individuals live for three periods: childhood,
adulthood, and old age. In childhood, they do not make decisions. At the beginning ofadulthood, each individual enters the marriage market and is matched with a member ofthe opposite sex. The couple (i.e., household) then determines the consumption plan,number of children to have, and labor supply. In old age, household members retire,
consume their savings, and have no bequest motive.
Men and women are identical in childhood and old age. In adulthood, couples invest
equal amounts of time and money in their male and female children, resulting in theaccumulation of the same level of human capital between genders. However, in adulthood,the couple’s labor decision is influenced by gender norms, which stipulate that womenshould do 𝑠 ∈ (0, ∞) times more housework and childcare than men, which we refer to as
the male-dominant social norm. For simplicity, the probability of having male and female
children is the same; hence, the male-to-female ratio is one for all generations.

3.2

Households

Each individual in adulthood in period 𝑡 maximizes the following utility:

𝑈𝑡 (𝑐 1,𝑡 , 𝑐 2,𝑡+1 , 𝑛𝑡 ) = ln 𝑐 1,𝑡 + 𝛽 ln 𝑐 2,𝑡+1 + 𝛾 ln 𝑛𝑡 ,(1)

where 𝑐 1,𝑡 denotes consumption in adulthood, 𝑐 2,𝑡+1 is consumption in old age, 𝑛𝑡 is thenumber of children each couple has in adulthood, and 𝛽 > 0 and 𝛾 > 0 represent thepreference parameters. The two genders, female and male, are denoted by 𝑖 ∈ { 𝑓 , 𝑚}
and we assume an equal probability of having a boy and a girl; the choice 𝑛𝑡 = 1 implies

13having one boy and one girl. Hence, the population dynamics equation is given by

𝑁𝑡+1 = 𝑛𝑡 𝑁𝑡 ,(2)

where 𝑁𝑡 denotes the number of couples in adulthood in period 𝑡. Women and men jointly
consume the final good in adulthood and old age. In addition, the presence of children is
public to their spouses. Hence, the couple’s utility function equals the individual utility
function of each household member.
Each adult is endowed with 1/2 units of time divided into housework time, includingchildcare, ℎ𝑖,𝑡 , and labor supply in the market, ℓ𝑖,𝑡 . Hence, the household’s time constraintis∑︁(ℎ𝑖,𝑡 + ℓ𝑖,𝑡 ) = 1.

(3)𝑖∈{ 𝑓 ,𝑚}Additionally, the household’s decision on housework is influenced by the male-dominantsocial norm as follows:ℎ 𝑓 ,𝑡 = 𝑠ℎ𝑚,𝑡 .

(4)

Hence, although the household can choose the total housework time, ℎ 𝑓 ,𝑡 + ℎ𝑚,𝑡 , optimally,
it cannot choose the ratio of women’s housework time to that of men.
The household budget constraint in adulthood in period 𝑡 is given by𝑐 1,𝑡 + 𝑎 𝑡 + 𝑒 𝑡 = 𝑤 𝑡 (1 − ℎ 𝑓 ,𝑡 − ℎ𝑚,𝑡 ),(5)where 𝑒 𝑡 denotes financial investment in children and 𝑎 𝑡 represents savings for old age.
𝑤 𝑡 is the market wage, which is the same for both genders because women and men havethe same level of human capital in adulthood and there is no gender discrimination in the14

labor market. The budget constraint in old age in period 𝑡 + 1 is given by𝑐 2,𝑡+1 = (1 + 𝑟 𝑡+1 )𝑎 𝑡 ,(6)where 𝑟 𝑡+1 is the interest rate.
The number of children is determined using the following home production function:𝜂𝑓𝑛𝑡 = 𝐻 (ℎ 𝑓 ,𝑡 , ℎ𝑚,𝑡 , 𝑒 𝑡 ) = 𝜉 (ℎ 𝑓 ,𝑡 ) (ℎ𝑚,𝑡 )

𝜂𝑚

𝑒𝑡
𝑤𝑡

 1−𝜂 𝑓 −𝜂𝑚,(7)where 𝜉 > 0 is the scale parameter. 𝜂 𝑓 ∈ (0, 1) and 𝜂𝑚 ∈ (0, 1), such that 𝜂 𝑓 +𝜂𝑚 < 1 are the parameters representing the relative importance of the time inputs for
women and men, respectively. The Cobb–Douglas form in Equation (7) indicates thecomplementarity between ℎ 𝑓 ,𝑡 , ℎ𝑚,𝑡 , and 𝑒 𝑡 . Importantly, the financial investment inchildren, 𝑒 𝑡 , is discounted by the wage, 𝑤 𝑡 . This assumption captures the fact that as the
economy grows, the standard level of investment in children also increases.3
We first consider the following cost minimization problem for raising children given
the number of children 𝑛:˜min𝑒 𝑡 + 𝑤 𝑡 ℎ 𝑓 ,𝑡 + 𝑤 𝑡 ℎ𝑚,𝑡 ,𝑒 𝑡 ,ℎ 𝑓 ,𝑡 ,ℎ 𝑚,𝑡s.t.

𝐻 (ℎ 𝑓 ,𝑡 , ℎ𝑚,𝑡 , 𝑒 𝑡 ) = 𝑛,˜
ℎ 𝑓 ,𝑡 = 𝑠ℎ𝑚,𝑡 .

The first-order conditions yield the following intratemporal condition:
𝜂 𝑓 + 𝜂𝑚𝑒𝑡·
= (1 + 𝑠)𝑤 𝑡 ,1 − 𝜂 𝑓 − 𝜂𝑚 ℎ𝑚,𝑡3Similarly, Prettner (2013) assumed that children’s consumption is proportional to that of adults and thenderived that fertility is constant to income. We show that without the income effect on fertility, international
differences in the conservativeness of gender norms could explain the observed positive relationships between
fertility rates and income per capita across high-income countries. Moreover, as mentioned in Section 2,
constant fertility rates over time are consistent with the real-world observations for high-income countries
over the past 40 years.

15

implying that the marginal rate of substitution between the time and monetary inputs forraising children equals their price ratio. The input demand functions are given byℎ 𝑓 ,𝑡 (𝑛𝑡 ) = 𝑠ℎ𝑚,𝑡 (𝑛𝑡 ),𝜂 𝑓 + 𝜂𝑚· 𝜒𝑛𝑡 ,
ℎ𝑚,𝑡 (𝑛𝑡 ) =
1+𝑠

(8)
(9)

𝑒 𝑡 (𝑛𝑡 ) = (1 − 𝜂 𝑓 − 𝜂𝑚 ) 𝜒𝑤 𝑡 𝑛𝑡 ,(10)𝑠−𝜂 𝑓 (1 + 𝑠) 𝜂 𝑓 +𝜂𝑚.
𝜉 (𝜂 𝑓 + 𝜂𝑚 ) 𝜂 𝑓 +𝜂𝑚 (1 − 𝜂 𝑓 − 𝜂𝑚 ) 1−𝜂 𝑓 −𝜂𝑚

(11)

where

𝜒 :=

Substituting Equations (8), (9), and (10) into the objective function yields the following
cost function:b(𝑛𝑡 ) = 𝜒𝑤 𝑡 𝑛𝑡 ,𝐶(12)which is linear with respect to 𝑛𝑡 because the home production function is homogeneousof degree one. We can interpret 𝜒𝑤 𝑡 as the shadow price of having and raising children.
As 𝜒 hinges on 𝑠, social norms affect fertility decisions through price effects. Referring
to Sakamoto and Kohara (2024), we obtain the following result.
Lemma 1. There exists 𝑠∗ such that 𝜒 increases in 𝑠 if and only if 𝑠 > 𝑠∗ .
Proof. Taking the derivative of 𝜒 with respect to 𝑠 yields𝑠−𝜂 𝑓 −1 (1 + 𝑠) 𝜂 𝑓 +𝜂𝑚 −1 (𝑠𝜂𝑚 − 𝜂 𝑓 )𝜕𝜒=,𝜕𝑠 𝜉 (𝜂 𝑓 + 𝜂𝑚 ) 𝜂 𝑓 +𝜂𝑚 (1 − 𝜂 𝑓 − 𝜂𝑚 ) 1−𝜂 𝑓 −𝜂𝑚which is positive if and only if𝑠𝜂𝑚 − 𝜂 𝑓 > 0 ⇐⇒ 𝑠 > 𝑠∗ ,16𝜂where 𝑠∗ := 𝜂𝑚𝑓 .

□Panel (a) in Figure 5 illustrates the relationship between the shadow price of having
children, 𝜒, and social norm, 𝑠. This lemma implies that when social norms are sufficiently
male-dominant (i.e., 𝑠 is higher than 𝑠∗ ), the shadow price increases with 𝑠. Additionally,
although this is not the subject of our analysis, it should be noted that 𝜒 increases as𝑠 decreases when 𝑠 is less than 𝑠∗ . This U-shaped relationship follows the fact thathousework and childcare are complementary for both women and men.4 Complementarity,
combined with their price ratio (i.e., the woman’s wage relative to that of the man), uniquelydetermines the efficient ratio of housework, ℎ 𝑓 ,𝑡 /ℎ𝑚,𝑡 , which equals 𝑠∗ . In other words,
without the male-dominant social norm, the household chooses ℎ 𝑓 ,𝑡 and ℎ𝑚,𝑡 such thatℎ 𝑓 ,𝑡 /ℎ𝑚,𝑡 = 𝑠∗ . However, households cannot adopt the efficient ratio because of themale-dominant social norm unless 𝑠 = 𝑠∗ .
𝑛∗

𝜒

𝛾
1+𝛽+𝛾

1

𝑂

𝑠∗

𝑠
𝑂

b
𝑠

(a) Relationships between 𝑠 and 𝜒

𝑠∗

𝑠
b
𝑠

(b) Relationships between 𝑠 and 𝑛∗

Fig. 5 Relationships between male-dominant social norms and the shadow price andfertility
Hence, we focus on the case in which 𝑠 ∈ [𝑠∗ , ∞) because we investigate the repercussions of the male-dominant social norm. Therefore, we interpret a society in which
4Many studies on intrahousehold resource allocation and time use suggest that wives’ and husbands’
housework and childcare are complementary (Cherchye et al., 2012; Hazan and Zoabi, 2015; Greenwood
et al., 2016; Goussé et al., 2017; Gayle and Shephard, 2019; Lise and Yamada, 2019).

17

𝑠 is sufficiently close to 𝑠∗ as a gender-equal society, whereas a society in which 𝑠 is
sufficiently high (compared with 𝑠∗ ) faces male-dominant social norms.
Substituting the input demand functions (8) and (10) into the budget constraint in
adulthood (5), we rewrite the household problem as follows:max
𝑐 1,𝑡 , 𝑐 2,𝑡 , 𝑛𝑡

ln 𝑐 1,𝑡 + 𝛽 ln 𝑐 2,𝑡+1 + 𝛾 ln 𝑛𝑡 ,s.t. 𝑐 1,𝑡 +𝑐 2,𝑡+1+ 𝜒𝑤 𝑡 𝑛𝑡 = 𝑤 𝑡 .
1 + 𝑟 𝑡+1

Using the first-order conditions, we obtain the intertemporal and intratemporal conditions
as follows:𝑐 2,𝑡+1 = 𝛽(1 + 𝑟 𝑡+1 )𝑐 1,𝑡 ,𝛾𝑐 1,𝑡= 𝜒𝑤 𝑡 .
𝑛𝑡
The latter condition implies that the marginal rate of substitution between consumption in
adulthood and having children equals the price ratio. Arranging these conditions yields
the following demand functions:
𝑤𝑡
,
1+𝛽+𝛾
𝛽𝑤 𝑡 (1 + 𝑟 𝑡+1 )𝑐∗2,𝑡+1 =
,
1+𝛽+𝛾
𝛾
𝑛𝑡∗ =
.
(1 + 𝛽 + 𝛾) 𝜒𝑐∗1,𝑡 =

(13)
(14)
(15)

Using the budget constraint in old age (6), we derive the saving function:𝑎 𝑡∗ =

𝛽𝑤 𝑡
.
1+𝛽+𝛾

(16)

Equations (13)–(16) indicate that the male-dominant social norm only affects the fertility
choice, 𝑛𝑡∗ , and has no effect on the consumption plan because each individual’s utility

18

function is additively separable. In addition, Equation (15) indicates that the equilibrium
fertility rate depends neither on wages nor on time, and thus wage growth does not affectfertility. Hereafter, we denote the fertility rate as 𝑛∗ .
Proposition 1. 𝑛∗ decreases in 𝑠 if and only if 𝑠 > 𝑠∗ . In addition, when 𝜉 is sufficiently
high, there exists b𝑠 ∈ [𝑠∗ , ∞) such that 𝑛∗ ≥ 1 if and only if 𝑠 ≤ b
𝑠. Conversely, when 𝜉 issufficiently low, it always holds that 𝑛∗ < 1.
Proof. Equation (15) implies that 𝑛𝑡∗ decreases with 𝜒. Combining this with Lemma 1, we
obtain the following result. For the second result, Equation (15) implies that 𝑛∗ ≥ 1 if and𝛾. This inequality holds only when the scale parameter 𝜉 is sufficiently
only if 𝜒 ≤ 1+𝛽+𝛾𝛾high. In this case, 𝜒 ≤ 1+𝛽+𝛾
if and only if 𝑠 ≤ b
𝑠 because 𝜒 increases with 𝑠 when 𝑠 ≥ 𝑠∗ ,and the threshold b𝑠 is implicitly given byb𝑠−𝜂 𝑓 (1 + b𝑠) 𝜂 𝑓 +𝜂𝑚𝛾=.
𝜉 (𝜂 𝑓 + 𝜂𝑚 ) 𝜂 𝑓 +𝜂𝑚 (1 − 𝜂 𝑓 − 𝜂𝑚 ) 1−𝜂 𝑓 −𝜂𝑚 1 + 𝛽 + 𝛾□
Panels (a) and (b) of Figure 5 illustrate the implications of Proposition 1. Panel (a)𝛾shows that when the social norm 𝑠 is lower than b𝑠, the shadow price 𝜒 is below 1+𝛽+𝛾.

However, the scale parameter 𝜉 governs the vertical position of the U-shaped curve on
the graph and an increase in 𝜉 shifts it downward. Hence, unless 𝜉 is sufficiently high,𝛾). By contrast, Panel (b)the curve will not intersect the horizontal line (i.e., 𝜒 = 1+𝛽+𝛾

illustrates the hump-shaped relationship between the social norm and equilibrium fertility
rate. In particular, focusing on our region of interest (i.e., 𝑠 ≥ 𝑠∗ ), 𝑛∗ decreases with 𝑠
because of the increased shadow price. When 𝑠 is higher than b𝑠, the equilibrium fertility
rate is below 1, implying that the population declines over time, and vice versa. Thus, we
assume that 𝜉 is sufficiently high to ensure b𝑠 in Proposition 1.
Substituting (15) into (8)–(10) yields the following demand functions for housework

19time and expenditure on children:𝛾(𝜂 𝑓 + 𝜂𝑚 )𝑠,(1 + 𝛽 + 𝛾)(1 + 𝑠)𝛾(𝜂 𝑓 + 𝜂𝑚 )ℎ∗𝑚,𝑡 =,
(1 + 𝛽 + 𝛾)(1 + 𝑠)𝛾(1 − 𝜂 𝑓 − 𝜂𝑚 )𝑤 𝑡.
𝑒 𝑡∗ =
1+𝛽+𝛾ℎ∗𝑓 ,𝑡 =

(17)
(18)
(19)

Combined with the time constraint, the labor supply function (for market work) is∗ = 1/2 − ℎ∗ . Equations (17)–(19) have crucial implications for the aggregate labor
ℓ𝑖,𝑡
𝑖,𝑡

supply over generations. First, by assumption, the male-dominant social norm increases
the ratio of a woman’s home production time to that of a man, whereas their sum ℎ∗𝑓 ,𝑡 + ℎ∗𝑚,𝑡
is unaffected. Combined with the time constraint in Equation (3), the male-dominant social∗ , which follows
norm does not affect the per-couple labor supply, denoted by ℓ𝑡∗ := ℓ ∗𝑓 ,𝑡 +ℓ𝑚,𝑡from the additive separability in the home production function.5 As the aggregate labor
supply in this economy is defined as 𝐿 𝑡∗ = 𝑁𝑡∗ ℓ𝑡∗ , the social norm influences 𝐿 𝑡∗ through 𝑁𝑡∗
but not through ℓ𝑡∗ (Proposition 1).

3.3

Production Sectors

As in Jones (1995) and Futagami and Konishi (2019), the economy is characterized bythree production sectors: final goods, intermediate goods, and R&D. The first sector
produces final goods that utilize both labor and intermediate goods. The second sector
produces intermediate goods solely using labor. Finally, the third sector generates new
ideas by integrating labor with existing knowledge, subsequently earning profits by sellingthese new ideas to entrepreneurs.
5Using a home production function of the CES form, Sakamoto and Kohara (2024) showed that the
male-dominant social norm increases the woman’s and man’s total labor supply.

20

3.3.1

Final Goods Sector

In this economy, a single type of final good exists and this is traded in a perfectly competitivemarket comprising numerous homogeneous firms. These firms purchase intermediate
goods, denoted by 𝑥 𝑗,𝑡 , from the intermediate goods sector and combine them with labor
inputs. The production function of a representative firm is expressed as

𝑌𝑡 = 𝐿𝑌1−𝛼,𝑡∫ 𝐴𝑡𝑥 𝛼𝑗,𝑡 𝑑𝑗,

0 < 𝛼 < 1,

(20)

0

where 𝐴𝑡 denotes the variety of intermediate goods available in period 𝑡. The total cost∫𝐴of production is given by 0 𝑡 𝑞 𝑗,𝑡 𝑥 𝑗,𝑡 𝑑𝑗 + 𝑤 𝑡 𝐿𝑌 ,𝑡 , where 𝑞 𝑗,𝑡 and 𝐿𝑌 ,𝑡 denote the price ofeach intermediate good and labor employed by the final goods sector, respectively. The
first-order conditions yield the following demand functions for intermediate goods andlabor:
𝛼−1
𝑞 𝑗,𝑡 = 𝛼𝐿𝑌1−𝛼,𝑡 𝑥 𝑗,𝑡 ,

(21)

𝑌𝑡
,
𝐿𝑌 ,𝑡

(22)

𝑤 𝑡 = (1 − 𝛼)implying that the quantities of each intermediate good and labor demand must equal theirrespective prices.

3.3.2

Intermediate Goods Sector

There are 𝐴𝑡 types of intermediate goods, each monopolistically produced and sold to thefinal goods sector by one of the 𝐴𝑡 intermediate goods firms. Each firm produces one unitof intermediate goods using one unit of labor. Hence, the profit of each firm, 𝜋 𝑗,𝑡 , is givenby (𝑞 𝑗,𝑡 − 𝑤 𝑡 )𝑥 𝑗,𝑡 . Combining the first-order condition with Equation (21) yields

𝑤𝑡
𝑞 𝑗,𝑡 = ,𝛼𝛼2
𝑥 𝑗,𝑡 =𝑤𝑡
21

 1−1 𝛼
𝐿𝑌 ,𝑡 .

(23)

Given the symmetry among intermediate goods firms, all firms produce identical quantities
of intermediate goods traded at a uniform equilibrium price. Therefore, we denote thesequantities and prices by 𝑥𝑡 ≡ 𝑥 𝑗,𝑡 and 𝑞 𝑡 ≡ 𝑞 𝑗,𝑡 , respectively.
Because each intermediate goods firm possesses market power, it can generate aflow profit, denoted by 𝜋𝜏 , for every 𝜏 ∈ [𝑡 + 1, ∞) following its inception in period 𝑡.
Consequently, the market value of each firm, denoted by 𝑣 𝑡 , is defined as the sum of the
discounted present value of the flow profits accrued from period 𝑡 + 1 to perpetuity.
3.3.3

R&D Sector

In the R&D sector, each firm produces new blueprints, denoted by 𝐴𝑡+1 − 𝐴𝑡 , by integrating
labor (i.e., researchers), 𝐿 𝐴,𝑡 , and existing knowledge in period 𝑡. These blueprints arethen traded in a perfectly competitive market. The R&D process is expressed as𝜙𝐴𝑡+1 − 𝐴𝑡 = 𝐴𝑡 𝐿 𝐴,𝑡 ,0 < 𝜙 < 1.

(24)

𝜙

When researchers produce a new blueprint, they can leverage existing knowledge, 𝐴𝑡(i.e., knowledge spillover). Equation (24) indicates that the cost of producing one unit of𝜙a new blueprint is 𝑤 𝑡 /𝐴𝑡 , while the revenue equals 𝑣 𝑡 . In conjunction with the perfectcompetition in this sector, the free entry condition ensures that the following expression
holds in equilibrium:

𝑣𝑡 ≤

𝑤𝑡
,
𝜙

with equality when 𝐿 𝐴,𝑡 > 0,

(25)

𝐴𝑡
implying that when the cost of producing a new blueprint exceeds the generated revenue,
no R&D activities are undertaken.

3.4

Market-clearing Conditions

The economy is characterized by three markets: capital, final goods, and labor. Aggregate
demand for assets is ( 𝐴𝑡+1 − 𝐴𝑡 )𝑣 𝑡 + 𝐴𝑡 𝑣 𝑡 . Combined with the household’s saving decision in
22

Equation (16), we express the market-clearing condition for the capital market as follows:( 𝐴𝑡+1 − 𝐴𝑡 )𝑣 𝑡 + 𝐴𝑡 𝑣 𝑡 = 𝑎 𝑡 𝑁𝑡 .

(26)

The first term on the left-hand side, ( 𝐴𝑡+1 − 𝐴𝑡 )𝑣 𝑡 , represents the value of newly establishedfirms in period 𝑡, whereas the second term, 𝐴𝑡 𝑣 𝑡 , is the value of existing firms at the
beginning of period 𝑡.
The final goods are produced by firms in the final goods sector and consumed byhouseholds in adulthood and old age. Hence, the market-clearing condition for the final
goods market is 𝑌𝑡 = 𝑐 1,𝑡 𝑁𝑡 + 𝑐 2,𝑡 𝑁𝑡−1 + 𝑒 𝑡 𝑁𝑡 .
Aggregate labor demand is the sum of labor demand by firms in the final goods,
intermediate goods, and R&D sectors, whereas the aggregate labor supply by households
is given by (1 − ℎ 𝑓 ,𝑡 − ℎ𝑚,𝑡 )𝑁𝑡 . Using Equations (17) and (18) yields the following labormarket-clearing condition:𝛾(𝜂 𝑓 + 𝜂𝑚 )𝑁𝑡 .
𝐿𝑌 ,𝑡 + 𝐴𝑡 𝑥𝑡 + 𝐿 𝐴,𝑡 = 1 −
1+𝛽+𝛾


(27)

4

Dynamics and Effects of Male-dominant Social Norms

4.1

Demographic Transition and Knowledge Accumulation

To analyze the dynamic system of the model, we derive a phase diagram for the ( 𝐴𝑡 , 𝑁𝑡 )plane. First, we focus on the case in which the free entry condition in the R&D sectorin Equation (25) holds with equality (i.e., R&D activities are undertaken). Substituting
Equations (16) and (25) into (26), we obtain

𝐴𝑡+1 =𝛽𝜙
𝑁 𝑡 𝐴𝑡 .
1+𝛽+𝛾

(28)

Conversely, when Equation (25) does not hold with equality, the knowledge stock in thiseconomy does not increase over time, and thus 𝐴𝑡+1 = 𝐴𝑡 . As the idea does not depreciate,23

there is no region such that 𝐴𝑡+1 < 𝐴𝑡 in the phase diagram. Consequently, the Δ𝐴𝑡 = 0
locus is expressed as follows:𝑁𝑡 =1 + 𝛽 + 𝛾 1−𝜙
𝐴𝑡
𝛽

(29)

Knowledge capital increases above the Δ𝐴𝑡 = 0 locus, but remains unchanged below thislocus.
Subsequently, we address the dynamics of population growth. Substituting the equilibrium fertility rate from Equation (15) into Equation (2), we express the resulting population
dynamics as follows:
𝑁𝑡+1 =𝛾𝑁𝑡 .
(1 + 𝛽 + 𝛾) 𝜒| {z }(30)𝑛∗This equation implies 𝑁𝑡+1 ≥ 𝑁𝑡 if and only if 𝑛∗ ≥ 1. In addition, from Proposition 1, it
holds that 𝑛∗ ≥ 1 if and only if 𝑠 ≤ b
𝑠.
The dynamic system in this economy is characterized by Equations (28) and (30),with the phase diagram on the ( 𝐴𝑡 , 𝑁𝑡 )-plane illustrated in Panels (a) and (b) of Figure
6. Notably, because both population and knowledge capital serve as state variables, thedynamics are examined given their initial points, 𝑁0 and 𝐴0 . Figure 6 indicates that the
male-dominant social norm significantly influences demographic transition and knowledge
accumulation. Panel (a) shows the phase diagram when the degree of conservativeness ofthe male-dominant social norm is sufficiently low (i.e., 𝑠 < b𝑠). In this case, the equilibrium
fertility rate 𝑛∗ exceeds 1, leading to population growth over time. Additionally, if 𝑁0 is
sufficiently large relative to 𝐴0 , the free entry condition in the R&D sector, as specified in
Equation (25), holds with equality, resulting in the accumulation of knowledge capital overtime. Consequently, the economy experiences a virtuous cycle: an increased labor force(i.e., the number of researchers) boosts R&D activities, enhances the productivity of firms
in the final goods sector, and ultimately raises household living standards. Importantly, as
the population grows exponentially, the growth rate of knowledge capital remains constant,suggesting the economy can sustain a balanced growth path.

24

𝑁𝑡

𝑁𝑡
𝐴𝑡+1 > 𝐴𝑡

𝐴𝑡+1 > 𝐴𝑡
Δ𝐴 = 0

Δ𝐴 = 0

𝑁0
𝐸
𝑁0

𝐸′

𝐴𝑡+1 = 𝐴𝑡

𝐴𝑡+1 = 𝐴𝑡
𝐸 ′′
𝐴𝑡

𝑂

𝐴𝑡
𝑂

𝐴0
(a) When 𝑛∗ > 1 (i.e., 𝑠 < b𝑠)𝐴0(b) When 𝑛∗ < 1 (i.e., 𝑠 > b
𝑠)Fig. 6 Phase diagram on the ( 𝐴𝑡 , 𝑁𝑡 ) plane
Conversely, Panel (b) shows the phase diagram for 𝑠 > b
𝑠. In this case, the population
decreases over time because 𝑛∗ is less than 1. By contrast, unless the free entry condition
in Equation (25) is satisfied with equality, R&D activities are conducted, leading to theaccumulation of knowledge capital over time. Indeed, Equation (28) indicates that theknowledge spillover effect captured by 𝜙 > 0 allows for the accumulation of knowledge
capital even under a negative population growth rate. However, Panel (b) suggests thatsuch knowledge accumulation is unsustainable; a persistent decline in the population will
eventually negate the knowledge spillover effect. Consequently, R&D activities cease,
thereby halting the accumulation of knowledge capital. Thus, the economy enters aphase of stagnation in its accumulation of knowledge capital coupled with a continuous
population decline, described as the empty planet scenario (Jones, 2022).

4.2

Aggregate Labor Supply and Income Growth

We next analyze the influence of the male-dominant social norm on income growth. To
this end, we first derive the equilibrium condition in the production sectors.
As each intermediate goods firm possesses the market power over the final goods firms,
substituting Equation (23) into (20) yields the equilibrium quantity of the final goods as25

follows:
𝛼2
𝑌𝑡 =
𝑤𝑡


 1−𝛼𝛼𝐴𝑡 𝐿𝑌 ,𝑡 .

(31)

Additionally, substituting Equation (31) into (22), we obtain the equilibrium wage asfollows:
𝑤 𝑡 = 𝛼𝐴ˆ 𝑡1−𝛼 ,(32)

where 𝛼ˆ ≡ 𝛼2𝛼 (1−𝛼) 1−𝛼 . Notably, Equation (32) is derived using the optimality conditions
for both the final and the intermediate goods firms. This equation implies that the wageis uniquely determined by the knowledge stock and they are positively associated. Given
that the final goods are numéraire, their price relative to the wage decreases as the variety
of intermediate goods increases.
Using the optimality condition in the production sector in Equation (32) and aggregate
labor supply function specified on the right-hand side of Equation (27), we investigate
the influence of male-dominant social norms on income growth. Figure 7 illustrates
the relationship between wages and labor quantity in equilibrium over time. Panel (a) of
Figure 7 depicts the case in which the conservativeness of the male-dominant social norm issufficiently low (i.e., 𝑠 ≤ b𝑠) and the free entry condition in the R&D sector is satisfied withequality in period 𝑡. The horizontal lines correspond to Equation (32) and the vertical lines
represent the aggregate labor supply.6 Panel (a) indicates that over time, both wages and thequantity of labor increase concurrently. In this economy, R&D activities are undertaken,
causing wages to rise over time because of the positive relationship between wages andknowledge capital, as specified in Equation (32). Simultaneously, a less conventionalsocial norm (i.e., 𝑠 < b𝑠) facilitates labor force growth. Therefore, the horizontal line
shifts upward, whereas the vertical line moves to the right. This finding aligns with thephase diagram in Panel (a) of Figure 6, which highlights that income growth that occurs
simultaneously with population growth is sustainable.
6The logarithmic utility function in Equation (1) combined with the Cobb–Douglas form of the home
production function in (7) implies that the substitution effect is precisely offset by the income effect.
Consequently, the (aggregate) labor supply function does not hinge on wages, resulting in the vertical line
in Figure 7. The positive elasticity of labor supply does not change the qualitative results.

26

𝑤𝑡
RHS of (27) at 𝑡 + 1
RHS of (27) at 𝑡

𝑡+1

∗
𝑤 𝑡+1

𝑤 𝑡∗

𝑡

𝑂

𝐿 𝑡∗

1−𝛼
𝑤 𝑡+1 = 𝛼𝐴
ˆ 𝑡+1

𝑤 𝑡 = 𝛼𝐴ˆ 𝑡1−𝛼

𝐿𝑡

∗
𝐿 𝑡+1

(a) When 𝑠∗ < 𝑠 < b𝑠, 𝐴𝑡+1 > 𝐴𝑡 , the wage and labor increase.

𝑤𝑡

𝑤𝑡
RHS of(27) at 𝑡
RHS of (27) at 𝑡 + 1

∗
𝑤 𝑡+1

𝑡+1

𝑂

1−𝛼
𝑤 𝑡+1 = 𝛼𝐴
ˆ 𝑡+1

𝑡

𝑤 𝑡∗

∗
𝐿 𝑡+1

RHS of(27) at 𝑡
RHS of (27) at 𝑡 + 1

𝐿 𝑡∗

𝑤 𝑡 = 𝛼𝐴ˆ 𝑡1−𝛼

𝑤 𝑡∗

𝐿𝑡
𝑂

𝑡+1

∗
𝐿 𝑡+1

𝑡

𝐿 𝑡∗

𝑤 𝑡 = 𝛼𝐴ˆ 𝑡1−𝛼𝐿𝑡(b) When 𝑠 > b
𝑠, 𝐴𝑡+1 > 𝐴𝑡 , labor decreases, while the wage (c) When 𝑠 > b
𝑠, 𝐴𝑡+1 = 𝐴𝑡 , labor decreases, while theincreases.
wage is constantFig. 7 Wages and labor quantities in equilibrium over time

By contrast, Panel (b) in Figure 7 depicts the relationship between wages and thequantity of labor over time when 𝑠 is higher than b𝑠 and the free entry condition in Equation(25) holds with equality in period 𝑡. Despite R&D activities leading to wage growth oversuccessive periods, there is a concomitant reduction in the labor force. Consequently, thehorizontal line shifts upward, whereas the vertical line shifts to the left. This phenomenon
corresponds to the transition from points 𝐸 to 𝐸 ′, as depicted in the phase diagram in
Panel (b) of Figure 6.
Finally, Panel (c) of Figure 7 illustrates the relationship between wages and the quantity27

of labor when 𝑠 exceeds b𝑠 and the free entry condition does not hold with equality. In
this case, R&D activities are no longer undertaken and thus wages remain constant overtime. A population decline shifts the labor supply curve (i.e., the vertical line) to the left,
leading to a decrease in the quantity of labor in the subsequent period. This phenomenon
is consistent with the transition from points 𝐸 ′ to 𝐸 ′′, as depicted in the phase diagram in
Panel (b) of Figure 6. We summarize the dynamic analysis in Sections 4.1 and 4.2.
Proposition 2. There exists b𝑠 ∈ [𝑠∗ , ∞) such that the economy exhibits sustained growthin both population and income per capita if and only if 𝑠 ≤ b
𝑠. Conversely, the economy
displays stagnation in income per capita growth and eventual population erosion if andonly if 𝑠 > b
𝑠.

4.3

Explaining the Observed Phenomena

We explain the phenomena described in Section 2 by classifying the high-income countries
in Figure 1 into three groups: (A) countries with a total fertility rate of approximately 2
and a positive income per capita growth rate, (B) countries with a total fertility rate of
approximately 1.5 and a positive income per capita growth rate, and (C) countries with a
total fertility rate of approximately 1.5 and an almost negligible income per capita growthrate. Groups A, B, and C include the United States, Italy, and Japan, respectively.
First, our theoretical model suggests that fertility rates are lower in countries withconventional gender norms than in those with less conventional gender norms. Consistent
with this model, cross-national comparisons confirm that Group A countries exhibit higher
fertility rates and less conventional gender norms, whereas those in Groups B and C
display lower fertility rates and conventional gender norms. According to our model, thehouseholds in the latter groups encounter a higher shadow price associated with having
and raising children, leading to reduced fertility rates and a subsequent population decline(Proposition 1). Moreover, it is also suggested that the fertility rates in the countries inGroups B and C are unlikely to recover without addressing conventional gender norms,
thereby approaching a state of population erosion.
28

Second, our model is useful for understanding the positive correlation between fertility
rates and income per capita. In Group A countries in which the fertility rate hovers
around 2, population levels are sustained, ensuring a stable labor supply. This stability inthe labor supply fosters increased R&D activities, thereby promoting income per capita
growth. Conversely, a declining population disrupts this virtuous cycle, making it lesseffective than in Group A. Therefore, conventional gender norms negatively affect fertility,
subsequently impeding economic growth and generating a positive association between
fertility rates and income per capita across high-income countries (Proposition 2).
Finally, we interpret the disparities between Groups B and C. As demonstrated in
Section 2, the income per capita in Group B countries increases constantly despite asignificant population decline. At first glance, this rapid population decline appears to
be inconsequential for sustained economic growth. However, our model indicates thatthese countries are experiencing precarious economic growth owing to their transition
from points 𝐸 to 𝐸 ′ in Panel (b) of Figure 6. Although knowledge capital and income areprojected to rise over time, income growth is expected to eventually stagnate (Figure 7).
Japan, classified into Group C, appears to have already entered this phase of stagnation,
experiencing the economic transition from points 𝐸 ′ to 𝐸 ′′ in Panel (b) in Figure 6. Without
intervention, Group B countries are likely to follow the same trajectory.

4.4

Policy Implications

Social norms have long been regarded as persistent (Alesina et al., 2013), resulting in a
temporal lag in the transition process relative to changes in the real economy (Fernández
et al., 2004; Feyrer et al., 2008). Within this context, Group B countries are unlikely to
avoid economic transition into stagnation in income growth, whereas those in Group C
must wait for eventual population erosion. Is there a radical solution?
Fortunately, recent experimental studies provide evidence that social norms can bemisperceived and that simple information interventions can correct these misperceptions.
For instance, Bursztyn et al. (2020) demonstrated that the vast majority of young married
29men in Saudi Arabia privately support women working outside the home and significantly
underestimate the support from similar men. Moreover, correcting these beliefs increases
men’s willingness to help their wives search for jobs. Additionally, using extensive datafrom 60 countries, Bursztyn et al. (2023) showed that such misperceptions of gendernorms are widespread globally. Based on these findings, the countries in Groups B and C
could avoid stagnation in economic growth through simple and cost-effective informationinterventions. It is imperative to address conventional gender norms because Group B
countries are steadily approaching a phase of economic stagnation, whereas those in GroupC are already experiencing this phase, with their populations shrinking.
These policy implications are relevant for developing countries. As noted by Cervellati
et al. (2023), technology spillovers have enabled developing countries to experience relatively rapid economic growth compared with their developed counterparts. Consequently,
these countries are likely to display pronounced disparities between women’s labor market
opportunities (i.e., the real economy) and the gender roles ingrained within and outside
households (i.e., gender norms). Our model suggests that to circumvent an economic transition characterized by stagnation in income growth and continuous population decline,
it is essential to implement timely corrections or adjustments to gender norms that alignwith the current stage of economic development.

5

Conclusions

This study explains international differences in fertility rates and income per capita by
constructing an overlapping generations model with endogenous fertility and labor supply. The proposed model incorporates gender norms and R&D activities to examine theirpotential negative impacts. We demonstrate that gender norms have undesirable effects
on fertility and economic growth. Conventional gender norms distort the allocation ofhousework and childcare between women and men, resulting in inefficient home production. This inefficiency results in a higher shadow price associated with having and raising30

children, which reduces fertility rates. The decline in fertility rates reduces the labor force
and undermines R&D activities, thereby negatively affecting the accumulation of knowledge capital and impeding economic growth. Consequently, in economies in which gendernorms are deeply ingrained, income growth stagnates and the population may decline overtime. Conversely, in economies in which gender norms are more progressive, sustained
growth is observed in both income per capita and population. Our study underscores
the importance of addressing conventional gender norms to ensure that both developed
and developing economies follow sustainable growth paths. Simple and cost-effective
information interventions may help achieve this goal (Bursztyn et al., 2020).
In future research, it would be valuable to incorporate the accumulation of humancapital, which is expected to be influenced by inefficiencies in home production andimpact economic growth. In addition, introducing the interaction between human andphysical capital is crucial. These extensions could enhance our understanding of therepercussions of gender norms and provide more detailed policy implications.

Acknowledgments
We thank Real Arai, Ryo Arawatari, Ryo Horii, Miki Kohara, Kazuo Mino, and Kizuku
Takao for their valuable comments and suggestions.

This study was supported by

JSPS KAKENHI (grant number JP24K22635) and JSPS KAKENHI (grant number
JP24KJ1584). Conflicts of interest: None

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