A THEORY OF THE CROSS‐SECTIONAL FERTILITY DIFFERENTIAL: JOB HETEROGENEITY APPROACH

• Published date: 01 February 2017
• DOI: http://doi.org/10.1111/iere.12217
• Author: Daishin Yasui
• Date: 01 February 2017

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 1, February 2017

A THEORY OF THE CROSS-SECTIONAL FERTILITY DIFFERENTIAL: JOB

HETEROGENEITY APPROACH∗

BYDAISHIN YASUI1

Kobe University, Japan

This article presents a theory of the cross-sectional fertility differential, which produces the negative wage–fertility

relationship based on job heterogeneity. Although evidence suggests the importance of job heterogeneity in the labor

market, it has largely been ignored in theories of fertility choice. I show that a theory incorporating job heterogeneity

requires only standard conditions on preferences to generate the negative wage–fertility relationship, and the negative

relationship derived from the model is robust to changes in economic environments (e.g., public policy and technology).

Furthermore, the theory reconciles the negative cross-sectional wage–fertility relationship with various time-series

variations in aggregate fertility.

1. INTRODUCTION

This article presents a tractable theory of the cross-sectional fertility differential, which

produces the negative relationship between wages and fertility based on the heterogeneity

of job productivity. Since the seminal work of Becker (1960), many studies have developed

fertility theories using microeconomic techniques. I introduce new insights into this literature by

focusing on the heterogeneity of job (or firm) productivity instead of that of individual ability.2

To introduce job heterogeneity, I construct a labor market model in which firms offer jobs that

specify wages and working hours, individuals apply for their preferred jobs, and one job and one

individual form a production unit. This contrasts with prior studies that conventionally assume

that individuals facing given per-time wages (or given wages per unit of human capital) allocate

their time between labor supply and child rearing. In my model, the cross-sectional fertility

differential arises as an equilibrium outcome in the competitive labor market, where jobs with

different productivity levels offer different labor contracts.3My theory captures the empirical

finding that job heterogeneity plays an important role in accounting for wage differentials and

obtains the result that fertility negatively correlates with wages under moderate restrictions on

preferences.4Moreover, the result is robust to changes in economic environments (e.g., public

policy and technology).

A widespread finding in the economics of fertility is the negative cross-sectional relationship

between wages and fertility: Wealthier parents tend to have fewer children. Many studies have

attempted to explain this negative relationship without assuming that children are an inferior

good. Such studies commonly assume that the cost of children is largely parents’ time. Thus,

parents with higher wages face a higher price of children, while they have more wealth. The usual

substitution and wealth effects coexist. If the substitution effect dominates the wealth effect,

∗Manuscript received December 2014; revised October 2015.

1This research is supported by JSPS KAKENHI Grant Number 15K17022. The author is grateful to three anonymous

referees and Masako Kimura for their valuable comments. Please address correspondence to: Daishin Yasui, Graduate

School of Economics, Kobe University, Rokkodai-cho 2-1, Kobe, Hyogo, Japan. E-mail: yasui@econ.kobe-u.ac.jp.

2Jones et al. (2011) provide an excellent overview of existing theories in the literature.

3Since the structure of my model differs considerably from those in other studies, one may argue that my results are

attributable to the special structure. However, this is incorrect. The structure is just an assumption for introducing job

heterogeneity, which is what differentiates my results from those of prior studies. See Subsection 4.1.

4See Subsection 4.2 on the importance of job heterogeneity in the real labor market.

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(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

288 YASUI

wealthier parents have fewer children. Thus, the literature conventionally imposes restrictive

assumptions on preferences that diminish the wealth effect relative to the substitution effect in

order to explain the negative effect of wages on fertility. Alternatively, some add the parental

choice on child’s quality to derive the negative relationship: Wealthier parents want more quality

and, thus, less quantity. However, adding the quality choice on its own does not generate

the negative relationship, and additional restrictive assumptions on preferences and/or the

child-quality production function are needed (e.g., Becker and Tomes, 1976; Moav, 2005).

Using U.S. data on 30 birth cohorts between 1830 and 1960, Jones and Tertilt (2008) find that

the negative cross-sectional relationship has been surprisingly stable. Over the same period,

technological progress has led to an increase in real wages, the educational level of the pop-

ulation has risen, the government has implemented various policies (e.g., tax, education, and

social-security reforms), and there has been a long secular decline in the average fertility rate

(interrupted by the baby boom). In the last two centuries of the United States, the cross-sectional

wage–fertility relationship remained negative, despite considerable changes in economic envi-

ronments and time-series variations in aggregate fertility. However, with few exceptions, the

negative relationships derived from existing theories are not robust to changes in assumptions,

such as changes in preferences, the education function, or the type and size of policy variables.

I construct a model in which the negative relationship is produced without imposing restrictive

assumptions on preferences and is robust to changes in economic environments.

The only crucial assumption in my model is that it takes time to raise children. I assume

ex ante homogeneous individuals.5They prefer higher consumption (i.e., higher wages) and

higher fertility. Given my assumption that child rearing takes time, longer working hours means

lower fertility. Thus, to induce individuals to work longer hours, firms must pay higher wages

to compensate for lower fertility. Firms are faced with this trade-off in offering labor contracts,

and firms with higher-productivity jobs want employees to work longer hours, even if they must

pay higher rewards, because these jobs produce greater output per unit time. In contrast to the

conventional fertility model based on individuals’ heterogeneity, my model does not entail a

welfare differential among individuals because ex ante homogeneous individuals with different

wages merely choose different contracts on the same indifference curve: There is a substitution

effect, but not a wealth effect. Therefore, my model needs no restriction on the relative size

between the substitution and wealth effects to generate the negative wage–fertility relationship.

Jones et al. (2011) share my motivation to produce a robust negative cross-sectional relation-

ship between wages and fertility and present a prospective theory. In contrast with my theory,

which focuses on the heterogeneity of job productivity, theirs sheds light on the heterogeneity

of individual preferences. They attribute the negative relationship to unobserved heterogene-

ity in parental preferences for fertility. Persons who prefer children receive less education in

anticipation of having more children and supplying less labor to the market in the future. As

a result, they actually earn lower wages and have more children.6The negative relationship

derived from their theory is quite robust to changes in the form of preferences (as is mine) in

my it does not depend on specific functional forms or parameter restrictions. An advantage

of my theory is that I do not need to introduce education into the model. Even in the United

States, in the 19th century, there was limited scope for human capital investments based on

one’s own choice, but the negative relationship was observed (Jones and Tertilt, 2008). My

theory is applied to an economy in which the free choice of employment is guaranteed, even

if the education system is underdeveloped. Mookherjee et al. (2012) have a similar motiva-

tion. They produce a robust negative cross-sectional relationship between wages and fertility

based on a dynamic general equilibrium model. In their model, the choice between skilled and

5See Subsection 4.1 for the effects of introducing individuals’ heterogeneity into my model.

6Kimura and Yasui (2007)also introduce parents’ own educational choice to derive the cross-sectional negative wage–

fertility relationship. In Kimura and Yasui (2007), the source of the education differential is not taste heterogeneity,

but the arbitrage between becoming skilled or remaining unskilled.