The causal effect of the number of children on gender‐specific labour supply elasticities to the firm

• Date: 01 January 2021
• Published date: 01 January 2021
• DOI: http://doi.org/10.1111/irj.12314

The causal effect of the number of children

on gender-specif‌ic labour supply elasticities

to the f‌irm

Céline Detilleux, PhD candidate and Nick Deschacht

ABSTRACT

We estimate the effect of the number of children on the female and the male wage

elasticities of labour supply to the f‌irm using instrumental variables estimation in data

from the US Current Population Survey (2000–19). Parents’number of children is in-

strumented with the sex mix of their f‌irst two children. We f‌ind that the male wage

elasticity of labour supply to the f‌irm signif‌icantly increases with the number of chil-

dren, while the female elasticity is not signif‌icantly altered. That is, we f‌ind evidence

that male labour markets become more competitive with the arrival of children.

Our results also show that f‌irms have substantial monopsonistic power and, in line

with the monopsony theory of the gender pay gap, that male labour markets are more

competitive than female markets.

1 INTRODUCTION

The effect of parenthood has been extensively investigated in the literature, and there

is clear evidence that children and family obligations have a substantial impact on the

labour market outcomes of men and women (Angelov et al., 2016; Angrist and

Evans, 1998; Cools et al., 2017; Lundberg and Rose, 2000, 2002). In fact, recent evi-

dence from Kleven et al. (2019) suggests that much of the remaining gender pay gap

in developed economies is due to children and that the fraction of gender inequality

attributable to children has increased dramatically over the past decades. One of

the channels that could explain the effects of children on male and female wages is

the monopsonistic wage setting power by employers. The explanation of gender pay

differences as a result of gender differences in the wage elasticity of labour supply

to the f‌irm and of employers in monopsonistic labour markets engaging in wage dis-

crimination goes back to Joan Robinson (1969), and recent empirical research sug-

gests that gender differences in the elasticity of labour supply go a long way in

explaining raw gender pay gaps (Barth and Dale-Olsen, 2009; Hirsch et al., 2010;

Ransom and Oaxaca, 2010; Sulis, 2011; Vick, 2017; Webber, 2016). Various factors

can cause a difference between male and female f‌irm-specif‌ic labour supply elastici-

ties, but children are an important determinant if the childcare obligations for

mothers, relative to fathers, limit the number of suitable jobs—for example, because

❒Céline Detilleux, Department of Economics, KU Leuven, Warmoesberg 26, Brussels 1000, Belgium and

Nick Deschacht, Department of Economics, KU Leuven, Warmoesberg 26, Brussels 1000, Belgium.

Correspondence should be addressed to: Céline Detilleux, Department of Economics, KU Leuven,

Warmoesberg 26, Brussels 1000, Belgium; email: celine.detilleux@kuleuven.be

Industrial Relations Journal 52:1, 2–24

ISSN 0019-8692

© 2021 Brian Towers (BRITOW) and John Wiley & Sons Ltd

these jobs are in a geographic location that is more compatible with childcare or be-

cause these jobs have f‌lexible work schedules or other family-friendly practices. How-

ever, to the best of our knowledge, there has been no research on the effects of

children on male and female labour supply elasticities to the f‌irm.

The aim of this article was to contribute to the developing literature on imperfect

labour markets of men and women by measuring the effect of parenthood on

gender-specif‌ic wage elasticities of labour supply to the f‌irm. In order to identify the

effect of the number of children, we adopt an instrumental variables (IV) approach

because omitted confounders are likely to produce bias in ordinary least squares anal-

yses of the effects of children on labour market outcomes. The IV approach allows re-

searchers to uncover the causal effect of the explanatory variable on the dependent

variable by inducing changes in the explanatory variable for reasons unrelated to

the dependent variable. We exploit the fact that parents exhibit preferences for a

mixed sex composition among their children; that is, parents who have two sons or

two daughters are somewhat more likely to have another child (Angrist and

Evans, 1998).

Using the Current Population Survey (CPS), we f‌ind that the effect of children

on separation rates is negative once we control for endogeneity. We also f‌ind evi-

dence of monopsony because the male and female wage elasticities of labour sup-

ply to the f‌irm are far from inf‌inity: our estimates suggest that women and men are

paid, respectively, 34 per cent and 46 per cent of their competitive wage. Looking

at our variable of interest, we f‌ind that female labour markets competitiveness is

not signif‌icantly altered when the number of children is increased. Alternatively,

male labour markets become signif‌icantly and substantially more competitive, sug-

gesting that f‌irms have less monopsonistic power over men as their number of chil-

dren increases.

The article is organised as follows: in the next section, we summarise the literature

on parenthood effects and monopsonistic gender wage discrimination. In section 3,

we present the empirical specif‌ication. Sections 4 and 5 present the data set and the

empirical results, and f‌inally, we draw our conclusions in section 6.

2 PREVIOUS LITERATURE

Monopsony in the strict sense means that there is only one employer in the labour

market, so it would be more accurate to def‌ine a market with multiple employers as

an ‘oligopsony’or ‘monopsonistic competition’. While the former describes a situa-

tion where buyers (employers) enjoy some market power despite competition in the

market, the latter is an oligopsony market with free entry so that employers’prof‌its

are driven to zero (Bhaskar et al., 2002). In the ‘new monopsony’framework, monop-

sony is more broadly def‌ined as any departure from perfect competition or any situ-

ation in which an employer faces an upward sloping labour supply curve so that

the f‌irm does not lose all its workers after lowering wages.

Empirically, the degree of monopsonistic power held by employers can be mea-

sured by the Pigouvian Exploitation Index (PEI). Under perfect competition, a

prof‌it-maximising f‌irm hires labour at the going market wage up to the point

where the wage is equal to the value of the workers’marginal product of labour

(MPL). Exercising their monopsony power, employers increase their prof‌its by pay-

ing workers at a rate that does not ref‌lect their productivity. The PEI measures the

gap between worker’s value of the MPL and his/her wage (w), and it can be

3-

© 2021 Brian Towers (BRITOW) and John Wiley & Sons Ltd