Household Formation, Female Labor Supply, and Savings

• Author: Hans Fehr,Fabian Kindermann,Manuel Kallweit
• Published date: 01 October 2016
• Date: 01 October 2016
• DOI: http://doi.org/10.1111/sjoe.12154

Scand. J. of Economics 118(4), 868–911, 2016

DOI: 10.1111/sjoe.12154

Household Formation, Female Labor

Supply, and Savings∗

Hans Fehr

University of Wuerzburg, DE-97070 Wuerzburg, Germany

hans.fehr@uni-wuerzburg.de

Manuel Kallweit

German Council of Economic Experts, DE-65180 Wiesbaden, Germany

manuel.kallweit@svr-wirtschaft.de

Fabian Kindermann

University of Bonn, DE-53113 Bonn, Germany

fabian.kindermann@uni-bonn.de

Abstract

In this paper, we aim to quantify the impact of changing family structures on labor supply and

savings in Western societies. Our dynamic general equilibrium model features both genders,

and it takes into account changes in marital status as a stochastic process. The numerical

results indicate that changes in household formation can partly explain the reallocation of

male and female labor supply observed during the last decades in Germany. We also find a

negative impact on capital accumulation, and we show that a combination of higher marital

risk and a narrowing gender wage gap can explain the changes in hours ratios between single

and married men and women.

Keywords: Home production; life-cycle model; marital risk; stochastic general equilibrium

JEL classification:J12; J22

I. Introduction

Almost all Western societies are currently experiencing an unprecedented

two-dimensional demographic transition. On the one hand, low fertility and

reduced mortality rates change the age structure of the population. On the

other hand, declining marriage and increasing divorce rates radically alter

the traditional family structure within cohorts. While numerous studies

∗We are grateful for helpful comments from Karl Ove Aarbu, Johann Brunner, Alexia

F¨

urnkranz-Prskawetz, Alfred Maussner, Lex Meijdam, two anonymous referees, and seminar

participants at the universities of Augsburg and Lund, DIW Berlin, NETSPAR Pension

Workshop, CESifo Munich, and the annual congresses of the German Economic Association

and ESPE. Financial support from NETSPAR and the Fritz Thyssen Stiftung is gratefully

acknowledged.

CThe editors of The Scandinavian Journal of Economics 2015.

H. Fehr, M. Kallweit, and F. Kindermann 869

have already evaluated the economic consequences of an aging population,

much less research has focused on the impact of the changing household

structure for various economic aggregates. Changes in the number of

couples and singles in an economy will alter the respective income

distribution as well as the structure of tax payments and public transfers.

In addition, precautionary behavior will be adjusted, as families offer an

(incomplete) insurance contract against lifespan (Kotlikoff and Spivak,

1981) and income risk (Attanasio et al., 2005; Halla and Scharler, 2012).

Consequently, the actual and the perceived future household structure will

affect life-cycle labor supply, consumption, and savings behavior, which in

turn might have severe effects on labor and capital markets.

In the present study, we attempt to quantify such macroeconomic

repercussions of the changing family structure. Therefore, we develop a

two-gender life-cycle family model with endogenous labor supply, which

accounts for income and lifespan uncertainty, and distinguishes between

market work and home production. Throughout their life cycle, individuals

are exposed to the (exogenous) risk of getting married and divorced. When

being single, individuals choose consumption, labor supply in the market,

the production of home goods, and savings. When married, two partners

have to decide about whether and how to make use of specialization within

the household.

We calibrate our model to the German economy, which has experienced

a transformation of household structures in the last decades that is typi-

cal for Western societies. In order to so, we use macroeconomic statistics

as well as microeconomic data on time use and labor productivity. Our

analysis then proceeds in three distinct steps. First, we identify the driving

forces that determine behavioral differences between married and single

men and women. Second, we quantify the impact of a change in marriage

and divorce probabilities on both individual behavior and the macroecon-

omy. Therefore, we run the model with two sets of probabilities: one set is

derived from the marital and divorce behavior observed in 1970, and the

other from current behavior. Third, in order to put our results into perspec-

tive, we use our model to clarify the effects of changes in the gender wage

gap during the same period on different types of households.

Our quantitative results indicate that differences in eduction and wages

between men and women as well as the fact that married partners can

make use of joint filing in the tax system are the major determinants of

specialization within the marriage. We also find that differences in life

expectancy mainly explain the disparities in savings behavior of men and

women.

When we alter marriage and divorce probabilities, macroeconomic ag-

gregates are affected by both a compositional and a behavioral effect.

Because married women work less than single women, aggregate female

CThe editors of The Scandinavian Journal of Economics 2015.

870 Household formation, female labor supply, and savings

labor supply increases when the share of married couples in the population

declines. The same argument applies to the labor supply of men, but vice

versa. As married couples have a higher savings rate, capital accumulation

is negatively affected by the changes in household structure. In terms of

individual behavior, we f ind that changes in marital risk have an impact

on the life-cycle labor supply and savings profiles of singles, while labor

supply of married couples is almost unaltered. This finding is related to the

implicit insurance provision of the family. In a marriage, partners can adapt

their labor supply and home production effort so as to absorb idiosyncratic

productivity shocks that are uncorrelated between the two spouses. Be-

neath this implicit insurance against labor market uncertainty, inheritances

from one partner to the other provide insurance against longevity risk. If

marriage becomes less likely, single individuals anticipate the loss of this

implicit insurance mechanism. As a consequence, they increase their labor

supply in the market at early stages in life to build up precautionary sav-

ings. However, in turn they decrease their labor supply towards the end of

the working life, and start to live off their savings earlier, so that labor

supply effects are mostly inter-temporal. In total, the change in marital and

divorce risk therefore comes along with an increase in aggregate female

labor supply and a decline in male labor supply. In terms of asset accumu-

lation, the negative compositional effect is almost washed out by the strong

increase in single individuals’ savings, so that aggregate savings decline

only slightly.

What the change in marital risk does not explain are the empirically

observed changes in hours ratios between men and women. Our simulations

reveal that these changes can mostly be attributed to the narrowing of the

gender wage gap between 1970 and 2010. Interestingly, our model is able

to capture the empirical fact that the hours ratio between married and

single women has significantly increased over the last decades, meaning

that the change in the gender wage gap had a much stronger impact on

married women’s labor supply than on single women. The reason for this

asymmetry is that a narrowing gender wage gap crowds out specialization

within the family, and increases the ability of women to participate in risk

sharing (see Heathcote et al., 2010).

Our approach is related to several strands of the recent literature using

calibrated models. First, it builds on Rogerson (2009) and Olovsson (2009),

who analyze labor supply issues in models with home production. Second,

it is linked to the large body of literature that tries to explain the long-run

changes in labor supply of married women (e.g., Greenwood et al., 2005;

Olivetti, 2006; Attanasio et al., 2008; Kaygusuz, 2010; Guner et al., 2012).

Finally, it is connected to family models (e.g., Caucutt et al., 2002; Chade

and Ventura, 2002; Greenwood and Guner, 2009), which either deal with

marriage issues or concentrate on the relationship between fertility and

CThe editors of The Scandinavian Journal of Economics 2015.