Life‐Cycle Consumption and Children: Evidence from a Structural Estimation
| Author | Thomas H. Jørgensen |
| DOI | http://doi.org/10.1111/obes.12170 |
| Date | 01 October 2017 |
| Published date | 01 October 2017 |
717
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
doi: 10.1111/obes.12170
Life-Cycle Consumption and Children: Evidence from
a Structural Estimation*
Thomas H. Jørgensen†,‡
†Department of Economics, University of Copenhagen, Øster Farimagsgade 5, building 26
DK-1353, Copenhagen, (e-mail: thomas.h.jorgensen@econ.ku.dk)
‡Centre for Applied Microeconometrics (CAM)
Abstract
I estimate by maximum likelihood a dynamic model of optimal intertemporal allocation
of consumption in the presence of children using high-quality Danish longitudinal data.
The number and age of all children can affect the marginal utility of consumption while
income uncertainty, credit constraints and postretirement motives also influence household
behaviour. While I estimate that children have a surprisingly small effect on the marginal
utility of non-durable consumption, data simulated from the estimated model replicates
similar correlations between log consumption growthand changing household composition
as found in the Danish data and typically found in UK and US data. To reconcile the
results with existing studies, I illustrate how ignoring precautionary motives increases the
estimated importance of children. The results indicate that precautionary motives might
play a larger role than children in explaining the observed consumption age profile.
I. Introduction
This study is concerned with the effect of children on the marginal utility of non-durable
consumption over the life cycle. The average number of children and non-durable con-
sumption share similar hump-shaped (inverted-U) age profiles. The extent to which chil-
dren affect the marginal utility of consumption has, therefore, received great attention over
the last two decades with an important role for children as the most common finding.1
JEL Classification numbers: D12, D14, D91.
*I am grateful to Mette Ejrnæs, Bertel Schjerning, Martin Browning, Jeppe Druedahl, Søren Leth-Petersen,
Christopher Carroll, John Rust, Richard Blundell, Orazio Attanasio, Hamish Low, Miles Kimball, Dennis Kris-
tensen, Daniel Borowczyk-Martins, Kjetil Storesletten, J´erˆome Adda,Anders Munk-Nielsen, Mette Foged, Damoun
Ashournia, Signe Dyrberg and conference participants at the EEA in Gothenburg 2013, the CAM December workshop
in Copenhagen, 2013, the IAAE in London, 2014, and the ESEM in Toulouse,2014, for comments and suggestions.
Financial support from the Danish Council for Independent Research in Social Sciences (FSE, grant no. 4091-00040)
is gratefully acknowledged. All errors are myown.
1Irvine (1978) might be one of the first to suggest that the hump in consumption could be due to changes in
household composition. Some important contributions to the literature on the effect of children on consumption are
due to Blundell, Browning and Meghir (1994); Banks, Blundell and Preston (1994); Attanasio and Weber (1995);
Attanasio and Browning (1995); Attanasio et al. (1999); Fern´andez-Villaverde and Krueger (2007) and Browning
and Ejrnæs (2009).
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 79, 5 (2017) 0305–9049
718 Bulletin
The same consumption profile can, however, be rationalized by alternative life cycle mo-
tives such as precautionary motives or non-separability between consumption and leisure
with very different policy implications.2Despite the amount of studies analysing the ef-
fect of demographics on consumption, allowing for multiple consumption-savingsmotives
simultaneously is rare in this literature.
I estimate the effect of children on the marginal utility of consumption by a novel
full-solution maximum likelihood (ML) estimator. The estimated dynamic model of in-
tertemporal allocation of consumption allows the number and age of children to affect the
marginal utility of consumption while income uncertainty,credit constraints and postretire-
ment motives also influence consumption and saving behaviour. I estimate the model using
Danish administrative register data giving detailed longitudinal information on household
characteristics, income and, importantly, most assets and liabilities. Net worth is a crucial
determinant of optimal intertemporal allocation of consumption and savings, which I use
to identify the parameters of interest.
I find an economically negligible effect of children on the marginalutility of consump-
tion. While I estimate that children have a surprisingly small effect on the marginal utility
of non-durable consumption, the risk aversion coefficients and subjective discount factors
are estimated in the range typically found. The estimated model fits the Danish data very
well and simulated data from the estimated model reproduce correlations between log con-
sumption growth and changing household composition as in the Danish data and typically
found in UK and US data. Particularly, applying a similar log-linearized Euler equation
estimator as in Attanasio et al. (1999) yields similar results for the Danish data and data
simulated from the estimated model.3The estimation results in Attanasio et al. (1999) and
the preferred specification in Alan, Attanasio and Browning (2009) imply that children
increase marginal utility of consumption by around 40% and 150% respectively. Brown-
ing and Ejrnæs (2009) find that the number and age of children can completely explain
the hump in consumption over the life cycle. Log-linearized Euler equation estimation
methods do not, however, perform well if households face precautionary motives (Carroll,
2001; Ludvigson and Paxson, 2001; Alan, Atalay and Crossley, 2012; Jørgensen, 2016).
To reconcile my results with existing studies, I investigate how ignoring precautionary
motives increases the estimated importance of children in the Danish data. As mentioned
above, log-linearized Euler equation estimates (which assumes away precautionary mo-
tives) are in the same magnitude as found in UK and US data. This is also the case when
simulating data from the model with small or no effects of children on the marginal util-
ity of consumption.4Furthermore, I find that the full-solution estimates of the effect of
2Thurow(1969) shows how impatient consumers facing credit constraints can generate a hump in the consumption
age profile and Heckman (1974) shows how non-separability betweenconsumption and leisure could be yet another
explanation for the observed consumption age profiles.
3Aggregating to cohort levels, the regression coefficient between log consumption growth and the growthin the
number of children is around 0.2 in the Danish data and 0.1 in the simulated data based on the estimated model. The
exact magnitudes differ slightly across educational groups. Attanasio et al. (1999) report a regression coefficient of
around 0.2 from synthetic cohorts based on the CEX (using IV estimation in a slightly different setup).
4This result stems from the fact that the inability or unwillingness of risk averse consumers to borrow against
future income growth produces a positive correlation between income growth and consumption growth.This is well
known and the excess sensitivity of consumption to income has often been attributed to credit constraints. However,
because children tend to arrive when income (and thus consumption) grows the most, this will produce a positive
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
To continue reading
Request your trial