A New Estimator of Search Duration and Its Application to the Marriage Market
| Published date | 01 December 2018 |
| Author | Pavel Jelnov |
| Date | 01 December 2018 |
| DOI | http://doi.org/10.1111/obes.12248 |
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©2018 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 80, 6 (2018) 0305–9049
doi: 10.1111/obes.12248
A New Estimator of Search Duration and Its
Application to the Marriage Market
Pavel Jelnov†
†Leibniz Universit¨at Hannover and IZA, Institut f¨ur Arbeits¨okonomik, K¨onigsworther Platz 1
D-30167 Hannover, Germany (e-mail: jelnov@aoek.uni-hannover.de)
Abstract
It is well known that female age at first marriage positively correlates with male income
inequality.The common inter pretation of this fact is that marital search takes longer when
the pool of potential mates is more unequal. This paper challenges that interpretation with a
novel econometric method. I utilize the fact that the female age at first marriage was shown
to be a sum of a skewedter m, possiblyrelated to search, and a normally distributed residual.
I estimate search duration as the expected skewed term. I find that in the American data
this term does not positively correlate with male income inequality and female education.
I. Introduction
A large body of studies documents a positive correlation between male income inequality
and female age at first marriage (Keeley, 1977, 1979; Bloom and Bennett, 1990; Danziger
and Neuman, 1999; Loughran, 2002; Gould and Paserman, 2003; Coughlin and Drewianka,
2011; Li, 2014; Yu and Xie, 2015). Generally, the literature interprets this correlation as a
positive correlation between male income inequality and female marital search duration.
This interpretation is made by assumption, intuitively inspired by the search theory. To the
best of my knowledge, no empirical study tested this assumption until now. The reason is
simple: search duration is an unobservable variable in almost every data set.To close this
gap, I propose a new econometric method that utilizes the contribution of Ansley Coale,
one of the most prominent demographers of the twentieth century, who discovered the
common age pattern of marriage across times and countries. Specifically, I rely on the
Coale–McNeil decomposition of the female age at first marriage to identify a possible
marital search duration. Coale and McNeil decompose the age of female marriage into
a skewed term, possibly related to search, and a normally distributed residual. Using the
American Vital Statistics for the age of marriage, I estimate the mean skewed term in 35
states for every year between 1968 and 1995. Using the Current Population Survey for
income inequality, mean female education, and other covariates on the state-year level,
I show that whileresidual male income inequality is positively correlated with mean female
JEL Classification numbers: J12, D83.
1090 Bulletin
age at first marriage, it may be negatively correlated with mean marital search duration.
This surprising finding implies that the channel that links female marital search to male
income inequality is not necessarily the one intuitively adopted by the literature.
Furthermore, female education is also positively correlated with female age at first
marriage, but by my method, it is found to be negatively ornot at all cor related with marital
search duration. This finding may be intuitively explained: while education is sometimes
associated with a postponed entrance into the marriage market, the search for a mate is
facilitated by interaction with classmates. Moreover, women who enter the market at an
older age may be under biological pressure to accept offers. Finally, the shorter marital
search of higher-educated women may also be related to their increased attractiveness,
leading to more frequent marriage offers.
This paper’s identification strategy relies on the fact that female age at first marriage
in different countries and times is shown (Coale and McNeil, 1972; hereafter CM) to be
a sum of two terms: a skewed term (a convolution of a few exponential distributions)
and a normally distributed residual. The identification assumption is that the skewed term
is related to marital search. This assumption relies on the association of the exponential
distribution with the waiting time. The CM paper, Kaneko(2003), and my findings provide
empirical support for this assumption. Particularly, CM show that in Frenchdata the skewed
term is indeed related to duration of stay in the marriage market. Kaneko (2003) shows in
Japanese data that the skewed term is shorter when marriages are arranged. In this paper,
I show that variables that may affect search and reservation values, particularly the male-
to-female sex ratio and availability of divorce, are indeed correlated with the skewed term
but not with the residual one. On the other hand, variables that are likely related onlyto the
age of entrance into the marriage market, particularly the minimal legal age of marriage,
are indeed correlated with the residual term but not with the skewed one.
Furthermore, I consider some theoretical concerns, particularly the question of whether
within-state variation across years in the residual male income inequality is the correct
measure in the case of marriage market. Marriage rates may correlate with within-state
inequality across years if they adjust to business cycles. This is a predictable relationship
of marriage timing and inequality, but, to the best of my knowledge, there is no certain
theoretical prediction about the relationship between search duration and business cycles.
Therefore, within-state variation across years maybe an inappropriate tool to test the search
theory. This concern is addressed by considering long-run levels of income inequality,
lagged values, and removal of state fixed effects. While the former two alternatives do not
alter the results significantly, removal of state fixed effects inflates many coefficients and
some coefficients change their sign. However, the negative effect of male inequality on the
mean skewed term is found to be quite robust. The relative robustness of the effects on
the skewed term also holds for other robustness checks, such as considering raw income
instead of residual income. Moreover, the year fixed effects are also more consistent over
the years once the mean skewed term and not the mean age of marriage is the dependent
variable in the regression. All these findings may be seen as supporting evidence for a
behavioural interpretation of the mean skewed term.
Kaneko (2003) rewrites the CM marriage age density function such that it has a single
shape parameter. This parameter is intuitive as it is directly related to the asymmetry of
the marriage-age distribution. The shape parameter has a statistical interpretation. For
©2018 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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