This paper examines the effects of the distribution of unemployment by age on the level of unemployment. We provide an extension of the standard equilibrium unemployment model that allows for age dependent job finding probabilities and quit rates. In the empirical part of the paper we apply a panel estimator on data for a set of OECD countries to test the implications of the theoretical model. The results provide the somewhat surprising evidence that the distribution of unemployment by age has a hump-shape effect on the unemployment rate.Distribution of Unemployment by Age, Duration of Unemployment

Carsten Ochsen

English

Research Papers in Economics

 
Thünen-Series of Applied Economic Theory 
Thünen-Reihe Angewandter Volkswirtschaftstheorie 
 
 
Working Paper No. 89 
 
 
 
The Distribution of Unemployment by Age and 
the Unemployment Rate - A Puzzle? 
 
 
 
by 
Carsten Ochsen 
 
 
 
 
 
Universität Rostock 
Wirtschafts- und Sozialwissenschaftliche Fakultät 
Institut für Volkswirtschaftslehre 
2008 The Distribution of Unemployment by Age and
the Unemployment Rate - A Puzzle?
Carsten Ochsen￿
June 4, 2008
Abstract
This paper examines the e⁄ects of the distribution of unemploy-
ment by age on the level of unemployment. We provide an extension
of the standard equilibrium unemployment model that allows for age
dependent job ￿nding probabilities and quit rates. In the empirical
part of the paper we apply a panel estimator on data for a set of
OECD countries to test the implications of the theoretical model. The
results provide the somewhat surprising evidence that the distribution
of unemployment by age has a hump-shape e⁄ect on the unemploy-
ment rate.
Keywords: Distribution of Unemployment by Age, Duration of Unem-
ployment
JEL classi￿cation: J11, J64
￿Department of Economics, University of Rostock; Correspondence: Carsten Ochsen,
Department of Economics, University of Rostock, Ulmenstrasse 69, 18057 Rostock, Ger-
many, e-mail: carsten.ochsen@uni-rostock.de
11 Introduction
This paper examines the e⁄ects of the distribution of unemployment by age
on the unemployment rate. Since aging of the labor force will fundamentally
change the shares of younger and older people that supply labor in most of
the industrialized countries, it seems to be important to analyze if shifts
in the age structure will change the level of the unemployment rate. From
unemployment statistics it is known that the unemployment rate for the
age group 55 to 64 years is lower than the unemployment rates for the age
group 16 to 24 years and the prime-age group (25 to 54 years) in most of the
OECD countries.1 Hence, there are age speci￿c di⁄erences. In addition, it is
observed empirically that the average duration of unemployment increases
with age while the quit rate decreases with increasing age.2
One way to estimate the e⁄ects of the age structure on unemployment
is the shift-share approach. An example is Shimer (1998), who attributes
changes in US unemployment to variations in the population shares of age
groups with low and high age-speci￿c unemployment rates. However, the
results are driven by the age group speci￿c cohort sizes and do not provide
information about age related ￿ ow rates. In contrast to this Shimer (2001)
estimates the impact of changes in the population share of the young (age
16 to 24) on unemployment in the US. In this case it is possible to draw
conclusions about the relative ￿ ow rates for the young only. The contribution
of this paper to the literature is twofold. First, our approach allows to
draw conclusions about di⁄erences in age dependent net ￿ ow rates on the
labor market. In contrast to Shimer (1998) we can separate the ￿ ow e⁄ects
from cohort e⁄ects and unlike Shimer (2001) we consider shifts in the age
distribution of the unemployed instead of a single population share. Second,
the empirical results are related to a set of 16 OECD countries and, hence,
allows more general conclusions.
In section 2 we provide an extension of the standard equilibrium un-
employment model that allows for age dependent job ￿nding probabilities
and quit rates. In section 3 we apply di⁄erent panel estimators on data for
16 OECD countries to test the implications of the theoretical model. The
results provide the somewhat surprising evidence that the distribution of
unemployment by age has a hump-shape e⁄ect on the unemployment rate.
That is, the larger the share of prime-age (25 to 54 years) unemployed, the
higher the unemployment rate.
1See, for example, the OECD Employment Outlook.
2See, for example, Burgess (1993), Pissarides and Wadsworth (1994), Coles and Smith
(1996).
22 The Model
The aim of this paper is to analyze how the distribution of unemployment
by age a⁄ects the level of the unemployment rate. Put di⁄erently, we want
to examine if age dependent net ￿ ow rates on the labor market exist and,
hence, a⁄ect the unemployment rate. Using a weighted summation of age
dependent unemployment rates is not suitable, because this would mix the
￿ ow rate di⁄erences with the cohort size di⁄erences. On this account we
favor an approach that is solely conditional on aggregated labor supply. We
extend the standard equilibrium unemployment model by age dependent
job ￿nding probabilities and quit rates. In the standard approach for steady
state unemployment stock-￿ ow models the equilibrium unemployment rate is
a function of idiosyncratic shocks, ￿, and the average job ￿nding probability,
p:
u =
￿
￿ + p(￿)
(1)
The equilibrium in search and matching models usually depends on a
measure of the tightness of the labor market de￿ned as the ratio of vacancies
to unemployed, ￿ = V=U. The probability p depends on the labor market
tightness ￿ because it determines how successful search is. It is easy to
see that the probability p(￿) can be interpreted as a weighted average with
weights, for example, given by the distribution of unemployment by age.
This follows directly from
pu = p
￿
U1
L
+
U2
L
+ ::: +
Un
L
￿
= p
X
i
ui
u
u = p
X
i
siu. (2)
Ui (with i = 1;2;:::;n) is the age related number of unemployed and L is
the labor force. The term si = Ui=U = ui=u is the age dependent share of all
unemployed. Equation (2) points out that the assumption of a constant p(￿)
for a given ￿ is a special case of a more general approach in which di⁄erent
age speci￿c reemployment probabilities are considered. Hence, according to
this equation the level of the unemployment rate depends on the di⁄erences
in age related reemployment probabilities for a given number of unemployed.
Similar to the average job ￿nding probability, the average idiosyncratic
shock in equation (1) can be interpreted as a weighted average with weights
given by the distribution of unemployment by age: ￿ =
P
i ￿isi
In the empirical part of the paper we distinguish between three di⁄erent
age groups only, due to data availability. Hence, for a model with young
(Y ), prime-age (P) and old (O) unemployed, a steady state equilibrium
unemployment is given by
3u =
￿Y sY + ￿PsP + ￿OsO
￿Y sY + ￿PsP + ￿OsO + pY (￿)sY + pP (￿)sP + pO (￿)sO
. (3)
While ￿i shifts the Beveridge curve outwards, pi shifts the curve inwards.
For si the e⁄ects are ambiguous. Simply because if one of the shares changes,
at least one of the others change too. In addition, it is ambiguous if the
net e⁄ect of in￿ ow minus out￿ ow for a speci￿c share is above or below the
average net value. Equation (3) includes age related job ￿nding probabilities
and quit rates that are not weighted by the corresponding labor force size.
This allows us to compare the age related net ￿ ow rates directly. This is an
important di⁄erence to the shift share approach mentioned above, for which
we are not able to distinguish between ￿ ow and cohort e⁄ects.
3 Empirical Analysis
In this section we investigate empirically the relation between the unem-
ployment rate and the distribution of unemployment by age. In order to
provide a ￿rst cross country evidence for our data we calculate correlation
coe¢ cients for all countries considered in this paper. Table 1 provides the
correlation coe¢ cients for the unemployment rate and the unemployment
shares of the age groups young (16 to 24 years), prime-age (25 to 55 years),
and old (55 to 64 years). The coe¢ cients refer to 16 OECD countries and
the period 1975 to 2000.
The unemployment rate is negatively related to the share of young and
old unemployed, but the correlation between the share of prime-age unem-
ployed and the unemployment rate is almost zero. This means that the net
￿ ow rates for the young and the old yield a lower unemployment rate. Re-
member that age group related unemployment rates may yield a di⁄erent
pattern if the corresponding labor force sizes have large di⁄erences. The
correlations between the shares reveal the shifts in the cohort size due to
the demographic change.
Table 1: Correlation Coe¢ cients: Age Groups
sY sP sO
sP -0.9081
sO -0.5428 0.1412
u -0.2131 0.0289 -0.5615
sY : share of young unemployed (15 to 24 years); sP: share of prime-age unemployed
(25 to 54 years); sO: share of old unemployed (55 to 64 years); u: unemployment rate.
4The data for the standardized unemployment rate (u) and unemploy-
ment by age is taken from the OECD online database. Unemployment by
age is subdivided into young unemployed (16 to 24 years old), prime-age
unemployed (25 to 54 years old), and old unemployed (55 to 64 years old).
The corresponding shares have a range of 0 - 1. To get reliable estimates we
consider a set of institutional and macroeconomic control variables that are
taken from Nickell and Nunciata (2002).3
With respect to the countries considered only those are accounted for
who provide data for the age groups at lest for ten years: Australia, Belgium,
Canada, Denmark, Finland, France, Germany, Japan, Netherlands, New
Zealand, Norway, Portugal, Spain, Sweden, United Kingdom, and USA.
The period is 1975 to 1995 due to data availability.
We now analyze econometrically whether the distribution of unemploy-
ment by age has an e⁄ect on the level of the unemployment rate. In the
estimates only two of the three shares can be included, since they sum up
to one. We therefore estimate all three possible combinations. This allows
to interpret the share e⁄ects more speci￿cally, since the estimated e⁄ects
are always on account of the excluded share. We argue that signi￿cantly
di⁄erent estimates for the shares correspond to signi￿cantly di⁄erent net
￿ ow rates.
The following equation will be estimated:
log(uit) = ￿0 + ￿1sjit + ￿2skit +
X
m
￿mXmit + ￿i + ￿t + ￿it
sj and sk are two of the three duration groups (sY ;sP;sO) and ￿i and ￿t
are ￿xed cross-country and time e⁄ects, respectively, and X is a vector of m
control variables. We consider two additional speci￿cations to account in a
di⁄erent way for unobserved heterogeneity. First, instead of time e⁄ects we
consider a time trend and country speci￿c ￿rst order autoregressive terms.
Second, we do the same but now with country speci￿c time trends instead of
the aggregated time trend. White robust covariances are used to control for
cross-equation correlation and di⁄erent error variances in each cross-section
unit.
Table 2 displays the main results.4 Regressions 1 to 3 are speci￿ed as
standard ￿xed e⁄ects models. The results are in line with the correlation
pattern between the shares and the unemployment rate in table 1. That is,
the larger the shares of young and old unemployed the lower the overall un-
employment rate. However, the e⁄ect is signi￿cant only for the share of the
3Institutional control variables are: Bene￿t replacement rate, bene￿t duration, em-
ployment protection, year to year changes in net union density, and coordination of bar-
gaining. Macroeconomic control variables are: Terms of Trade shocks, labor demand
shocks, total factor productivity, real interest rate, and vacancy rate.
4Complete results will be provided upon request.
5old. Regressions 4 to 6 and 7 to 9 have di⁄erent speci￿cations with respect
to unobserved heterogeneity. According to these results the unemployment
rate increases signi￿cantly with the share of prime-age unemployed. In ad-
dition, we ￿nd no statistically signi￿cant di⁄erence between the net ￿ ows of
the young and the old. The results provide evidence that the distribution of
unemployment by age has a hump-shape e⁄ect on the unemployment rate.
That is, although the average duration of unemployment increases with age,
the overall e⁄ect for the age group 55 to 64 years is lower than the e⁄ect of
the prime-age group (25 to 54 years).
Table 2: Main regression results
1 2 3 4 5 6 7 8 9
sY 1.55 -0.59 -0.95 -2.15z -0.69 -2.37z
(1.12) (0.52) (0.68) (0.38) (0.77) (0.30)
sP 2.14y 0.59 1.19] 2.15z 1.68y 2.37z
(1.01) (0.52) (0.63) (0.38) (0.71) (0.30)
sO -2.14y -1.55 -1.19] 0.95 -1.68y 0.69
(1.01) (1.12) (0.63) (0.68) (0.71) (0.77)
R2 0.90 0.90 0.90 0.97 0.97 0.97 0.98 0.98 0.98
fe X X X X X X X X X
te X X X
at X X X
ct X X X
ar X X X X X X
n 286 286 286 270 270 270 270 270 270
Notes: dependent variable: log of unemployment rate; sY : share of young unem-
ployed; sP: share of prime-age unemployed; sO: share of old unemployed; fe: ￿xed
e⁄ects; te: time e⁄ects; at: aggregated time trend; ct: country time trend; ar: ￿rst
order autoregressive term; n: observations; z, y, ]: signi￿cant at the 1% level, 5%
level, 10% level; robust standard error in parenthesis.
This puzzle can be explained by a simple relation. Any given level of
aggregated unemployment can arise from a certain number of persons un-
employed for a short period of time or a smaller number of unemployed for a
long period. Given that the age group 55 to 64 years has the least job ￿nd-
ing probability, the in￿ ow rate for the prime-age group must be larger than
the corresponding rate for the old unemployed. The surprising part in this
result is that this di⁄erence has a stronger impact on the unemployment rate
than the di⁄erence between the age dependent duration of unemployment.
64 Conclusions
This paper examines the e⁄ects of the distribution of unemployment by
age on the level of unemployment. The results provide evidence that the
distribution of unemployment by age has a hump-shape e⁄ect on the un-
employment rate. This puzzle can be explained by di⁄erences in net ￿ ow
rates. That is, the larger the share of prime-age (25 to 54 years) unem-
ployed, the higher the unemployment rate. This is surprising if one takes
the di⁄erent pattern of age related unemployment rates into account. With
respect to the ongoing demographic change this is an important result. Pro-
vided that the share of people 25 to 54 years on the labor market deceases
for the bene￿t of older worker (55 to 64 years) in the future, aging on the
labor market reduces the unemployment rate, if these e⁄ects are not related
to birth cohorts (baby boomer or not baby boomer) and age related labor
market participation rates do not change noticeable.
5 References
Burgess, S. 1993, A Model of Competition between Unemployed and Em-
ployed Searchers: An Application to the Unemployment Out￿ ows in
Britain, Economic Journal 103, 1190-1204.
Coles, M. and E. Smith, 1996, Cross-Section Estimation on the Matching
Function: Evidence from England and Wales, Economica 63, 589-597.
Nickell, S.J.; Nunziata, L., 2002, Labour Market Institutions Database,
version 2, Centre for Economic Performance.
OECD Online Database, http://www.oecd.org/statsportal/0,2639,en_2825
_293564_1_1_1_1_1,00.html
Pissarides, C.A. and J. Wadsworth, 1994, On-the-Job Search: Some Empir-
ical Evidence from Britain, European Economic Review 38, 385-401.
Shimer, R., 1998, Why is the U.S. Unemployment Rate so Much Lower?, in
B. Bernacke and J. Rotemberg eds, NBER Macroeconomics Annual,
XIII, Cambridge, MA: MIT Press, 11-61.
Shimer, R., 2001, The Impact of Young Workers on the Aggregate Labor
market, Quarterly Journal of Economics 116 (3), 969-1007.
7

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