A thorny problem in identifying the determinants of reservation wages and particularly the role of continued joblessness in their evolution is the simultaneity issue. We deploy a natural control function approach to the problem that involves conditioning elapsed duration on completed unemployment duration in the reservation wage equation. Our analysis confirms that the use of elapsed duration alone compounds two separate and opposing influences. Only with the inclusion of completed duration is the negative effect of continued joblessness on reservation wages apparent. For its part, the completed duration coefficient suggests that higher reservation wages negatively influence the probability of exiting unemployment.reservation wages, unemployment duration, control function

Addison, John T.

Machado, José

Portugal, Pedro

English

Research Papers in Economics

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Forschungsinstitut 
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Institute for the Study 
of Labor 
The Reservation Wage Unemployment Duration 
Nexus
IZA DP No. 5077
July 2010
John T. Addison
José A. F. Machado
Pedro Portugal 
The Reservation Wage 
Unemployment Duration Nexus 
 
 
John T. Addison 
University of South Carolina 
and IZA  
 
José A. F. Machado 
Universidade NOVA de Lisboa 
 
Pedro Portugal 
Banco de Portugal, 
Universidade NOVA de Lisboa and IZA 
 
 
 
Discussion Paper No. 5077 
July 2010 
 
 
 
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available directly from the author. IZA Discussion Paper No. 5077 
July 2010 
 
 
 
 
 
 
 
 
 
 
 
 
ABSTRACT 
 
The Reservation Wage Unemployment Duration Nexus
* 
 
A thorny problem in identifying the determinants of reservation wages and particularly the 
role of continued joblessness in their evolution is the simultaneity issue. We deploy a natural 
control function approach to the problem that involves conditioning elapsed duration on 
completed unemployment duration in the reservation wage equation. Our analysis confirms 
that the use of elapsed duration alone compounds two separate and opposing influences. 
Only with the inclusion of completed duration is the negative effect of continued joblessness 
on reservation wages apparent. For its part, the completed duration coefficient suggests that 
higher reservation wages negatively influence the probability of exiting unemployment. 
 
 
JEL Classification:  J64, J65 
  
Keywords:  reservation wages, unemployment duration, control function 
 
 
Corresponding author: 
 
John T. Addison 
Department of Economics 
Moore School of Business 
University of South Carolina 
1705 College Street 
Columbia, SC 29208 
USA 
E-mail: ecceaddi@moore.sc.edu   
 
                                                 
* The authors gratefully acknowledge partial financial support from the Fundação para a Ciência e a 
Tecnologia. The usual disclaimer applies. 1 Introduction
The question of whether reservation wages are constant or declining through time
is of no small interest. In particular, the constant reservation wage hypothesis
provides a useful and parsimonious way of recouping the structural parameters of
the optimal job search model. However, on the rather few occasions on which the
hypothesis has been tested in the past it has typically been rejected (see Kiefer
and Neumann, 1979). On the other hand, failure to reject the hypothesis in more
recent treatments, falls far short of a ringing endorsement of theory. The problem
in a nutshell in both cases is that the reservation wage and unemployment duration
may be simultaneously determined.
One way to tackle the endogeneity problem is to instrument for unemployment
duration in the reservation wage equation using variables that are unlikely to
have additional eﬀects on reservation wages. Instruments chosen in the literature
include dummies for marital status, presence of an outstanding mortgage, and
schooling (e.g. Addison, Centeno, and Portugal, 2004).1
The principal problem with this approach is generic and concerns the fragility
of available instruments. In the present treatment, therefore, we propose an al-
ternative approach that sidesteps the problem, exploiting the distinction between
ongoing and completed spells. As is well known, information on the distribu-
tion of elapsed duration is not representative of the distribution the unemployed
population: long jobless durations will be overrepresented (length-bias sampling).
Alternatively put, elapsed duration is driven by completed duration. In order to
obtain an unbiased estimate of the eﬀect of elapsed duration on reservation wages,
therefore, we need to condition upon on completed duration. Irrespective of the
point reached in the jobless spell, we can then get a ﬁx on the impact of incremen-
tal unemployment on reservation wages uncontaminated by simultaneity (i.e. the
fact that those still unemployed will have high reservation wages as higher reserva-
tion wages cause higher ultimate duration). Hence we deploy two unemployment
1Others have sought to instrument for reservation wages in the unemployment duration equation, using either
unemployment insurance beneﬁts (Jones, 1988) or this variable supplemented with dummies for marital status
and presence of school-age children (Prasad, 2003).
2regressors in the reservation wage equation: the individual’s elapsed duration and,
in addition, his/her completed duration.
Our interest is in testing whether an individual’s reservation wage declines over
the course of a jobless spell and not strictly whether the magnitude of the reserva-
tion wage determinescompletedduration. In this sense, our treatment is analogous
to that of Abraham and Farber’s (1987) test of the tenure-earnings model, wherein
completed job duration (in our case, completed jobless duration) instruments for
current tenure (elapsed duration) taken in conjunction with that variable. So we
are testing for declining reservation wages in the framework of a search model.
Admittedly, that model does not assume stationary reservation wages, and hence
will inevitably entail some further elaboration of the underlying model, but fully
accepts the line of causation running from reservation wages to (completed) jobless
duration.
To anticipate our central ﬁnding, we report that reservation wages only decline
with elapsed jobless duration conditional on completed duration. Otherwise, the
association is statistically insigniﬁcant. Our secondary result, as it were, is that
the association between completed duration and reservation wage is positive and
well determined, on secure standard search-theoretic reasoning.
2 The estimation approach
Let W denote the reservation wage, Z a vector of observed exogenous variables
(individual and calendar eﬀects), U backward recurrence time, and ǫ explanatory
unobserved variables. V will represent continuing duration of stay in the state of
unemployment (forward recurrence time), so that a complete unemployment spell
will have duration S = U + V .
We want to estimate the model
W = α
′Z + βU + ǫ,
with the additional equation
U = γ
′Z + δV + ω
3and the restrictions
E[ω|Z,V] = 0 and E[ǫ|Z,V,ω] = E[ǫ|ω].
(See Heckman and Robb, 1985; Newey, Powell, and Vella, 1999; Matzkin, 2004.)
A couple of remarks are in order.
1. U and V are, in general statistically dependent (Lancaster, 1990, 94). The
exception occurs when the ﬂow of entrants in unemployment is exponential
(conditional on Z). Then δ = 0.
2. The second equation together with the moment restrictions characterizes the
endogeneity of U for W: For given U, higher reservation wages induce higher
continuing durations (an implication of basic job search theory) which, being
correlated with elapsed durations, establish the reverse causation mechanism.
Now notice that
E[W|Z,U,V] = α
′Z + βU + E[ǫ|ω]
= α
′Z + βU + CF(ω)
= α
′Z + βU + CF(U − γ
′Z − δV )
for some function CF(·), the so-called control function (Heckman and Robb, 1985).
Assuming that CF(·) is linear (as would be the case if (ǫ,ω) were jointly nor-
mally distributed), that is CF(ω) = λω, we may write (substituting V = S − U),
E[W|Z,U,V] = α
′Z + βU + λ(U − γ
′Z − δ(S − U))
= ˜ α
′Z + ˜ βU + ˜ δS,
where the ˜ (·) denotes obvious tranformations of the original parameters. This
regression can be estimated by OLS.2
2A simple (but rather telling) alternative speciﬁcation, and one that avoids by construction the endogeneity
of unemployment duration, would be to use the ratio between elapsed and completed unemployment duration as
a regressor. Estimation of this model generated a negative and statistically signiﬁcant coeﬃcient for the ratio
variable.
43 Data
Our data are taken from the ﬁrst six waves of the European Community House-
hold Panel (EHCP), 1994-99. The ECHP is a survey based on a standardized
questionnaire administered annually to a representative panel of households and
individuals in 15 EU member states and oﬀers detailed information on the respon-
dent’s labor market experience, inter al. (see EUROSTAT, 1999). We used data
for 13 of the countries, excluding Luxembourg and Sweden, where it is not possible
to follow individuals through time.3
The key pieces of information taken from the survey are reservation wages
and elapsed duration. In the EHCP each individual actively looking for work is
asked two questions pertaining ﬁrst to desired hours of work and second to the
minimum income required to work these hours. The actual questions asked are
these: Assuming you could ﬁnd regular work, how many hours would you prefer to
work in this new job? and What is the minimum net monthly income you would
accept to work [these number of] hours a week in this new job? We construct an
hourly net reservation wage, computed as the ratio of desired net monthly income
to the optimal number of hours. This variable is deﬂated by the respective national
consumer price index.
The other crucial variables are the duration of the current unemployment spell
and its ultimate duration. The ECHP sampling procedure considers only jobless
spells of individuals with previous work experience for whom we are able to identify
the onset of unemployment by month and year. Given that, with one exception,
we know the month and year of the interview we compute elapsed duration as
the period from the point of job loss up to the interview. (That one exception is
Germany, for whom we assume that all the interviews were conducted in October.)
As far as completed duration is concerned, since we can follow the individual
between surveys up to the point of reemployment, we can simply add the residual
calendar months spent unemployed in the subsequent interval to compute elapsed
3The countries are Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Portugal,
Spain, The Netherlands, and the United Kingdom.
5duration.
In the present exercise, we were interestedin using most the parsimonious model
consistent with a declining reservation wages. Accordingly, the RHS arguments
additional to elapsed and completed duration were limited simply to a gender
dummy, three schooling dummies, four age dummies, ﬁve time dummies, and
thirteen country dummies. We also deployed a continuous measure of the overall
unemployment rate at the time of the survey.4
4 Findings
Summary results of ﬁtting the reservation model separately for elapsed duration
and completed duration are givenin the ﬁrst two columns of Table 1. The elasticity
of reservation wages with respect to elapsed duration is negative but statistically
insigniﬁcant at conventional levels. The point estimate is tiny, suggesting that a
1 percent increase in the duration of an ongoing spell is associated with a 0.002
percent decrease in reservation wages. For its part, the elasticity of the reservation
wage with respect to completed duration is positive but again small in magnitude
(0.004) and statistically insigniﬁcant as well.
However, as is apparent from the penultimate column of the table, when both
duration variables are included in the reservation wage equation, each is statis-
tically signiﬁcant. And indeed each elasticity is sharply higher: -.015 and .024,
respectively. Conditioning on completed duration, then, there is every indication
of a small but nontrivial and well-determined decline in reservation wages over the
course of joblessness. The positive association between completed duration and
reservation wages is of course indicative of the reverse line of causation running
from reservation wages to jobless duration.
As noted above, the speciﬁcations in Table 1 include 13 country dummies. If,
however, country heterogeneity may be expected to assist in the identiﬁcation of
the impact of unemployment duration on reservation wages, we might usefully drop
4We also experimented using a variable identifying the order of distinct unemployment spells as well as the
receipt (or otherwise) of unemployment insurance beneﬁts. In neither case, however, were the results reported
below disturbed by their inclusion.
6the country dummies. In the ﬁnal column of the table, therefore, we provide results
for the correct speciﬁcation, including both duration measures but omitting the
country ﬁxed eﬀects. Compared with the results in the preceding column, it can
be seen that the point estimates for the duration measures strengthen in absolute
magnitude.
Speciﬁcation
Variable (1) (2) (3) (4)
U -0.002 -0.015 -0.025
(0.002) (0.004) (0.005)
S 0.004 0.024 0.070
(0.004) (0.006) (0.007)
Country dummies Yes Yes Yes No
R2 0.418 0.418 0.419 0.166
number of observations 10003 10003 10003 10003
Table 1: The Determinants of Reservation Wages. Robust Standard Errors in paren-
thesis. The regressions also include a continuous unemployment rate variable, a gender
dummy, 3 Schooling, 4 age, and 5 year dummies.
As a robustness check, we re-ran the preferred reservation wage equation by
gender, with and without country dummies. The summary results are given in
Table 2. We see that, conditioning on completed duration, reservation wages are
decreasing in ongoing joblessness for both males and females. The results are
however stronger, in terms of both absolute magnitude and statistical signiﬁcance
for males, as indeed is the reverse line of causation running from reservation wage
to unemployment duration. On this occasion, however, removing the country
dummies yielded almost identical point estimates by gender.
5 Conclusions
The fact that reservation wages and unemployment duration are simultaneously
determined has preoccupied analysts in this area and arguably would have proven
more disruptive had direct information on reservation wages been more readily
available. In the present treatment, we have been able to exploit such information
7Variable Males Females
U -0.020 -0.025 -0.009 -0.024
(0.006) (0.007) (0.005) (0.006)
S 0.031 0.071 0.016 0.071
(0.010) (0.011) (0.008) (0.010)
Country dummies Yes No Yes No
R2 0.371 0.154 0.468 0.155
number of observations 5181 5181 4822 4822
Table 2: The Determinants of Reservation Wages by Gender. Robust Standard Er-
rors in parenthesis. The regressions also include a continuous unemployment rate vari-
able, a gender dummy, 3 Schooling, 4 age, and 5 year dummies.
to demonstrate how the true eﬀect of the unemployment experience on reservation
wages can be modeled. The approach which is to condition elapsed duration on
completed duration is analogous to that used by Abraham and Farber (1987) in
addressing the bias attaching to the pro-productive tenure argument in the aug-
mented Mincerian earnings function, which we have formally approached as an
omitted variables problem. We have shown that reservation wages are declining
over the course of the unemployment or jobless spell. While rejecting the as-
sumption of stationary reservation wages, we note that the elasticity/elasticities
of reservation wage with respect to elapsed duration are rather small and, further,
that there is well-determined direct association between completed duration and
reservation wages which is to be construed as higher reservation wages lead to
higher jobless duration. By failing to control for completed jobless duration we
conﬂate the two opposing eﬀects.
8References
Abraham, Katherine T. and Henry S. Farber (1987) ”Job Duration
Seniority, and Earnings.” American Economic Review, 7 (3): 278-297.
Addison, John T., Mario Centeno, and Pedro Portugal (2004)
”Reservation Wages, Search Duration, and Accepted Wages in Europe.” IZA
Discussion Paper No. 1252. Bonn: Institute for the Study of Labor/IZA.
Heckman, James and Richard Robb (1985). ”Using Longitudinal Data
to Estimate Age, Period and Cohort Eﬀects in Earnings Equations.” In
William M. Mason and Stephen E. Feinberg (eds.), Cohort Analysis in So-
cial Research Beyond the Identiﬁcation Problem. New York: Springer-Verlag,
New York.
Kiefer, Nicholas M. and George R. Neumann (1979) ”An Empirical
Job-Search Model with a Test of the Constant Reservation Wage Hypothesis.”
Journal of Political Economy 87 (1): 89-107.
EUROSTAT (1999) European Community Household Panel. Longitudinal
Users’ Database. Waves 1, 2 and 3. Manual. Luxembourg: EUROSTAT.
Lancaster, Tony (1990) The Econometric Analysis of Transition Data.
Cambridge: Cambridge University Presss.
Matzkin, Rola L. (2004) ”Unobservable Instruments.” mimeo.
Newey, Whitney K., James L. Powell and Francis Vella (1999)
”Nonparametric Estimation of Triangular Simultaneous Equations Models.”
Econometrica 67 (3): 565-603.
Prasad, Eswar (2003) ”What Determines the Reservation Wages of Unem-
ployed Workers? New Evidence from German Micro Data.” IZA Discussion
Paper No. 694, Bonn: Institute for the Study of Labor/IZA.
9

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