This paper exploits the informational value of search theory, after Lancaster and Chesher (1983), in conjunction with survey data on the unemployed to calculate key reservation wage and duration elasticities for most EU-15 nations.

John T. Addison

Mário Centeno

Pedro Portugal

English

Research Papers in Economics

BANCO DE PORTUGAL
Economic Research Department
KEY ELASTICITIES IN JOB SEARCH THEORY:
INTERNATIONAL EVIDENCE
John T. Addison
Mário Centeno
Pedro Portugal
WP 12-04 September 2004
The analyses, opinions and findings of these papers represent the views of the
authors, they are not necessarily those of the Banco de Portugal.
Please address correspondence to Pedro Portugal, Economic Research Department,
Banco de Portugal, Av. Almirante Reis nº. 71, 1150-165 Lisboa, Portugal;
Tel:351-213 128 410; Fax 351-213 107 804 email: jppdias@bportugal.pt  
 
 
 
 
Key Elasticities in Job Search Theory: International Evidence 
 
 
 
John T. Addison,* Mário Centeno,** and Pedro Portugal*** 
 
 
*    University of South Carolina (U.S.A.) and IZA Bonn (Germany) 
**  Banco de Portugal and Universidade Técnica de Lisboa (Portugal) 
***Banco de Portugal and Universidade Nova de Lisboa (Portugal) 
 
 
 
 
August 2004 
 
 
 
Abstract 
This paper exploits the informational value of search theory, after Lancaster and Chesher 
(1983), in conjunction with survey data on the unemployed to calculate key reservation 
wage and duration elasticities for almost all EU-15 nations. 
  
 
JEL Classification:   J64, J65      
 
Keywords: reservation wages, probability of reemployment, accepted wages, 
unemployment benefits, Pareto wage offer distribution 
 
 
 
 
 
 
 
 
    
1
I. Introduction 
The present treatment calculates four key elasticities in job search theory that are of 
importance for policy, using data from a unique international dataset containing 
information on individuals’ reservation wages, unemployment benefits, and accepted 
wages. Specifically, we follow Lancaster and Chesher (1983) in providing estimates of 
the elasticity of the reservation wage with respect to the level of unemployment benefits, 
the elasticity of reservation wages with respect to the rate of job offers, the elasticity of 
unemployment duration with respect to the level of unemployment benefits, and the 
elasticity of unemployment duration with respect to the rate of job offers.  
For the stationary optimal search model, Lancaster and Chesher show that these 
elasticities can be deduced by differentiating partially the optimality condition (for the 
reservation wage, ξ) with respect to the level of unemployment benefits, b, the job offer 
arrival rate, λ, and the hazard function, θ, with respect to λ and ξ. Writing the conditional 
expected wage as x, they obtain the following solution formulae for the elasticity of the 
reservation wage with respect to the level of unemployment benefits ( b , ξ η ) and the 
elasticity of reservation wages with respect to the rate of job offers ( λ ξ η , ), as follows: 
b x
x b
b
b −
−
=
∂
∂
=
ξ
ξ
ξ
ηξ log
log
, ,                                                                                       (1) 
and  
b x
x b
−
− −
=
∂
∂
=
ξ
ξ
ξ
λ
ξ
η λ ξ log
log
, .                                                                                 (2) 
To obtain the solutions for the two remaining elasticities, however, some 
assumption has to be made concerning the hazard function of the offer distribution at the 
selected reservation wage, or
) (
) (
ξ
ξ
F
f
. The authors assume that the portion of the wage 
offer distribution exceeding the benefit level follows a Pareto distribution, allowing them 
to write the solution formulae for the elasticity of unemployment duration with respect to 
the level of unemployment benefits ( b , θ η ), and the elasticity of unemployment duration 
with respect to the rate of job offers ( λ θ η , ) as:    
2
 
b x
x b
b
b −
−
− =
∂
∂
=
ξ
σξ
θ
ηθ log
log
, ,                                                                                 (3) 
and 
b x
x b
−
− −
− =
∂
∂
=
ξ
σξ
ξ
λ
θ
η λ θ 1
log
log
, ,                                                                            (4) 
where ơ is the standard deviation of (log) wage offers.
1 Note that if an individual moves 
through time with constant hazard θ, then his or her completed unemployment duration is 
exponentially distributed with mean unemployment duration equal to 1/θ. The benefit and 
offer probability elasticities of mean duration are now the negative of (3) and (4), and it is 
these transformed values that will be reported below.  
Lancaster and Chesher provide elasticities for Britain in the 1970s. We provide 
updated estimates for Britain in the 1990s and for most other European Union (EU) 
nations as well (viz. Germany, Denmark, the Netherlands, Belgium France, Ireland, Italy, 
Greece, Spain, Portugal and Austria).   
 
II. Data 
Our data are taken from six waves of the European Community Household Panel 
(ECHP), 1994-99, covering all the (then) 15 nations in the European Union (but see 
below).
2 As we have seen, calculating our key elasticities requires information on three 
variables. Beginning with reservation wages, the ECHP asks of those individuals actively 
looking for work first “Assuming you could find suitable work, how many hours per week 
would you prefer to work in this new job?” and, second, “What is the minimal net 
monthly income would you accept to work [number of hours in previous question] hours 
a week in this new job?” The reservation wage measure used here is the monthly net 
reservation wage construct, and along with all other variables is deflated by the relevant 
national consumer price index. We need add that for Germany reservation wage data is 
available for just the first three waves of the panel. 
  The data on unemployment benefits contained in the ECHP is with one exception 
a monthly measure. It is comparable to the Lancaster-Chesher measure of unemployment 
income but, as is the case for all our variables, is provided in continuous rather than     
3
categorical form. Monthly benefit entitlements are not provided for Finland, which 
country is therefore excluded.  
Unlike the dataset(s) used by Lancaster and Chesher, the ECHP does not contain 
information on expected wages; rather, the closest information we have is the monthly 
remployment wage subsequently received. This is used to form an expected hourly wage 
measure for the sample, which is further reduced by two countries – Sweden and 
Luxembourg – where the data do not allow us to unemployed individuals through time. 
We do not here adjust our counterpart of the ‘expected wage’ for selection in to 
reemployment, although we have elsewhere reported on applying this procedure (see 
Addison, Centeno, and Portugal, 2004.) Note also that the reported number of hours 
worked per month in the reemployment job can diverge from the individual’s optimal 
number of hours reported in the reservation wage question.  
 Finally, theory requires that that no individual has a reservation wage less than 
his or her level of unemployment benefit entitlement. Further, reservation wages should 
not exceed expected wages. We investigate the effect of imposing these two sets of 
restictions on the data. The effect of the former is to reduce the sample by 10 percent, 
while the latter results in a larger reduction in sample size of approximately 43 percent. 
 
III. Findings 
Computed elasticities are contained in Table 1. Panel (a) of the table gives results for the 
unrestricted sample. Note the perversely signed estimates for the benefit elasticity of 
reservation wages and the offer probability elasticity of reservation wages in the case of 
Greece. Also, in some cases the estimated median elasticities are zero, meaning that, at 
the median, reservation wages are equal to accepted wages.  Observe that the net effect of 
an increase in the probability of an offer on duration is (generally) negative, meaning that 
its effect on the asking price outweighs the effect of more offers. 
(Table 1 near here) 
  Imposing the restriction that reservation wages exceed benefit levels in panel (b) 
results in the loss of roughly one-tenth of the sample. Instances of perversely signed 
elasticities are again confined to the Greek data. The estimates obtained for the U.K. are    
4
in absolute terms in each case below those calculated by Lancaster and Chesher ( b , ξ η = 
0.135;  λ ξ η , =  0.107; - b , θ η =  1.03; and - λ θ η , = -0.190). 
  A much larger loss in sample size of around 43 percent is occasioned when in 
panel (c) we impose the restriction that accepted wages cannot lie below reservation 
wages. Not surprisingly, the effect of imposing this second theoretical restriction is 
significant: the estimated elasticities typically increase in magnitude and there are no 
longer any errant signs. In the case of the U.K. it is apparent that our estimates are now 
very much closer to those calculated by Lancaster and Chesher. Furthermore, these 
figures are, in general, considerably larger than those summarized in Cahuc and 
Zylberberg (2004, pp.157-58).  
  Finally, there is one obvious pattern in the data shown in panel (c) of the table that 
we mention without further comment. Countries with higher benefit elasticities of 
reservation wages have higher benefit elasticities of unemployment duration 
( 209 . 0 ; ˆ 159 . 0 056 . 0 ˆ
2
, , = + = R b b ξ θ η η  ).
3    
 
IV. Conclusion 
In an important paper, Lancaster and Chesher (1983) used survey data on unemployed 
persons in Britain and economic theory to deduce – rather than estimate via a formal 
statistical model – the structural parameters of the optimal search model. We follow their 
methodology to derive updated elasticities for Britain and for eleven other European 
nations as well. Our findings are numerically consistent with the theory once two critical 
restrictions are imposed on the international data.  
 
    
5
Endnotes 
1.  The  σ parameter is obtained from 
x
x ξ
σ
−
= . 
2. For a description of this unique dataset, see for example, EUROSTAT (1999). 
 
3.  On the maintained hypothesis that countries with more flexible labor markets might 
well have larger elasticities, we regressed the four measures in panel (c) on OECD 
indicators of the country’s unemployment benefit replacement rate and the stringency of 
its employment protection regime. The results, which are available on request, were 
uniformly statistically insignificant.  
 
 
References 
Addison, J.T., Portugal, P., Centeno, M., 2004. Reservation wages, search duration, and 
accepted wages in Europe. IZA Discussion Paper No. 1252. Bonn: IZA.  
 
Cahuc, P., Zylberberg, A. 2004. Labor Economics, MIT Press, Cambridge, MA. 
 
EUROSTAT, 1999. European Community Household Panel. Longitudinal Users’ 
Database. Waves 1, 2 and 3. Manual. Luxembourg: EUROSTAT. 
 
Lancaster, T., Chesher, A., 1983. An econometric analysis of reservation wages. 
Econometrica 51, 1661-1676.    
6
 
 
 
Table 1:  Median Benefit and Offer Probability Elasticities of Reservation Wages and Unemployment Duration by Country, 1993-98   
 
____________________________________________________________________________________________________________________________________ 
                               The     
Country/Elasticity Germany Denmark Netherlands Belgium  France U.K.  Ireland Italy  Greece Spain  Portugal  Austria 
 
(a)   No sample restrictions 
 ηξ, b  0.0657 0.2150  0.0433  0.0000 0.1173  0.1280 0.0343  0.0863  -0.0588 0.1221 0.2502  0.1953 
 ηξ, λ  0.0000 0.0075  0.0000  0.0000 0.0078  0.0250 0.0254  0.0000  -0.0929 0.0000 0.0184  0.0889 
-ηθ,b  1.1250 2.0536  1.3586  0.7284 0.7955  0.5132 0.9331  0.5697  0.7059 1.5966 1.2865  1.2727 
-ηθ,λ  -0.0793 -0.2849  -0.1419  -0.0132 -0.1401  -0.1280 -0.0490  -0.1237  0.0879 -0.1767 -0.3420  -0.2368 
n  237 302  68  229 507  133 107 56  101 358 166 63 
 
(b) Restriction:  reservation wage > unemployment benefits 
 ηξ, b  0.0465 0.1900  0.0363  0.0000 0.0564  0.0679 0.0303  0.0646  -0.0598 0.0843 0.2267  0.1847 
 ηξ, λ  0.0233 0.0181  0.0233  0.0000 0.0337  0.0879 0.0312  0.0533  -0.0892 0.0143 0.0313  0.1091 
-ηθ,b  1.1784 2.0463  1.6459  0.7105 0.7841  0.4809 0.9097  0.7016  0.7059 1.5542 1.3268  1.2489 
-ηθ, λ  -0.0543 -0.2535  -0.0382  -0.0022 -0.0679  -0.0679 -0.0343  -0.0908  0.0884 -0.1314 -0.2657  -0.2246 
n  201 283  50  214  458  113 105 45  100 324 155 53 
 
(c) Restriction:   reservation wages < accepted wages 
 ηξ,, b  0.2273 0.3269  0.2276  0.1158 0.2917  0.3138 0.2391  0.1000  0.1456 0.3118 0.2618  0.2269 
 ηξ,, λ  0.1000 0.0628  0.0497  0.0809 0.1029  0.1757 0.1690  0.0612  0.2026 0.0615 0.0401  0.0963 
-ηθ, b  1.2328 2.4894  1.6571  0.9314 0.9557  0.5394 0.8145  0.9444  0.7419 1.9465 2.2289  1.3351 
-ηθ, λ  -0.2457  -0.4046 -0.4623 -0.1561  -0.3267  -0.3138  -0.2449  -0.1467 -0.1480  -0.3845  -0.3429  -0.2800 
n  111  159 37  103  301  87  64  27 58  163  53  34 
 
Source:  European Community Household Panel, 1994-99 
 
 
  
 WORKING PAPERS
2000
1/00 UNEMPLOYMENT DURATION: COMPETING AND DEFECTIVE RISKS
— John T. Addison, Pedro Portugal
2/00 THE ESTIMATION OF RISK PREMIUM IMPLICIT IN OIL PRICES
— Jorge Barros Luís
3/00 EVALUATING CORE INFLATION INDICATORS
— Carlos Robalo Marques, Pedro Duarte Neves, Luís Morais Sarmento
4/00 LABOR MARKETS AND KALEIDOSCOPIC COMPARATIVE ADVANTAGE
— Daniel A. Traça
5/00 WHY SHOULD CENTRAL BANKS AVOID THE USE OF THE UNDERLYING INFLATION INDICATOR?
— Carlos Robalo Marques, Pedro Duarte Neves, Afonso Gonçalves da Silva
6/00 USING THE ASYMMETRIC TRIMMED MEAN AS A CORE INFLATION INDICATOR
— Carlos Robalo Marques, João Machado Mota
2001
1/01 THE SURVIVAL OF NEW DOMESTIC AND FOREIGN OWNED FIRMS
— José Mata, Pedro Portugal
2/01 GAPS AND TRIANGLES
— Bernardino Adão, Isabel Correia, Pedro Teles
3/01 A NEW REPRESENTATION FOR THE FOREIGN CURRENCY RISK PREMIUM
— Bernardino Adão, Fátima Silva
4/01 ENTRY MISTAKES WITH STRATEGIC PRICING
— Bernardino Adão
5/01 FINANCING IN THE EUROSYSTEM: FIXED VERSUS VARIABLE RATE TENDERS
— Margarida Catalão-Lopes
6/01 AGGREGATION, PERSISTENCE AND VOLATILITY IN A MACROMODEL
— Karim Abadir, Gabriel Talmain
7/01 SOME FACTS ABOUT THE CYCLICAL CONVERGENCE IN THE EURO ZONE
— Frederico Belo
8/01 TENURE, BUSINESS CYCLE AND THE WAGE-SETTING PROCESS
— Leandro Arozamena, Mário Centeno
9/01 USING THE FIRST PRINCIPAL COMPONENT AS A CORE INFLATION INDICATOR
José Ferreira Machado, Carlos Robalo Marques, Pedro Duarte Neves, Afonso Gonçalves da Silva
10/01 IDENTIFICATION WITH AVERAGED DATA AND IMPLICATIONS FOR HEDONIC REGRESSION STUDIES
— José A.F. Machado, João M.C. Santos Silva
2002
1/02 QUANTILE REGRESSION ANALYSIS OF TRANSITION DATA
— José A.F. Machado, Pedro Portugal
2/02 SHOULD WE DISTINGUISH BETWEEN STATIC AND DYNAMIC LONG RUN EQUILIBRIUM IN ERROR
CORRECTION MODELS?
— Susana Botas, Carlos Robalo Marques
Banco de Portugal / Working Papers i3/02 MODELLING TAYLOR RULE UNCERTAINTY
— Fernando Martins, José A. F. Machado, Paulo Soares Esteves
4/02 PATTERNS OF ENTRY, POST-ENTRY GROWTH AND SURVIVAL: A COMPARISON BETWEEN DOMESTIC
AND FOREIGN OWNED FIRMS
— José Mata, Pedro Portugal
5/02 BUSINESS CYCLES: CYCLICAL COMOVEMENT WITHIN THE EUROPEAN UNION IN THE PERIOD
1960-1999. A FREQUENCY DOMAIN APPROACH
— João Valle e Azevedo
6/02 AN “ART”, NOT A “SCIENCE”? CENTRAL BANK MANAGEMENT IN PORTUGAL UNDER THE GOLD
STANDARD, 1854-1891
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7/02 MERGE OR CONCENTRATE? SOME INSIGHTS FOR ANTITRUST POLICY
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8/02 DISENTANGLING THE MINIMUM WAGE PUZZLE: ANALYSIS OF WORKER ACCESSIONS AND
SEPARATIONS FROM A LONGITUDINAL MATCHED EMPLOYER-EMPLOYEE DATA SET
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9/02 THE MATCH QUALITY GAINS FROM UNEMPLOYMENT INSURANCE
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10/02 HEDONIC PRICES INDEXES FOR NEW PASSENGER CARS IN PORTUGAL (1997-2001)
— Hugo J. Reis, J.M.C. Santos Silva
11/02 THE ANALYSIS OF SEASONAL RETURN ANOMALIES IN THE PORTUGUESE STOCK MARKET
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12/02 DOES MONEY GRANGER CAUSE INFLATION IN THE EURO AREA?
— Carlos Robalo Marques, Joaquim Pina
13/02 INSTITUTIONS AND ECONOMIC DEVELOPMENT: HOW STRONG IS THE RELATION?
— Tiago V.de V. Cavalcanti, Álvaro A. Novo
2003
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— P.A. Geroski, José Mata, Pedro Portugal
2/03 THE TIMING AND PROBABILITY OF FDI:
An Application to the United States Multinational Enterprises
— José Brandão de Brito, Felipa de Mello Sampayo
3/03 OPTIMAL FISCAL AND MONETARY POLICY: EQUIVALENCE RESULTS
— Isabel Correia, Juan Pablo Nicolini, Pedro Teles
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— Ricardo Mourinho Félix, Luís C. Nunes
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— Bernardino Adão, Isabel Correia, Pedro Teles
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— Nuno C. Martins, Ernesto Villanueva
15/03 THE CAREERS OF TOP MANAGERS AND FIRM OPENNESS: INTERNAL VERSUS EXTERNAL LABOUR
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16/03 TRACKING GROWTH AND THE BUSINESS CYCLE: A STOCHASTIC COMMON CYCLE MODEL FOR THE
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12/04 KEY ELASTICITIES IN JOB SEARCH THEORY: INTERNATIONAL EVIDENCE
— John T. Addison, Mário Centeno, Pedro Portugal
Banco de Portugal / Working Papers iv

(b) Restriction: reservation wage > unemployment benefits ηξ,

(c) Restriction: reservation wages < accepted wages ηξ,,

An econometric analysis of reservation wages.

European Community Household Panel. Longitudinal Users’ Database.

Reservation wages, search duration, and accepted wages

sample restrictions ηξ,

Source: European Community Household Panel,

Table 1: Median Benefit and Offer Probability Elasticities of Reservation Wages and Unemployment Duration by Country,

Key Elasticities in Job Search Theory: International Evidence

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