The Beveridge curve depicts a negative relationship between unemployed workers and job vacancies, a robust finding across countries. The position of the economy on the curve gives an idea as to the state of the labour market. The modern underlying theory is the search and matching model, with workers and firms engaging in costly search leading to random matching. The Beveridge curve depicts the steady state of the model, whereby inflows into unemployment are equal to the outflows from it, generated by matching.business cycle, job search, matching function, Phillips curve, unemployment, vacancies, wage inflation

Eran Yashiv

English

Research Papers in Economics

 
 
 
 
 
CEP Discussion Paper No 807 
June 2007 
The Beveridge Curve 
Eran Yashiv 
  
   
Abstract 
The Beveridge curve depicts a negative relationship between unemployed workers and job 
vacancies, a robust finding across countries. The position of the economy on the curve gives 
an idea as to the state of the labour market. The modern underlying theory is the search and 
matching model, with workers and firms engaging in costly search leading to random 
matching. The Beveridge curve depicts the steady state of the model, whereby inflows into 
unemployment are equal to the outflows from it, generated by matching.  
 
 
JEL Classifications: E24, E32, J63, J64 
Keywords: business cycle, job search, matching function, Phillips curve, unemployment, 
vacancies, wage inflation 
 
 
 
This paper was produced as part of the Centre’s Macro Programme.  The Centre for 
Economic Performance is financed by the Economic and Social Research Council. 
 
 
 
 
Acknowledgements 
‘The Beveridge Curve’ was prepared for inclusion in The New Palgrave Dictionary of Economics, 
2nd edition (forthcoming). 
  Eran Yashiv is an Associate of the Centre for Economic Performance, London School 
of Economics. He is also a lecturer at Tel Aviv University, Israel. 
 
 
 
 
 
 
 
Published by 
Centre for Economic Performance 
London School of Economics and Political Science 
Houghton Street 
London WC2A 2AE 
 
All rights reserved.  No part of this publication may be reproduced, stored in a retrieval 
system or transmitted in any form or by any means without the prior permission in writing of 
the publisher nor be issued to the public or circulated in any form other than that in which it 
is published. 
 
Requests for permission to reproduce any article or part of the Working Paper should be sent 
to the editor at the above address. 
 
© E. Yashiv, submitted 2007 
 
ISBN 978 0 85328 012 5   2
 
The  Beveridge  curve  depicts  a  negative  relationship  between 
unemployed workers (u) and job vacancies (v). The interest in the curve is 
related to the role it plays in aggregate models, which study labour market 
outcomes and dynamics. The position of the economy on the curve gives an 
idea as to the state of the labour market; for example, a high level of vacancies 
and a low level of unemployment would indicate a ‘tight’ labour market. The 
literature  has  attempted  to  explain  the  coexistence  of  unemployment  and 
vacancies, their negative relationship, and the implied dynamics.  
The  curve  is  named  after  William  Beveridge,  a  British  lord,  lawyer, 
head  of  academic  institutions,  Member  of  Parliament,  and  founder  of  the 
modern British welfare state. In a 1944 report (Beveridge, 1944), Beveridge 
discussed  the  relationship  between  the  demand  for  workers,  captured  by 
vacancies, and the rate of unemployment. While he did not plot a curve or 
present a table with a comparison of u and v, he offered detailed data on these 
variables and discussed them at some length. His analysis implied that there 
is a negative relationship between them. In this early work he tackled many of 
the  issues  that  remain  under  study  in  this  field:  the  potential  mismatch 
between unemployed workers and job vacancies, aggregate demand factors 
versus reallocation factors (for example, deficient overall demand for labour 
as  opposed  to  low  demand  in  particular  industries),  trend  versus  cyclical 
changes  (for  example,  changes  in  u  and  v  along  the  business  cycle  versus 
long‐run  changes),  and  measurement  issues  (such  as  the  various  possible 
ways of mismeasuring vacancies).  
  The  negative  u−v  relationship  is  a  robust  finding  across  countries, 
though shifts of the curve over time are often observed. This can be seen, for 
example,  in  a  16‐country  graphical  description  of  the  curve  presented  in 
Layard,  Nickell  and  Jackman  (2005,  pp.  36–7).  Detailed  descriptions  and 
analyses  of  the  empirical  findings  concerning  the  Beveridge  curve  for  the   3
United States are to be found in Blanchard and Diamond (1989), and for the 
UK in Pissarides (1986).  
What underlies this negative relationship? The early literature of the 
late 1950s and in the 1960s dealt with the curve in the context of exploring 
excess demand in the labour market and its influence on wage inflation. This 
was motivated by the extensive study of the Phillips curve that took place in 
those  years.  The  literature  typically  defined  excess  demand  as  unfilled 
vacancies less unemployed workers, considered the data on these variables, 
and then looked at the relationship between measures of excess demand and 
wage behaviour. This literature recognized that, even when there is no excess 
supply,  there  is  positive  unemployment  due  to  frictions.  It  derived  a 
negatively  sloped  u−v  curve  from  a  model  of  distinct  labour  markets, 
interacting at different levels of disequilibrium, with the markets at points off 
both labor supply and labor demand curves. The u−v curve was shown to be 
stationary  and  observed  u  and  v  points  were  expected  to  cycle  around  it. 
Movements  up  and  down  the  curve  reflect  increases  and  decreases  in  the 
excess demand for labour. The curve itself can shift as a result of changes in 
the speed of market clearing or changes in the sectoral composition of labour 
demand. The observed u−v data may be a compound of structural shifts of the 
curve together with cyclical movements about it.  Key contributions to this 
strand of work were progressively made by Dow and Dicks‐Mireaux (1958), 
Lipsey (1960), Holt and David (1966), Hansen (1970), and Bowden (1980). 
In the 1970s and 1980s an alternative approach was developed – the 
search and matching model. A key difference between this model and the 
early literature is its derivation of vacancies and unemployment as equilibria, 
rather than disequilibria, phenomena. The model was developed in the work 
of  Peter  Diamond,  Dale  Mortensen,  and  Christopher  Pissarides  (see 
Pissarides,  2000,  for  a  detailed  exposition,  and  Yashiv,  2006,  for  a  recent 
survey). The model may be briefly described as follows. Workers and firms   4
engage  in  costly  search  to  find  each  other.  Firms  spend  resources  on 
advertising,  on  posting  job  vacancies,  on  screening  and,  subsequently,  on 
training.  Workers  spend  resources  on  job  search,  with  costs  pertaining  to 
activities such as collecting information and applying for jobs.  Workers and 
firms are assumed to be randomly matched. After matching, the worker and 
the firm engage in bilateral bargaining over the wage. The matching process 
assumes  frictions  such  as  informational  or  locational  imperfections.  It  is 
formalized by a ‘matching function’ that takes searching workers and vacant 
jobs as arguments and produces a flow of matches (m), and is given by m = 
m(u,v). It is continuous, non‐negative, increasing in both its arguments, and 
concave. Typically, it is assumed to be constant returns to scale. The flow into 
unemployment results from job‐specific shocks to matches that arrive at the 
Poisson  rate  λ.  These  shocks  may  be  explained  as  shifts  in  demand  or 
productivity shocks. Once a shock arrives, the firm closes the job down. The 
evolution of the unemployment rate (u & ) is therefore given by the difference 
between the separation flow (λ times the employment rate 1 − u) and the 
matching flow:  
  (1 ) ( ) uu m u v λ = −− , . &   (1) 
Denote the rate at which workers are matched to jobs (the job finding rate) by 
m
u p =  so that m = pu. In the steady state the rate of unemployment is constant, 
so setting  0 u = &  the following obtains:  
  u
p
λ
λ
= .
+
  (2) 
This is the Beveridge curve: as p depends on m, it depends on both u 
and v, and this equation can be represented in vacancy (v) – unemployment 
(u)  space  by  a  downward‐sloping  curve.  The  mechanism  is  the  following.  
When vacancies v rise, matching m rises, and so the job finding rate p rises. 
Workers find jobs at a faster rate and unemployment u declines. Vacancies   5
themselves are determined by a firm optimality equation, equating vacancy 
costs and benefits at the margin.  
As can be seen in the equations above, the matching function plays a 
crucial  role  in  generating  the  Beveridge  curve.  Petrongolo  and  Pissarides 
(2001) provide a comprehensive survey of estimation of this function, finding 
the following main features: (a) the prevalent specification is Cobb–Douglas, 
that is,  mu v
α β µ = ; (b) usually constant returns to scale (α + β = 1) is found, 
though some studies have produced evidence in favour of increasing returns 
to scale; (c) many studies have added other variables – such as demographical 
or geographical variables, incidence of long‐term unemployment, and UI – 
finding some of them significant, but not changing the preceding findings; (d) 
these general patterns are robust across countries and time periods.  
Research  along  the  lines  of  this  model  –  in  progress  –  is  likely  to 
provide  a  richer  account  of  the  Beveridge  curve:  the  matching  function  is 
studied  for  microfoundations,  heterogeneity  is  explicitly  explored, 
endogenous separations are allowed for, interactions with capital investment 
are  considered,  and  learning  and  on‐the‐job  search  leading  to  job‐to‐job 
movements  are  incorporated.  Going  beyond  this  strand  of  the  literature, 
research  is  also  beginning  to  explore  equilibrium  search  models,  which 
feature  a  Beveridge  curve,  with  alternative  u−v  meeting  processes,  not 
modelled as matching functions. Thus, the Beveridge curve remains a topic of 
active research in macroeconomics and labour economics, more than 60 years 
after it was first studied.  
   6
 
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The Beveridge Curve

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