This paper considers a model in which the unemployed have to incur a c
ost to maintain their skills. If whether they have done so is not obse
rvable, the economy has multiple equilibria supported by self-fulfilli
ng beliefs on the part of the employers. One of these equilibria, whic
h we argue is more likely to arise, has equilibrium discrimination aga
inst the long-term unemployed, who in response decide to let their ski
lls atrophy. As a result, in this equilibrium the exit probabilities f
rom unemployment are duration-dependent. It is shown that equilibrium
discrimination survives even if workers are allowed to accept negative
wages at the beginning of the employment relation. Since this equilib
rium is highly inefficient, constructive government action in the form
of positive discrimination, subsidies and labour market policies are
suggested to correct the market failures. However, subsidies and posit
ive discrimination by private firms are shown not to have beneficial e
ffects. Labour market policies in the form of retraining of the long-t
erm unemployed are beneficial but reduce the likelihood of a switch to
the Pareto-preferred equilibrium. The most useful policy appears to b
e a limited form of positive discrimination by a government sector.