Qualification-Mismatch and Long-Term Unemployment in a Growth-Matching Model

that technological knowledge of the unemployed does not grow with the same rate
as technological progress. The underlying matching technology is defined as

M = m(V,U ; λ) = V¹~^βU^βλ~¹,                     (2)

with β as the search intensity of the average unemployed worker and the matching
function is assumed to be homogeneous of degree one. Furthermore, the indicator for
labor market tightness is denoted by the ratio of vacancies to unemployed θ = V∕U
and

p(θ) := M∕U = m(V∕U, 1; λ), p_θ > 0                   (3)

is the matching-probability for the unemployed and

,ʌ,

q(θ) := M∕V = m(1,U∕V; λ), q_e < 0                  (4)

is the probability of filling vacancies. Both probabilities depend on labor market
tightness and reflect the externalities each trading partner faces. If the number of
jobless workers increases, the matching-probability for the average unemployed will
decrease and simultaneously the probability of filling vacancies will increase.

Due to constant returns of scale, the average duration in unemployment is defined
as

p(θ) := U∕M, p_e < 0                          (5)

and it rises when the labor market becomes tighter which is characterized by in-
creasing unemployment for given vacancies.

Furthermore, two types of jobless workers are distinguished: short-term and
long-term unemployed, U^s respectively U^b, and the heterogeneous unemployment
pool is defined as

U = U^s + U^l

U = [1 - φ(p; λ)]U + φ(p; X)U, 0 <φ< 1, φ_p,φ₁> 0,

with φ(p; ^λ)U as the long-term unemployed. The long-term jobless workers show
significant different search behavior than short-term unemployed. They are looking
for new jobs with less search intensity and, due to the long unemployment duration,
they are demoralized and discouraged.⁹ During their jobless time their human cap-
ital is exposed to large depreciation losses and, since they are not trained and do
⁹Seealso Layard, Nickell, Jackmax (1991).

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