By Yoram Weiss, Gideon Fishelson

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Ra [ ~ p(i)(6Ia)"' { I-Ptk-I) ;U [I-PU-I)]} ]. 13) is smaller than 1. Also, since ()/a < 1, then A(k)y{)/a < IIp(a) for every k, and thus, 0 < JB(k)J < IIp(a) for every k. 12) yields: Vf = Eo {~8kA(k)P(k)Y } + (1-{)Vf)Eo { Let D = Eo { ~ 6k[B(k)-(1-p(k) )B(k)+ 1»). 1 we now know that given this solution, vo(k) has a unique solution for every kE {O,1,2, ... 8». D. 32 Search Unemployment: Theory and Measurement Since each worker is checked every period, k can be identified with t (the number of periods the worker has been in the process).

It is important to notice that the fall in wage does not reflect the fact that the worker's value to the firm falls. It reflects the fact that ex ante (before the check), a worker with a smaller number of checks is considered to be 'better' than a worker with a higher number of checks. Therefore, the decrease in wage reflects a worsening in the bargaining position of the worker as the number of checks he has been through increases. As example 1 demonstrates, our results may be generated by exogenous unobserved characteristics.

Indeed I/Tu// oo S ~ p(t, j)[I-oEvf + o(I-0Evf)] + [1-p(t,j)]o(I-0Ev f) = (l':"- OEvf [0(1- Ip) 2 + 1 p]. w Now, 0(1 - ~ p) + ~ p S 1. To see this, notice that this expression is positive and increasing in 0, and for 0 = 1 it equals 1. Therefore, I/Tul/ oo S 1-6Evf' Also, Tis monotone and, for any constant r, T(u+r) Berkovitch: Stigma Theory of Unemployment 43 ~ Tu + Or. It follows, therefore, that T is a contraction mapping in the sup norm on U of modulus 0, and T has a unique fixed point. Moreover, since this solution is bounded by l-oEvf' then the bargaining problem is well defined.

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