By Yoram Weiss, Gideon Fishelson

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**Extra info for Advances in the Theory and Measurement of Unemployment**

**Sample text**

First, the worker's productivity is now known (with certainty); second, the alternative the worker is facing is his market value after a successful test, as opposed to staying with the same history in the pre-check contract. The fact that no agreement is made prior to the check raises the interesting problem of information structure, namely, whether or not the result of the test is private information. This problem is redundant in the pre-check contract, because of the enforceability assumption.

1 There exist unique equilibrium values (Ev~, {v~(t, j)}~. 12) as usual. It can be seen that (Tu) maps U into itself, and that it is monotonic. 25p(t, j)a 1-0+(0/2)a b I + -1 p(t,j)b + [l-p(t,j)]b r 2 ~(Tu)+Or where the inequality follows from the fact that a/2 -----~1. 1-0+(0/2)a Indeed, this expression is increasing in 0, and at 0 = 1 it equals 1. Therefore, Tu is a contraction mapping in the sum norm, and Vo (t, j) has a unique solution for every (t, j) NxN. 2, this implies that EVf has a unique solution too.

This follows from the facts that a > 1, o/a < 1, and ~j~k p(k) IIJ~k [1-p(j-1)] = 1 (this is the probability that the worker will find a good match). 8) gives the value of vo(k) when Vf is given. In turn, given a sequence of market values for each type of workers, Vf has a unique solution. 9) To see how V f is calculated, note that in general, firms expect to get different payoffs from different types of workers. Since the number of workers of type k in the market changes stochastically (due to the stochastic nature of the outcome of the match), firms may face, in different periods, different probabilities to meet each type of workers.