# Reject worker after match

In the DMP family of labor models, we typically have $V$ denoting a vacancy and $J$ denoting the value of a job. $V$ typically becomes 0 through free entry.

Say a firm get matched with a worker of value $J_i$ and could reject him, to search again. In order to do so, it would need to hold that $V > J_i$. But as (through free entry) $V = 0$, that would only be the case if the worker has zero value to the firm.

However, in the real world, we see firms rejecting applicants and searching for new applicants. How do DMP models achieve to generate this observation?

• The papers in this area I've read were a bit ambiguous about what exactly in the real world was the match part and which was the search part. I always assumed that the application and interview part of hiring were part of search, not part of the match as you indicate. – BKay May 1 '15 at 15:33

## 1 Answer

In the standard model, all workers have the same productivity. So if J < 0, your expected value of a vacancy would also be negative. That the reason why, once a match is made, the only variable to be set is the wage. In the real world, they have to deal with different expected productivities.

Pissarides 94 distinguished between two kinds of applicants (but in this case, the firm is passive in the decisions).

• Would you know any paper which argues more on this matter? – FooBar May 1 '15 at 22:31
• If you want a paper in which the productivities are heterogeneous, have a look at Cahuc (2006, econometrica). But there again once a match is made, they only set the wage according to each outside option. – Yann May 2 '15 at 9:47