Equilibria in Signaling and Screening I am now studying the Spence's job market model using both signaling and screening. 

It turns out that, when a worker's reservation value = 0 (she can get 0 if she does not get employed), then both pooling and separating equilibria always exist in signaling. However, in screening, pooling equilibrium does not exist, and the range for separating is also narrower than in signaling.

Why is that so? Does it have anything to do with the refinements such as intuition criterion?

Is it true that screening will always be stricter than signaling?

(Sorry for being verbose - still quite new to this area and do not know how to describe the problem easily.)

(Reference: The question is discussed in the 13th chapter of MWG's textbook.)
The difference between signaling and screening stems from the fundamental difference in bargaining power- who offers the contract for which her utility is the highest. While in screening the uniformed party proposes the contracts, in signaling it is the informed party.

For your general conjecture, I refer to Stiglitz and Weiss (1990): "Sorting Out the Differences Between Signaling and Screening Models": 


  However, if the indifference carves of the informed agents satisfy what roughly would amount to a single crossing property in two dimensions, and some technical conditions hold, then all contacts in the screening game break even, and the set of outcomes of the screening game is a subset of the outcomes of the corresponding signaling game. 


It has nothing to do with refinements such as the intuitive criterion, divinity and so on. These refinements are useful to "refine away unreasonable equilibria". Here, the issue is that the set of PBE is potentially quite rich while some equilibria rely on "unreasonable beliefs". The refinements formalize which of those beliefs are "unreasonable".

If you are interested, you can also look at settings that combine signaling and screening. This is the literature on informed principals, initiated by Myerson and Maskin &amp; Tirole (1990, 1992). The informed principal first offers a contract to screen the agent while the contract proposal itself may reveal private information of the principal.