Do WTO Disputes Increase Trade?

It seems obvious that a successful WTO complaint, properly implemented by the responding party, would bring down trade barriers and increase trade.  But a recent paper by some political scientists calls that into question:

To assess whether disputes increase trade, we analyze detailed data on imports values at the country-product-year level from 1995-2010. Since disputes are most often about specific products, as opposed to broad sectors, we use the most disaggregated product-level data available for all countries in the sample—6-digit Harmonized System (HS) level. We then code data describing the occurrence of a dispute against that particular country (the respondent) over that particular product. We also code relevant characteristics of the dispute, such as its outcome, issue area, as well as characteristics of the respondent. We analyze monadic, rather than dyadic data, since our question relates to whether disputes increase total trade flows across the membership, regardless of participation in the dispute. In other words, we are interested in whether dispute settlement increases the size of the pie, not in who gets a bigger slice.

Our analysis yields little evidence that the occurrence of a dispute increases trade, on average. In models that account for unobserved country-year and country-product heterogeneity, the value of the respondent’s imports of the disputed products is only modestly higher after a dispute, compared to the value before the dispute. Specifically, a dispute increases import values by less than 10% and this effect is not statistically significant. These null results are also apparent in non-parametric analysis of import values before and after disputes.

...

In the aggregate, disputes are not associated with a statistically significant increase in imports. Looking at particular dispute outcomes and issue areas, only certain types of disputes have been associated with increased trade, and many have resulted in decreases. Moreover, certain respondents are more “responsive” to disputes than others. Disputes against some countries have resulted in increased imports, while disputes against others have failed to do so. We do not find strong evidence of a systematic explanation for this variation.

I have a hard time figuring out what to make of their conclusions.  I think it would help to look at a few case studies.  What are some of the disputes that did not lead to more trade?  It seems to me that if you had, say, an anti-dumping tariff or an SPS-based import ban, and that measure was completely removed, trade should clearly rise in most or all cases.  Is this really not happening?  They found that:  "Looking at dispute issue-areas, disputes over safeguards appear to result in greater trade ex post, while disputes over SPS, antidumping, and agriculture do not."  I can't think of an explanation, but as noted, I'd like to see the cases in question to help understand what's going on.  Are they just looking at the existence of a dispute, rather than looking at successful disputes in which the ruling is implemented? (Apologies to the authors if they answered this in the paper.  When I see lots of equations, I tend to start skimming an article, and may miss some things.)