Timothy Taylor, managing editor of the JEP, points to some recent literature on the effect of trade adjustment assistance. In Contemporary Economic Policy, Kara M. Reynolds and John S. Palatucci find that

using propensity score matching techniques we find that while the required training component of the program improves the employment outcomes of beneficiaries, on average the TAA program has no discernible impact on the employment outcomes of the participants…

We do find strong evidence, however, suggesting that those workers who participate in TAA-funded training opportunities are more likely to obtain reemployment, and at higher wages, when compared to TAA beneficiaries who do not participate in training.

That’s in line with prior research suggesting that the only realized benefits accrue to trainees. But note that due to some data limitations:

It is possible that these results are being  driven by differences between the training and  nontraining participant samples that we are  unable to control for. Recall that although TAA  beneficiaries must participate in training in order  to receive extended unemployment benefits,  nearly 20% of TAA participants receive a waiver  from the training requirement. Program administrators are allowed to grant waivers for a wide  variety of reasons, including the health, age,  and skill level of the worker. Waivers are also  granted to workers who can prove that training  is unavailable in their area. Although we control  for such characteristics as the age and education level of the participant, we do not have  information on other characteristics such as the  health status or the local labor market conditions  of the participant. It is likely that workers in poor  health would be both more likely to receive a  waiver and more likely to remain unemployed.  Moreover, workers in small rural areas may be  limited in both the number of training and the  number of new employment opportunities.