What's a singular model in economics?
I have tried to grab the article to read it, but my library apparently doesn't subscribe to JME as full text.  However, when I have seen the word singular used in economics it is usually in the framework of a singular matrix.  As this article appears to be a criticism of another model, it would appear they are arguing the other model would not give rise to an invertible matrix.  In the above set of comments, it is implying that the stochastic component is vanishing and that the model is deterministic, despite the fact, there are no actual deterministic models in economics if you have to measure things.

My guess is that they are criticizing the other model by showing it can't work.