Can I publish research as "working paper" after journal submission? I am aware that (at least in the field of economics) typically one first publishes their research as a working paper and later on submits to journals. (Where "later on" could be as short as the same day.)

In our case it so happened that a deadline was tight, and we have now submitted the article to a journal first. While we are waiting for a response from the journal, can we proceed to further prepare and publish our work as a working paper or would such a thing only be appropriate after learning of a negative response from the journal (i.e. only after our paper is no longer considered there)?
Most journal publishers have policies allowing you to release the manuscript that you have submitted to the journal (usually called the pre-print because it is pre-peer review) as long as you meet some requirements. Requirements vary by publisher, but commonly include only being able to put your manuscript on certain web sites and having to add a note to the manuscript saying it has been submitted to that journal. 

You can find the policy that applies to the journal you've submitted to by searching for 'pre print policy' or similar on their website. You could also look at a website such as Sherpa Romeo, which act as a searchable database of different journals' policies.