I agree with James that it is best to go third pary, but I have seen data and heard from customers that while they will discount the validity of any materials coming from the vendor as being slanted, they will pay attention to results metrics and use them in their buying decisions.
So I believe it is still worth the effort to measure and present economic impact results to prospects and customers, even if you don't have the option to go with best practice.
If you are going to do this in house, I suggest starting small with a partial economic analysis as opposed to total. You'll need three key pieces to conduct any supportable economic analysis: 1) a definition for the metrics you want to track, 2) the "before" measurement, and 3) the "after" measurement. The hardest part in my experience is getting the "before" measurement from customers. Chances are they aren't reliably tracking the metrics you need, or at least not in the way you prefer they do.
So once you have defined 3-5 metrics you want to track (for example, sales velocity measured as average length of deal cycle in days, don't make it complicated), you'll need to train your sales team and/or professional services team to capture this information from the prospect during the sales cycle or before go-live. Give them a clear place to capture this information, such as a dedicated field in CRM. I also suggest training your team on how to ask for this information without making it a burden on the customer. If you can't rely on other teams to get this information for you, figure out a way to get it for yourself.
Then, you'll need to make sure there is a point or mulitple points in the customer journey during which the "after" information is captured. Partner with your Customer Success teams for this. They want to show their success as much as you do.
Hope this is helpful!