Is there any research that shows what the economic impact was to the British economy stemming from the 13 Colonies obtaining independence?
It could be either a narrower estimate of purely tax losses or, ideally, the overall economic impact, including positive or negative effects on trade, etc...
This does NOT include the costs of waging the war itself.
I'm looking for short term impact (say, within 10-20 years of the war).
The American colonies were Britain's primary trading partner, and the British economy benefited much more from trade with the colonies than it could hope to make from the increased taxes put in place to cover the costs of the French and Indian War. The British fixation on getting repaid for the war costs ratcheted up the tensions between Britain and the colonies and eventually provoked the revolution even though most colonists initially favored remaining part of Britain. See Barbara Tuchman's The March of Folly: From Troy to Vietnam and Don Cook's The Long Fuse: How England Lost the American Colonies 1760-1785.
The key thing to consider here is that Britain was a mercantilist empire, and colonies were a means to bolster the wealth and power of Britain the state as well as the monarchy as individuals.
The real money in the colonies was made in the classic "triangle trade"; that is shipping slaves to the New World, sugar and rum to Europe, and manufactured goods back to the colonies. Traders were licensed and each European country had a monopoly on trade to its colonies. The climate in North America wasn't suited to sugar production, so hot market here was the Caribbean. North America was a backwater -- so much so that the French traded all of Canada to England for the island of Martinique, which was a huge sugar production center.
So in the short-term, the financial losses, while significant, weren't that big of a deal. The biggest impact was the loss of sales of manufactured goods, as Americans could buy tea directly from China, goods from France, Spain or domestic sources, etc.
Long-term, it was disastrous for England, as sugar declined in profitability compared to cotton-based textiles. Losing control of the colonies meant that the great mills of England in the 19th century would face competition from the mills of New England, and the US would compete globally on the sale of fabrics and goods for China purchased in trade.
