Categorisation of Harmonised System codes for economic analysis I work a lot with Harmonised System Codes (https://en.wikipedia.org/wiki/Harmonized_System). In a nutshell, the Harmonised System (HS) provides a way to record all goods based trade in and out of a country. Countries also impose tariffs (taxes) and other conditions on goods based off the HS system.

The problem with the HS system is that some of the groupings are not "free standing", meaning that they have words such as "not elsewhere specified", or "includes goods other than those under this HS code."

As a consequence, some analyst will introduce a grouping system on top of the HS. For example, they say that this chunk of HS codes will be summarised as "beef and veal", these codes as "cars" etc. However, many analyst also don't declare what the groupings mean when they publish their research.

There is a Standard International Trade Classification (SITC)(https://en.wikipedia.org/wiki/Standard_International_Trade_Classification) but this does not match well with the HS codes.  This means I can't group HS codes by SITC, report the trade values and tariffs in a database.

My question whether the community has come across any grouping system that works with the HS coding system? From my research, I noticed that DG Agri has this system but it is only for agricultural products.
https://ec.europa.eu/agriculture/sites/agriculture/files/trade-analysis/statistics/outside-eu/2015/product-classes-details_en.pdf 

Also on agriculture, the World Trade Organization has a single grouping for "Agriculture" (using Annex 1 of the Agreement on Agriculture) but doesn't split the groupings any further.
If you are looking for classification like Agri-food trade presentation that covers products other than agricultural, you should check out the Combined Nomenclature (CN) of the European Union and its Explanatory Notes.

It is established on the basis of the Harmonized System and it covers all the products that can be subject to customs and tariffs in the EU. Seek Annex I to the the basic CN Regulation (Council Regulation (EEC) No 2658/87 on the tariff and statistical nomenclature and on the Common Customs Tariff). Be sure to use the latest version, though, as it is updated on a yearly basis. Here's a link to 2018 version, but if you want to be accurate, you should also include amendments (there were five of those since publication of 2018 verion). Perhaps the most readable is of course Explanatory Notes to the CN (so something like this).

If you are interested in jurisdictions other than EU, please find links to cusoms nomenclature under Harmonized System's wikipedia page, you've posted. I'm sure all of them will have the same problems as Harmonized System. It is simply impossible to explicitly list all the products in the World and such listings will always be half open with use of phrases like 'not elsewhere specified'.

Hope that helps.