In macroeconomics, we're really only concerned about countries, in the sense of do they measure their economy, and do they have policies that might affect it.
But the sources for this information come mostly from the countries themselves. Or more correctly from the states that claim to run those countries (see Chapter VI in the Handbook for the distinction).
It's a bit disconcerting for some students to find out that there isn't an official list of official countries. This shows up in the Handbook, and the Wikipedia pages underlying it, where different international agencies that gather data report different numbers of countries.
It should also be a little disconcerting to everyone in the bigger context of things because the UN says every country gets 1 vote, and no one else gets to vote. This may substantially increase the international political and macroeconomic power of some pretty tiny places.†
Anyway, I found a cute video (12 minutes) that goes over all the different ways to count countries.
† Here's something to annoy you going forward in your life. At various times in the U.S., the party holding most of the power will complain about all the states getting 2 votes in the Senate and 2 additional electoral votes (currently it's the Democrats complaining about this, but give it time). I've noticed over the years that the same people who do complain about the equal votes in the Senate do not complain about equal votes in the U.N. To me this suggests that this an argument of convenience (formally called an appeal to consequences) that's only pulled out when you don't have many better ones. My personal advice is to get doubly-suspicious when you hear it used. ;-)
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