Some of the Krugman posts I like most are the ones where he explains some aspect of economics (generally macro). They tend to generate some back and forth among other economic bloggers and, when I can tease out the conversation, Krugman ends up being right. The latest back and forth (see Krugman's post) has been harder to figure.
Nearest I can tell, his main detractor on this is right on the identity but then is using a single local project to justify the whole of macro behavior, which is, as far as I can tell, wrong. A lot of macro doesn't jibe with case studies specifically because it is counter intuitive. What works well for one company just doesn't work for the entire economy of a country, and what works well for one country's economy doesn't scale up to the global economy.
Wages and trade deficit/surplus are places where this becomes rather obvious. WalMart can gain lots of advantages by paying workers poorly, not letting them unionize and not giving them benefits like health care or retirement plans, but if every company in the US did that we would be a much poorer nation. Germany can be a net exporter and have a strong economy as a result, but until we find an extraterrestrial planet to trade with, any net exporter on Earth must be balanced by a net importer elsewhere.
The S=I seems to be a similar thing. While my saving extra money (whether in a credit union account, a fund of some sort or by paying off debt) may be a good thing for me personally, if everyone did the same, then something would have to happen to offset, and the result, from Krugman's graph is that GDP falls. How? I don't know, but maybe a reduction in spending means lots of companies have excess inventory and have to lay a whole mess of people off, so they can no longer save as they want because they have to spend every bit they can manage to get by, so higher desired savings means higher unemployment and lower economy wide savings (and investment).
I didn't finish this earlier, and I now see Krugman has a post saying essentially the same thing. It makes me feel a bit smarter.