The basic idea of the theory is this: It is expensive to move products around. This means that if you have a factory, you want to locate it close to where your customers are, to avoid paying a bunch of shipping costs. Now consider two factories. The workers in the first factory will be the consumers for the second factory, and vice versa. So the two factories want to locate near each other ("agglomeration"). As for the workers/consumers, they want to go where the jobs are, so they move near the factories. Result: a city. The world becomes divided into an industrial "Core" and a much poorer agricultural "Periphery" that produces food, energy, and minerals for the Core.
Now when you have different countries, the situation gets more interesting. Capital can flow relatively easily across borders (i.e. you can put your factory anywhere you like), but labor cannot. If you start with a world where everyone's a farmer, agglomeration starts in one country, but that country gets maxed out when the costs of density (high land prices) start to cancel out the effect of agglomeration. As transport costs fall and the economy grows, the industrial Core spreads from country to country. Often this spread is quite abrupt, resulting in successive "growth miracles" that get faster and faster (as each new industrial region starts out with a bigger global customer base). The evidence strongly indicates that agglomeration is the driver behind developing-world growth.
But here's the thing: in the theory, the "old Core" doesn't keep getting richer. In fact, under some scenarios, it even gets slightly poorer while the "new Core" catches up. For a while, the negative effects of relocation trump the positive effects of progress.
So this could explain why we in the rich world are getting poorer. In the 50s, America was the only industrial "Core" that was not a pile of rubble. But since the 60s, we have seen successive "growth miracles": Japan and Europe in the 60s/70s, then Taiwan/Korea/Singapore in the 80s, then China since then, and now even India. In a New Economic Geography world, we would expect these successive relocations of manufacturing to hold down income growth in the U.S., even if technology was advancing as usual.
Smith calls this the "Great Location". I called it the "Great Redistribution". Smith emphasizes structural economic factors, while I tried to also incorporate political factors. But in general the two stories are congruous and probably complementary. (Arnold Kling has written a fair amount on this too.)
Cowen says in response to Smith that this doesn't tell us everything we want to know because "Median income begins to stagnate in 1973, before this trend is significantly underway". But I'm not sure about that. Is it just a coincidence that the Great Movement began right at the end of the Bretton Woods system? There was a series of perturbations in global markets related to the re-industrialization of Europe and Japan in the 1960s (as Smith notes). And even if the internationalist story can't explain everything, it can arguably explain more than a stagnation hypothesis, which can't account for the fact that average incomes have grown at roughly the same rates post-1973 as pre-1973. What has changed is the divergence between the mean and median of the distribution. This does not imply (to me, at least) a general economic stagnation, but rather a shift in how the economy is organized. Additionally, any account of changes to the US economy over the past 40 years that does not consider international factors is likely to be under-specified.
I had some of this "economic geography" logic in mind when I wrote my posts, but I honestly don't know that literature well enough to say much of anything about it other than the basic story that Smith laid out. That is, I'm sure people have empirically examined these questions in some depth; I just don't know where the consensus lies, if there is one. Clearly it's important enough, since a Nobel Prize was awarded for it. I'm just not sure what the state of that particular literature is.
Anyway, I'm happy to see international dynamics be brought into this discussion.