The argument that U.S. hegemony is beneficial on net to the rest of the world is most famously made in this book, but the arguments in support depend on the U.S. behaving a certain way. I was planning to write a post on how the United States is not fulfilling its unofficial responsibilities as hegemon to provide public goods in the midst of a global economic slowdown, but I see that Drezner has beaten me to the punch:
There's something else going on that should bother IR scholars. One of the benefits of having a hegemon is supposed to be greater provision of global public goods. According to hegemonic stability theory, if the United States is really still the hegemon, then it should be providing the following things:
Provisions of liquidity
Market for distressed goods
Long-term counter-cyclical lending
The U.S. did all of these things during the Asian financial crisis, for example.
This time around, the U.S. grade is not as high.
Drezner says the U.S. is doing the worst at counter-cyclical lending, linking to this NY Times piece that discusses how the continuing strength of the dollar indicates that the U.S. is hoarding capital that is strongly desired by other countries.
There's an aspect of this that may yield benefits for the rest of the world, however, especially countries that heavily rely on exports. The Times piece is about private capital flows to the U.S. Treasury, which have then been turned around and disbursed to the American populace as fiscal stimulus. If the stimulus has any positive effect at all, it will mean that U.S. consumers are spending their stimulus checks. And with the dollar high relative to almost every other currency in the world, that means that American consumers will be importing a lot. In other words, the American stimulus could function as something of a subsidy to the exporting industries of the rest of the world, which could boost employment and government revenues in places like Eastern Europe and Southeast Asia that desperately need a boost.
Indeed, this aspect is exactly what U.S. policymakers were hoping to avoid in the stimulus bill. Thus, the "Buy American" provisions. But those only apply to government infrastructure projects (and possibly not even then); American consumers are free to spend their money however they like. And discount chains like Walmart, which are often heavy importers, can reap some countercyclical benefits in a downturn. The net result could be a transfer from private investors to the U.S. Treasury, from the Treasury to American consumers, from consumers to retailers selling (imported) inferior goods, and from those retailers to the export-biased economies in the developing world.
It's not clear that this sort of movement is what the global economy needs, as it could prolong needed adjustment, but it is line with the theoretical role of the hegemon as a global stabilizer. The mechanism is more indirect, but that doesn't mean it isn't real.