Richard Fisher, president and CEO, and Michael Cox, senior vice president and chief economist, at the Federal Reserve Bank of Dallas say "yes indeed", on the opinion page of today's Wall Street Journal:

In teaching inflation's causes and cures, economics professors have for generations invoked the famous Equation of Exchange...

The implications are powerful -- and quite familiar. First, too much money ignites inflationary fires, a path the U.S. traveled in the 1970s. Second, faster output growth dampens inflationary pressures, a scenario played out during the country's long-lasting boom of the 1990s.

But...

This simple link between inflation and money and output has held a revered spot in economic doctrine because it offers a good representation of the forces determining prices -- at least for an economy where global interactions didn't matter much.

But we're now in an age of globalization. Freer movement of goods, services, people and ideas stretches production to the far reaches of the planet. China, India and other newcomers with huge labor resources and productive capacity are becoming important players. Each year, the part of our economy isolated from global competition becomes smaller.

It seems unlikely that inflation would remain a purely domestic affair in our globalizing economy. Research by a handful of economists like Harvard's Ken Rogoff has found important links between foreign production and U.S. inflation. The empirical studies are changing some minds on the subject of globalization and inflation, but we also need new doctrine -- an equation of exchange for the new economy.

A new formula emerges from an economic model being developed by the Federal Reserve Bank of Dallas. It reveals something the traditional doctrine misses: Inflation varies inversely with growth not only in the domestic economy but also with growth in other countries.

The implications?

An important tenet of the classical equation of exchange holds in a globalized world. Inflation still varies positively with money growth. Only domestic money matters, a significant finding that suggests reckless monetary policy in one country won't spread across borders...

Our revised equation of exchange tells us that central bankers can no longer afford to contemplate inflation without regard to world-wide output. Getting policy right will involve a great deal of additional data and overcoming blind spots about what's going on in key parts of the world.

I couldn't find the details about the "new formula" on the Dallas website, so the best we can do at the moment is revisit the article by Ken Rogoff that President Fisher and Dr. Cox reference:

The second section of the paper begins by exploring whether the popular view that "China exports deflation" has any real content, and other issues related to the effect of of the global productivity boom on inflation.  At some level this view confuses terms of trade gains with deflation.  Indeed, over the medium term,it would be more accurate to say that China is exporting inflation to the prices of other goods in the economy.  Nevertheless, there is an important truth to the argument also, in that the central banks may reasonably choose to allow inflation to drift below target in in response to favorable terms of trade shifts, just as they may choose to allow inflation to drift temporarily above target in response to adverse oil shocks.  More speculatively, some have argued that favorable trend terms of trade changes, combined with greater competitiveness and flexibility, allow central banks to target slightly lower trend inflation rates than they might otherwise.

In other words -- in my words, more fairly -- if imports and exports become an increasingly important aspect of economic activity, changes in the price of imports relative to the price of exports (the terms of trade) will very likely exert a greater impact on a country's measured prices, at least in the short-run.  The connection is a bit complicated, as changes in the prices of goods that are traded can impact the prices of goods that are not traded in the opposite direction -- a phenomenon known to economists as the Balassa-Samuleson effect, and what I presume Rogoff is thinking about when he says "over the medium term, it would be more accurate to say that China is exporting inflation to the prices of other goods in the economy." 

In a sense, there is nothing really new about this, as what seems to be at play are the transitory effects on measured inflation from what are sometimes referred to as "cost-push" shocks.  Perhaps, as Rogoff's speculative "some" argue, you could generate a decline in trend inflation with a change of the trend in the terms-of-trade, but that could only apply to the countries on the favorable side of the relative price equation. One country's disinflationary pressure is, by definition, another's inflationary pressures. Unless changes in global productivity growth are common across all countries -- in which case the traditional equation of exchange ought to be fully adequate for any given country -- we are left without much in the way of a new explanation for why low inflation has broken out all over the world.

In fact, both Professor Rogoff and the Dallas authors maintain that "domestic money matters."  I have little doubt that globalization factors in, but I would appeal to the influence on the strategic behavior of central bankers, as emphasized recently by Federal Reserve Governor Randall Kroszner and Federal Reserve Bank of Cleveland President Sandra Pianalto.    Sight unseen, I'm going to guess that the essential insight of the Dallas analysis is that closed-economy models are becoming increasingly suspect as tools of policy analysis.  But I have some doubts that replacing domestic "potential" GDP growth with something like global potential really gets at the underlying effects of increased trade on inflation dynamics.