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Answer: No, Not Directly, but Yes, Indirectly
Channeling the FOMC

I remember once when the head of the trading desk at the New York Fed was giving his report on international operations, the FOMC broke into applause when he announced that there had been no dollar intervention during the past year. While fixed exchange rates was once the orthodoxy, central bankers came to appreciate their ability to concentrate on domestic economic needs under flexible exchange rates. Do what's right for the domestic economy and let the exchange rate adjust to that. The alternative is to target the exchange rate and let the domestic economy do the adjusting. Fortunately, sound domestic policy promoting low inflation is more likely than not to produce a strong dollar.

So, when talking heads say the Fed's job is to support the dollar, Fed policy-makers agree, but they view supporting the dollar as protecting its domestic purchasing power. That's not usually what the critic had in mind; but they rarely acknowledge the downside of targeting the dollar.

Skeptics worry that the Fed won't be able to avoid having the current financial crisis end in hyperinflation, given all the "liquidity" that's already been created, and given the size of the budget deficits and growing debt. It will be tricky, but conceptually it's not very hard. As the depressed velocity of money begins to rise toward more normal levels, the FOMC will promote a slower growth in money so that money growth times velocity is sufficient for growth but not fast enough to promote inflation.

Given the slack in the economy, with the unemployment rate likely to be in the neighborhood of 10 percent and with capacity utilization in the 60s, the appropriate rate of spending (Money x Velocity) won't have to be held back that much at first. Spending that would normally be inflationary won't be until slack is used up. So some gentle tapping on the brakes and watching the result will be appropriate.

What about the complicating factor of large deficits?

The FOMC should ignore the fiscal deficits. They should buy just enough government debt in the open market to hit their monetary target–no more, no less. That means that some of the deficits will be monetized and some won't. Most likely the volume of debt not monetized will gradually put upward pressure on interest rates as the slack in the economy is used up. Crowding out may eventually become an issue, but not at first, and not abruptly. No week-end meetings will be necessary.

Rising interest rates in the short term should attract foreign capital and sustain the dollar in foreign exchange markets. The FOMC's success in achieving the transition without serious inflation will tend to support the dollar in the longer run. A strong and stable dollar will not be the target of policy, but it will be the by-product of policy.

What I'm describing here is Milton Friedman's prescription: control over the quantity of money domestically with flexible exchange rates to reconcile the domestic ideal with foreign realities.

A footnote on Helicopters:

I don't know how Chairman Bernanke feels about his nickname, Helicopter Ben? It probably makes him smile. I don't want to rob him of that smile, but it bothers me that so many people seem not to realize that that image was around long before he uttered those words. Somehow, I think many people actually believe that his use of them as a joke reveals a predilection he has toward monetary recklessness.

I don't recall or know who used it first, but I do recall it being commonplace when I was studying money and banking in the 1960s. One context was how to get out of a Keynesian liquidity trap, when interest rates won't go lower as a result of more money being pumped into the economy. The answer was to keep pumping–drop money from helicopters if necessary. At some point people will start spending it. (Diminishing marginal utility applies to money too, you know.)

Economics majors from that era might recall it in the context of the Pigou Effect or the Pigou-Patinkin Effect. Anyway, our Ben was making a little inside joke. Lets go along with it, but don't take it too seriously.