I have to do some teaching on the subject of the falling dollar and whether it’s recessionary. So herewith some ruminations. WARNING: FAIRLY WONKISH.

First, we need a model. My starting point is to think of the Fed as setting “the” interest rate (more on that later), and facing two tradeoffs. On one side, the lower the interest rate the higher is employment. On the other side, the lower the interest rate the lower the dollar. In normal times the Fed tries to set the interest rate so as to achieve more or less full employment, and lets the dollar fall where it may.

Now along comes a change in investor expectations that makes the dollar weaker at any given interest rate. This also, with some lag, makes the economy stronger at any given interest rate, because a weaker dollar means stronger exports and less imports.

So what would we expect the effect of changing expectations that weaken the dollar to be? We’d expect it to lead to a weaker dollar (duh) and also higher interest rates — but the latter effect would happen only because the Fed is trying to offset the expansionary effect of that weaker dollar. It shouldn’t depress the economy at all.

OK, so how do we make this story more pessimistic?

One way is to argue that the Fed will have to raise interest rates more than is necessary to stabilize employment. The usual reason given is that the falling dollar will be inflationary, so the Fed will have to support the dollar with higher interest rates to ward off this inflation. OK, this could be right, but I have a hard time making the numbers look big enough to get worried about: imports are only 16 percent of GDP, and exchange rates are much less than fully passed through into import prices. The big dollar fall from 1985 to 1988 wasn’t notably inflationary.

Another argument I used to make was that a dollar plunge would pop the housing bubble, setting in motion a rapid fall in domestic demand that would outpace any rise in exports. But the bubble popped all on its own, so I don’t think this is still valid.

Finally, there’s a fairly subtle argument about term structure and timing.

You see, the Fed only controls short-term interest rates, while investment spending depends on long-term rates. Meanwhile, the effects of a weak dollar on exports take a while, maybe as much as two years, to take full effect.

So there’s a story that runs something like this: a plunging dollar will eventually be very expansionary, and will force the Fed to raise rates to cool off the economy — not now, but a year or two from now. But the expectation of this future rise in short-term rates will push up long-term rates now, causing a recession even if the Fed does nothing.

This story depends on the effect of interest rates on demand working faster than the effect of the exchange rate on exports.

I guess this could work. But it’s a fairly tricky story, and a lot subtler than the alarm I’ve been hearing.

There’s always the possibility that I’m missing something big, but right now that’s where my thinking is.

Followup: Great comments. A few general thoughts:

1. A fair number of commentators are skeptical about whether a weak dollar really increases exports and reduces imports. There is room to worry about how big those effects are, but the direction is quite clear. Over the past year real exports are up about 10 percent, a lot faster than overall growth, while real imports are up only about 2 percent, slower than overall growth; all this is presumably the effect of the weak dollar, and there’s probably a lot more to come. Overall, the improving trade picture added about 1 percent to the economy’s growth rate, which is modest but significant.

2. When people wonder why anyone would invest in the US without a rise in interest rates, you have to make the distinction between a falling dollar and a fallen dollar. If the dollar gets really weak, investors will see US assets as a bargain, and flock here even without higher rates. The question is how far the dollar has to fall to make that happen, and whether the Fed can let that big a fall happen.