Good news in today’s jobs report, and the dollar shot higher. But a stronger dollar will make US goods less competitive, and act as a brake on further recovery. So how do we think about this? How much of the US recovery will be diffused to other countries via dollar strength and a bigger trade deficit?

Time for a bit of analytical thinking, which is good for the soul in any case. Not to keep you in suspense, here’s the punchline: the US economy reaps the bulk of the gains from rising demand relative to other countries if and only if that relative rise is perceived by markets as temporary. If it’s seen as permanent – if, say, investors see strong US demand but Europe stuck in secular stagnation – we should expect a strong dollar to undo a lot of the gains.

I could work this out in a fully specified intertemporal model, but I’m not in the mood, and anyway the intuition is the thing; so the full Obstfeld-Rogoffization is left as an exercise for readers.

So, let’s start by thinking about an economy in normal times, i.e., not at the zero lower bound (which is squishier than we thought, but still relevant.) It looks like this:

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We can think of demand as being determined by an IS curve, with real spending higher the lower the interest rate. What about the exchange rate and the trade balance? Hold off on that for a minute. And in normal times the central bank will adjust the interest rate to stabilize the economy, which for current purposes we can think of as meaning that it achieves full employment.

What happens if there is an increase in demand, say because household balance sheets have improved? The IS curve shifts right:

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But if the central bank was doing its job, the economy was already at full employment. So this increase in demand will be reflected not in higher output, but in a rise in interest rates.

Now, open economy: we expect capital flows to equalize expected returns across countries. But the rise in demand initially raises rates in our country but not abroad. So what happens? Our currency rises, which causes a larger trade deficit; demand for domestic goods falls, while demand abroad rises, reducing the gap in interest rates. If the initial shock is perceived as permanent, this process should go all the way: the rise in US demand leads to an equal rise in interest rates around the world, and most of the demand shock is effectively diffused abroad.

Next step: look at the abnormal times we currently live in. Monetary policy is constrained by the zero lower bound, so that we’re below full employment:

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What determines the exchange rate? If expected returns at home and abroad must be equal, and interest rates are zero both at home and abroad, the current exchange rate must equal the expected future exchange rate, which as we’ve seen is tied down by the requirement that the interest rates consistent with full employment be equalized.

Now consider two pure cases of rising US demand.

In case #1, everyone sees the relative strength of US spending as temporary – either they see it as a one-time blip that will go away, or they expect the rest of the world to exhibit a similar surge in demand in the not-too-distant future. In that case the dollar doesn’t move, and the bulk of the demand surge stays in the US.

In case #2, everyone sees the strength of US spending relative to the rest of the world as more or less permanent. In that case the dollar rises sharply, effectively sharing the rise in US demand more or less evenly around the world. It’s important to note, by the way, that this is not just ordinary leakage via the import content of spending; it works via financial markets and the dollar, and happens even if the direct leakage through imports is fairly small.

So, what’s actually happening? The dollar is rising a lot, which suggests that markets regard the relative rise in US demand as a fairly long-term phenomenon – which in turn should mean that a lot of the rise in US demand ends up benefiting other countries. In other words, the strong dollar probably is going to be a major drag on recovery.