# Why is the 30-year forward yen at about 50 to the dollar?

Nick Rowe likes to teach PPP with a thought experiment, asking students to imagine how they might guess an exchange rate between the dollar and a foreign currency. Thus if you went to Japan and noticed that most prices seem to be about 100 times higher than in the US, you might guess that 100 yen equals one dollar. Of course PPP often does not hold true, but it’s still probably the best first guess for the exchange rate, if you had absolutely nothing else to go on.

In that case, it is more useful to think of the exchange rate being caused by the Japanese price level being 100 times higher than in the US? Or should we think about the price level difference being caused by the exchange rate? Is this even a meaningful question?

I like to think about the two price levels as being in some sense more *fundamental*, as I could imagine a case with no contract between the two countries. Then once contact is made by Commodore Perry, the exchange rate conforms to the pre-existing price levels. But you can also imagine a new country being settled by England, and choosing to use the dollar rather than the pound. In that case the two price levels would be determined by the choice of the exchange rate. The adoption of the euro is an obvious recent example, which caused Italian prices to plummet dramatically.

In a recent comment section I’ve discussed the fact that the 30-year forward dollar trades at roughly 50 yen (actually 49.332). Is that exchange rate caused by the interest rate differential, or is the interest rate differential caused by the forward exchange rate? People in the financial markets may focus on interest rate differentials as the primary factor, as the 30-year forward exchange rate is not very liquid and seems to be roughly 50Y/$ merely to prevent easy arbitrage opportunities, given the interest rate differential.

[I tried to see if interest parity held, but I don’t know the interest rate on 30-year zero coupon bonds. So I took the yields on actual 30-year bonds as a proxy. The US 30-year bond yields 3.17% and the Japanese bond yields 0.747%. The differential is 2.423%. Then I took 1.02423, and raised it to the 30th power, which equals 2.0508. Then I took the actual exchange rate of 106.17, and divided by 2.0508, and got 51.77 as the implied 30-year forward yen. Is that right?]

In my view, it makes more sense to think of the expected 30-year forward exchange rate of 50 as the fundamental factor, and the interest rate differential as contingent on that expected future exchange rate. Conversely, consider what would happen if we were to start with the interest rate differential as fundamental. Then thinking in terms of interest rates, what would the BOJ have to do to prevent the yen from getting so strong in 30 years? Obviously they need to make monetary policy more expansionary. That’s how you weaken a currency. But how do you do that in terms of the interest rate differential? Obviously you need to get rid of the interest rate differential if you want the yen to be worth roughly 106 out in the year 2048. But how do you get rid of the interest rate differential, while making monetary policy much more expansionary?

Let’s assume the BOJ cannot do anything about the level of interest rates in the US. If they want the yen to be worth 106Y/$ in the year 2048, they need to get Japanese interest rates up to 3.17% on 30-year Japanese government bonds. Even more daunting, they must do so with a *highly expansionary monetary policy*. (Cochrane and Williamson are smiling at this point.)

So how do you do that? Normally, a decision to raise interest rates is treated by the financial markets as a tight money policy, which causes the currency to appreciate. So the BOJ needs to get interest rates up to 3.17% on 30-year bonds, and keep the exchange rate close to 106Y/$. So how do they do that? The simplest solution is to go back to Bretton Woods, and peg the yen to the dollar at 106. If credible, that will cause Japanese 30-year bond yields to rise to 3.17%, and after 30 years the exchange rate will still be 106. Because of PPP, Japan’s inflation rate over the next 30 years probably won’t be much different from the US inflation rate. More importantly, the current *expected *inflation rate will rise to roughly 2%, just as in the US.

The fact that investors now expect the yen to be trading at about 50Y/$ in 2048 tells you just how far away from success the BOJ remains. This is why I say that any talk of exiting from monetary stimulus is crazy. Monetary policy in Japan remains extremely tight, expected to produce very low inflation over the next 30 years. They need more than tinkering; they need a dramatic regime change. I don’t advocate a fixed exchange rate system, but that’s one example of a radical regime change that would “work”. A better option might be level targeting, combined with a “do whatever it takes” approach to monetary policy implementation. I.e. buy as many assets as needed to get prices or NGDP rising along the desired level targeting path.

We don’t have that regime today, which makes the 30-year forward yen a useful proxy for policy credibility. Only when the 30-year forward yen rises far above the current level of 50 can the BOJ start relaxing. The BOJ has had some success in boosting prices and NGDP, but very little success in convincing the markets that this policy will continue in the very long run. It seems like markets believe that once Abe is gone the BOJ will revert to its old habits.

PS. If the regime change is credible they won’t have to buy very many assets.