# Living on a one dimensional planet

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ÂThis post is a bit long and slightly technical, but I also believe it is important. Think about the following pairs of statements:

The Wicksellian natural rate of interest is the policy rate that leads to stable prices.

The Wicksellian natural exchange rate is the policy exchange rate that leads to stable prices.

Monetary policy affects the economy by moving the policy interest rate relative to the natural rate.

Monetary policy affects the economy by moving the policy exchange rate relative to the natural rate.

A fall in the policy interest rate does not necessarily mean easier money, as the natural rate is often falling even more rapidly.

A fall in the policy exchange rate does not necessarily mean easier money, as the natural rate may be falling even more rapidly.

You get the idea.Â Monetary policy can be described in terms of either interest rates or exchange rates.Â In both cases, they are subject to misinterpretation.Â In fact, interest rates are far more inadequate.Â To see why, consider one more pair of statements:

What matters is not so much the change in the current short-term interest rate, but rather the change in the entire path of expected future interest rates.

What matters is not so much the change in the current spot exchange rate, but rather the change in the entire path of expected future exchange rates.

This is where interest rates are radically different from exchange rates, and greatly inferior.Â To simplify the explanation, consider a small country that does not impact other countries, and also assume the interest parity condition holds. (It doesn’t hold perfectly, but it holds well enough to justify the general points I plan to make.)

A monetary policy announcement at time=0 immediately impacts the current one-year interest rate, as well as the set of expected future one-year interest rates.

A monetary policy announcement at time=0 immediately impact the current spot exchange rate, as well as the set of expected future exchange rates.

Because of the interest parity condition, we know that these two sets will be closely related.Â The change in the current one-year interest rate will be the negative of the change in the forward premium of the exchange rate over the spot exchange rate.Â In other words, if the policy announcement causes current one-year interest rates to fall by 1%, then the one-year forward exchange rate will appreciate by 1% more than the spot exchange rate.Â Investors must be compensated for lower interest rates with a higher expected appreciation in the currency.Â (That’s what the interest parity condition means.)Â And even if this is not exactly true, it is approximately true.

So far, it looks like the two data sets are telling the same story.Â By looking at the change in the expected path of exchange rates we can “back out” the change in the expected path of interest rates.Â But the opposite is not true!Â That’s because the path of interest rates tells us nothing about the change in the *level* of exchange rates, only changes in the various forward premia—the differentials.

Consider a central bank that uses exchange rates as its policy instrument, such as the Bank of Singapore.Â If there is a policy announcement, I can describe its effect by looking at the impact on the spot exchange rate, and all forward exchange rates.Â From that data, we can back out the impact on interest rates.Â Â But if I describe the impact on interest rates, we have no way on knowing the impact on the *level* of various exchange rates.

Alternatively, suppose I told you that the Bank of Singapore’s action had caused the forward premium on the one-year forward exchange rate to rise by 30 basis points.Â I don’t know about you, but I’d be kind of exasperated by that information.Â “Yes, that’s all well and good, but what happened to the actual spot exchange rate?”Â That would be the information that I’d be most interested in learning.

When someone tells you what happened to the one-year interest rate in response to a monetary policy shock, it’s like telling you what happened to the forward premium on the exchange rate, *without even describing the impact on the level of the exchange rate*.Â That’s just totally inadequate.Â It’s not that the changes in the various forward premia are completely useless, but they certainly are not the key piece of information that you’d like to know.

In March 2009, the Fed announced its first QE program, and interest rates fell sharply.Â In January 2015, the Swiss announced they were abandoning their franc/euro exchange rate peg, and interest rates also fell sharply.Â If interest rates were actually informative, then those two policy shocks would have been kind of similar in a qualitative sense.Â In fact, they were about as different as one can imagine.Â The QE announcement caused the spot exchange rate for the dollar to suddenly depreciate by over 4%, whereas the Swiss policy change caused the franc to suddenly appreciate by over 10%.Â Only by looking at changes in the *levels* of the spot and forward exchange rates can we actually see what happened.Â The change in the path of interest rates (or the change in the various forward exchange rate premia) tells us very little of value.

Markets understand this distinction, even if economists are often confused.Â Stocks rose sharply on the US expansionary policy of lower interest rates when QE1 was announced, and fell sharply on the Swiss contractionary policy of lower interest rates in January 2015.Â Markets focus on *levels.*

If you’ve followed my argument, you’ll see that I’ve explained the dispute between Keynesians and NeoFisherians.Â Neither side is correct, because both describe monetary policy in an inadequate way, using the language of changes in interest rates.Â They are like beings who think they are on a one-dimensional planet trying to understand a two dimensional region.Â They think in terms of X going left or right along as line, whereas monetary policy simultaneously impacts X (levels) and Y (rates of change.)

This confusion distorts monetary policy.Â One useful reform would be to move back to targeting levels, as we did under the gold standard and Bretton Woods.Â But those specific level targets weren’t optimal; we need to target the level of prices, or much better yet NGDP.

If we had an NGDP futures market, then monetary policy shocks could be well described by their impact on the *level* of expected current NGDP (this quarter) as well as the impact on the *level* of expected future NGDP in future quarters.Â We need such a market.

Even more so, we need NGDP futures “guardrails” on monetary policy, to keep expected one-year forward NGDP growth from drifting outside the 3% to 5% range.

PS.Â If you are confused by the two dimensional analogy, consider a two-period model.Â There is one interest rate, for bonds bought today and maturing next period.Â There are two exchange rates, the spot exchange rate and the one period forward rate.Â Shocks to the spot and forward exchange rates would appear on a two dimensional diagram.Â Shocks to interest rates would appear on a one dimensional diagram.

PPS.Â In a closed economy model you can replace the exchange rate with the money supply, the price of gold, CPI futures prices or NGDP futures prices.