THE question of when interest rates will rise gets frequent attention. Less energy is spent wondering where they will end up in the long-run. But for companies thinking about long-term investment projects, and savers planning for retirement—who will need to contribute more to their pension pots should rates stay low—the second question is at least as important as the first. Two new papers from the Brookings Institution, presented at a conference on October 30th, seek to answer it.

In the long-term, interest rates are beyond the control of central banks like America’s Federal Reserve. If the Fed sets rates too high or too low, inflation will veer off-course. Where rates must eventually settle to keep inflation stable depends on economic circumstances. In particular, it depends on what “real” interest rate—the return to saving, adjusted for inflation—balances the economy’s demand with what it can supply. This elusive sweet spot is called the “equilibrium real rate”.

A long list of factors should, in theory, affect the equilibrium real rate. Top of the list is economic growth. If the economy is expanding quickly, people will expect higher incomes in future, causing them to spend more and save less today. That pushes up the equilibrium real rate. Similarly, weak growth should depress the equilibrium real rate.

But James Hamilton of the University of California at San Diego and three co-authors put this relationship to the test using data stretching back to the 19th century, and argue that it is, in fact, quite weak. For instance, in the early 1980s real rates hovered around 6% while growth was a little over 1%, but in the 1990s both growth and real rates were around 3%.

A whole lot of other stuff matters for the real rate too, such as productivity, demographics, and conditions in financial markets. The authors say that this creates much uncertainty as to where the equilibrium rate is today; their best guess is that it lies somewhere between 0% and 2%.

This uncertainty, they argue, should make policy more inert. Often, rate-setters assess whether policy is tight or loose by comparing real interest rates to the equilibrium real rate. But when they do not know what the equilibrium real rate is, their next best option is to make changes in rates respond to the data.

Rates should rise when the economy looks too hot, and fall when it looks too cold.

Today, that would mean holding rates at zero until the economy heats up a bit; if it then overheats, the tightening should be steeper. This is in stark contrast to the approach argued for by Janet Yellen, the Fed’s chair, who speaks frequently of the need to raise rates in advance of any overheating, but only gradually.  

The second paper, by Thomas Laubach of the Fed and John Williams of the San Francisco Fed (and currently a voting member of the Fed’s rate-setting committee), estimates the natural rate of interest by matching a model of the economy to the data. The authors find the real rate has trended down from about 3% at the turn of the millennium to close to zero in the aftermath of the financial crisis. A decline in growth accounts for about half of the increase; the rest, again, is more mysterious. The authors gloomily note that many models have erroneously forecasted a return to normality for several years, and been proved wrong. As things stand, the low equilibrium real rate shows no sign of picking up.

That too has implications for policy. With the equilibrium real rate close to zero, and an inflation target of 2%, the Fed’s policy rate can also be expected eventually to hover around 2%.  Given that the Fed cannot cut rates below zero, this gives rate-setters only two percentage points of leeway to cut rates when the economy falls into recession (the Fed went into the last recession with the scope to cut rates by over 5 percentage points).

One potential solution to this is a higher inflation target, as was advocated by Olivier Blanchard, then the chief economist of the International Monetary Fund, in 2010. Were the inflation target, say, 4%, the Fed’s policy rate would eventually settle around 4%. That would give rate-setters more wiggle-room. Unfortunately, higher inflation is costly. The best solution would be to find some way to raise the equilibrium real rate. But that, note the authors, is “outside the scope of monetary policy″.