Are low real interest rates in the US here to stay? Or will the long-delayed, but presumably upcoming round of nominal rate hikes lead to real interest rates comparable to those that prevailed prior to the Great Recession?

There seems to be a consensus that we are heading towards a new world where the equilibrium – or long-run – value of the safe real interest rate will be lower than was conventionally thought to be normal. The Federal Open Market’s Summary of Economic Projections provides a baseline for conventional values. In December 2012, across the members of the Federal Open Market’s Summary, the median ‘longer-run’ forecast for the nominal Federal funds rate was 4%, for inflation it was 2% The implied safe real rate is thus 2%.

By contrast, Summers (2013) says that we may need to “think about how we manage an economy in which the zero nominal interest rate is... chronic”. Financial markets agree that typical rates have fallen. As of this writing, Federal funds futures over the next three years peak at about 1.5%. And in September 2015, in the Fed’s most recent Summary of Economic Projections, the median longer-run forecast for the Federal funds rate fell slightly to 3.5%. With an inflation forecast of 2%, all three sources quoted suggest a steady state real rate that is spectacular, either notably (Fed funds futures) or modestly (Summary of Economic Projections) below the 2% value that once was conventional wisdom.

Using reduced form evidence, we argue that it would be foolish to attempt to pin down a precise value for the steady state real rate. This rate is highly uncertain. It is also highly variable. Presumed constancy at 2% or any other value was a fiction even prior to the Great Recession. In addition, the steady state real rate is influenced by many variables.

In our view, a plausible range for the steady state real rate is wide, from a little above zero to a little below 2%.^{1}

## Determinants of the steady state real rate

An influential literature has zeroed in on growth in potential output or productivity as a prime determinant of the equilibrium rate.^{2} Unfortunately, the link does not seem to be present in the data, at least not in a clear or even moderately supportive way. Using rolling averages as a measure of steady state values, we find that the correlation between steady state output growth and steady state real rate is numerically small, with a sign that is sensitive to the exact sample used. This applies to averages over business cycles in the US going back to 1869 and to cross-data as well.

Here is one illustration: for the most recent seven business cycles in the US, Figure 1 plots peak to peak values of average GDP growth and of the average ex ante real rate of interest.^{3} To understand the figure, consider the dot corresponding to the peak in 1980:1. In the 25 quarters between the previous peak in 1973:4 and the 1980:1 peak, GDP growth averaged 2.8% and the real interest rate averaged 0.7%. Other dots are interpreted similarly.

**Figure 1**. Peak-to-peak average real GDP growth versus average *r*, quarterly data, 1969:4-2007:4

It is manifest that the link between steady state output growth and the steady state real rate is noisy. Clearly peak-to-peak GDP growth of approximately 3% can be associated with a wide range of peak-to-peak average values of the ex ante real rate – 0.7 % (1980:1), 2.9 % (2001:1) and 5.0% (1990:3). Clearly the correlation is negative (at -0.4, it so happens), rather than positive as suggested by theory. Just as clearly, dropping the 1981:3 peak would turn the correlation positive (+0.3).

We do not doubt that lower safe real rates are associated with higher spending and thus higher output, and vice versa for higher safe real rates. But that association is mediated by a host of factors, so much so that a simple bivariate relationship seems to be more noise than signal over periods as long as a business cycle. For example, the high (4.9%) average value for the real rate in the 1981:3-1990:1 cycle can be attributed in part to the overhang of high inflation from the 1970s. Investors demanded high insurance against inflation taking off again. Over time, that concern about a resurgence of inflation abated, contributing to the fall in the average value of the real rate to 2.9% in the 1990:1-2001:1 cycle. During these and other episodes, trends in inflation, time varying volatility, financial frictions, incomplete markets, heterogeneous agents, bubbles and other factors contributed substantially to the value of the steady state real rate.

The post-war average value of the ex ante real rate is 1.95%. As well, in episodes in which the rate was low, it stayed low temporarily. For example, in the cycle that ended in 2007:4, the ex ante real rate was at or below 0.3% for nearly four years (2001:4-2005:3), and below zero for over two years (2002:4-2005:1). It subsequently peaked at 3.1% in 2006:4. Hence there is evidence that mean reversion has acted as a powerful force. We are doubtful that secular stagnation looms as a force to overrule mean reversion. The possibility of such mean reversion accounts for the upper end of our 0-2% range for a possible value for the steady state rate.

## Long-run tendencies of the real rate

The lower end of our 0-2% range results from a dramatically different tack. First, we look to long-term annual data. Second, we model the real rate as non-stationary. Third, we compute the steady state as an explicit time series forecast. We do so in a bivariate error correction model in which the US ex ante rate is co-integrated with a measure of the long-run, or steady state, world rate. In a given year, the world steady state rate is the median, across the 17 countries, of country-specific steady state rates. Country specific steady state rates are computed from rolling 30-year samples.

Figure 2 plots the US rate and the long-run world rate. One can see that the annual ex ante real rate is highly variable. In the last century, this rate has shown long secular swings, going down roughly from the end for World War I to the late 1940s, up from the late 1940s to the late 1970s, and down from the late 1970s to the present. In the estimates of the error correction model, we find that if the US rate is (say) 1% below the world rate, then all else equal, we expect the US rate to move 40 basis points closer to the world rate in the next year.^{4} Peculiarly, there is little evidence of a symmetric effect for the long-run world rate to be pulled to the US rate. In the equation for the long-run world rate, the parallel movement is 2 rather than 40 basis points. In any event, the fit is noisy. In the equation for the US rate, the standard deviation of the residual is 260 basis points: despite co-integration, in any given year, substantial divergence between US and world rate is possible.

**Figure 2. **Long-run world real rate (* ^{lt'}* in blue) and U.S. ex-ante real rate (

*in black)*

^{rUS,t'}Figure 3 plots a forecast for the US rate and the long-run world rate. The forecast for the US rate asymptotes at about 0.4%, with a huge confidence interval. This 0.4% figure rationalises the lower end of our 0%-2% plausible range.

**Figure 3**. Forecasts for US and long-run world real rates along with 90% confidence intervals for the latter.

## Monetary policy implications

All our evidence – from mean reversion or from unit roots, from narrative evidence or from formal regressions – indicates considerable uncertainty about the steady state real rate. Using a small scale New Keynesian model, Orphanides and Williams (2003) argue that uncertainty about exact value of the equilibrium rate will lead a policymaker to move interest rates more slowly than she would in the absence of such uncertainty.

We have evaluated this proposition with the Fed’s ‘FRB/US’ model (the US Federal Reserve Board model), using data that ended in 2014:4. We take data from the December 2014 Survey of Economic Projections as a baseline path for the Federal funds rate and inflation. We assume that policymakers recognise that the actual path may be above or below the baseline. We find that such uncertainty about the future real rate leads to more inertial policy. Lift-off is delayed, and there is a steeper path once rates are raised (see Figure 4).

**Figure 4**. Alternative funds rate paths

## Conclusion

There is much uncertainty about the steady state, or equilibrium, real rate. This rate varies considerably over time. Its determinants are manifold and time-varying, with the effects of trend output growth generally dominated by those of other factors. Looking forward, a plausible range for the equilibrium rate is wide, perhaps ranging from a little above zero up to 2%. The lower end is consistent with a view that the rate is trendy, or unit root like. The upper end is consistent with the view that the rate will mean revert to its traditional level.

## References

Hamilton, J D, E S Harris, J Hatzius and K D West (2015), “The Equilibrium Real Funds Rate: Past, Present and Future” ,*Proceedings of the US Monetary Policy Forum*.

Laubach, T and J C Williams (2003), “Measuring the Natural Rate of Interest”, *The Review of Economics and Statistics* 85(4): 1063-1070

Orphanides, A and J C Williams, (2002), “Robust Monetary Policy Rules with Unknown Natural Rates”, *Brookings Papers on Economic Activity* 2002(2): 63-145.

Summers, L (2013), “Larry Summers Remarks at IMF Annual Research Conference”, available at https://www.facebook.com/notes/randy-fellmy/transcript-of-larry-summers-speech-at-the-imf-economic-forum-nov-8-2013/585630634864563 [3].

## Footnotes

1 Details on the discussion below may be found in Hamilton et al. (2015).

2 For example, Laubach and Williams (2003).

3 The ex-ante rate was computed from Federal funds and a forecast of inflation computed from rolling auto-regressions in GDP inflation.

4 For this and other numbers in this paragraph, see equations (5.4) and (5.5) and associated discussion in Hamilton et al. (2015).