Following the Global Crisis, central banks around the world brought their policy rates close to zero, as shown in Figures 1 and 2. And now a few – including the ECB, the Swedish Riksbank, and the Swiss National Bank – have crossed the zero-rate threshold and instituted negative interest rates. A period of nearly seven years of extremely low interest rates has spurred a debate over whether interest rates will return to more normal levels. Will they rebound once the effects of the global financial crisis are finally behind us? Or are low rates a permanent feature of the economic landscape? The resolution to this debate has important implications for the economy and monetary policy (Summers 2014).

**Figure 1**. Near-zero interest rates following the Global Financial Crisis

*Source*: OECD, Federal Reserve Board.

**Figure 2**. Negative short-term interest rates become more common

*Source*: OECD.

Economists have a laundry list of developments that, in theory, could cause the trend in real (inflation-adjusted) interest rates to change over time. These include persistent shifts in the rate of productivity growth, demographics, risk aversion, fiscal policy, and international factors (Congressional Budget Office 2015, IMF 2014, Council of Economic Advisers 2015, Hamilton *et al* 2015). However, it has proven more challenging to gauge their quantitative impact on trend interest rates.

Unfortunately, standard statistical techniques are poorly suited to distinguish whether a permanent shift in interest rates will emerge from the current situation – an extended period of low rates instituted in response to an unusually deep recession and sluggish recovery. As discussed in Laubach and Williams (2015), the fact that rates have been very low for close to seven years implies that standard statistical methods indicate that the fall in real rates is entirely due to a downward shift in trend. In particular, these methods indicate that the current trend short-term rate in the US is about –1.5. A similar conclusion is drawn for global interest rates (Hamilton *et al* 2015).

One way around this problem is to use a macroeconomic model that explicitly takes into account the combined behaviours of inflation, output, and interest rates in estimating the trend in real interest rates. In the Laubach-Williams (LW) model, the trend, or ‘natural,’ real interest rate is implicitly defined as that which occurs when the economy is operating at its full potential and there are no inflationary pressures in either direction. This model assumes that the trend real interest rate depends on the estimated trend growth rate of real GDP and other unspecified influences.

The model is estimated using the Kalman filter. The Kalman filter operates on the principle that one should partially adjust one’s estimate of the unobserved variables –the trend natural rate of interest, the level of potential output, and its trend growth rate – based on the discrepancies between the model’s predictions for real GDP and inflation, and the actual data. In particular, if real GDP is lower than the model predicts, the estimate of the natural rate of interest is reduced by a small fraction of the forecast error. The output gap estimate, in turn, is based on a Phillips curve relationship between inflation, the output gap, and other variables. If, for example, inflation turns out lower than predicted, the level of potential output is revised *up* (that is, for a given level of real GDP, the output gap is revised *down*) by a small fraction, as is the estimate of the trend growth rate of potential output.

The LW estimates of the natural rate of interest display a moderate secular decline over the two decades preceding the Great Recession and a second, more substantial decline during the Great Recession (Williams 2015). Figure 3 shows the estimates of the natural rate of interest from 1980 to 2015. The estimate of the natural rate was about 3.5% for 1990, gradually declining to about 2% in 2007, on the cusp of the Great Recession. In the recession years of 2008 and 2009, the estimated natural rate plummets to about zero, where it has remained ever since. This is an unprecedented decline and historical low for the natural rate.

**Figure 3**. Laubach-Williams estimates of trend short-term real interest

*Note*: Grey bands denote NBER recessions.

What accounts for the decline in natural rates? According to the LW model, a falling trend rate of potential output growth accounts for about half of the decline. The final two rows of Table 1 show the contributions from changes in trend growth and the catch-all ‘other factors’ to the decline in the estimated natural rate for the periods 1990–2007 and 2007–2015. Figure 4 shows the LW model estimates of the trend growth rate of potential output over 1980–2015. Estimated trend potential output growth was about 3.5% in 1990, declining to 3% in 2007, then falling sharply to about 2%. Note that the model does not attribute these movements in trend potential output growth to specific sources; rather they are treated as exogenous shifts.

**Table 1**. Alternative measures of trend real short-term interest rates

**Figure 4**. Laubach-Williams estimates of the trend growth rate of GDP

*Note*: Grey bands denote NBER recessions.

There is robust evidence of a persistent decline in the trend real interest rates using alternative approaches to estimate trend real interest rates. Laubach and Williams (2015) explore alternative versions of the LW model and in each case the current estimate of trend real rates is very low. In addition, a number of other studies have examined whether trend real interest rates are permanently lower. Although individual estimates differ, it is striking that a wide variety of approaches point to historically low levels of future real interest rates (Hamilton *et al* 2015, Johannsen and Mertens 2015, Kiley 2015, Lubik and Matthes 2015).

Economic forecasters and financial market participants appear to have embraced this perspective, as seen in economists’ surveys and yields on Treasury Inflation-Protected Securities (TIPS). The first row of Table 1 reports natural rate estimates implied by the long-run forecasts from the Blue Chip survey of forecasters. The second row reports real interest rates five to ten years in the future based on TIPS yields (note that TIPS did not exist in 1990). The third row reports the LW estimates. The pattern of declining trend interest rates is consistent across the three measures, although the movements in the LW estimates are noticeably larger than the other two.

What are the implications of the sizeable decline in the trend real rate of interest? First, if sustained, it implies that longer-term interest rates will also be correspondingly lower on average. Second, a lower average real interest rate implies that episodes of monetary policy being constrained at the zero lower bound are likely to be more frequent and longer (Reifschneider and Williams 2000). Third, it is a powerful reminder that one should not treat the natural rate of interest as fixed, as is often done in discussions of monetary policy rules such as the Taylor rule. Finally, estimates of trend or natural rates are subject to a great deal of uncertainty (Orphanides and Williams 2002, Laubach and Williams 2003). The various measures of trend interest rates differ by as much as 1.5 percentage points, an unusually large deviation in estimates compared to the period before the Great Recession.

So, will interest rates be permanently lower? While an unequivocal answer is not possible with the information at hand, the evidence suggests a significant decline in the trend in real interest rates. And there is little, if any, sign of a return to a more normal trend. Taken together, this evidence suggests that it is likely that the trend in real short-term interest rates is lower than it was in previous decades, with the possibility that it may even have fallen below 1%.

*Author’s note: The views presented in this article are the author’s alone, and do not necessarily reflect those of other members of the Federal Reserve System.*

## References

Congressional Budget Office (2015) *The 2015 Long-Term Budget Outlook [5]*, June 16.

Council of Economic Advisers (2015) “Long-term interest rates: A survey [6]”, July.

Hamilton, J D, E S Harris, J Hatzius and K D West (2015) “The equilibrium real funds rate: Past, present, and future [7]”, Hutchins Center on Fiscal & Monetary Policy at Brookings, Working Paper 16, October 30.

International Monetary Fund (2014) *World Economic Outlook: April 2014 [8]*.

Johannsen, B K and E Mertens (2015) “The shadow rate of interest, macroeconomic trends, and time-varying uncertainty [9]”, Unpublished manuscript.

Kiley, M T (2015) “What can the data tell us about the equilibrium real interest rate? [10]” Finance and Economics Discussion Series 2015-077, Washington: Board of Governors of the Federal Reserve System, August.

Laubach, T and J C Williams (2003) “Measuring the natural rate of interest”, *Review of Economics and Statistics*, 85(4): 1,063–1,070. Updated estimates here [11].

Laubach, T and J C Williams (2015) “Measuring the natural rate of interest redux [12]”, Federal Reserve Bank of San Francisco, Working Paper 2015-16, October.

Lubik, T A and C Matthes (2015) “Calculating the natural rate of interest: A comparison of two alternative approaches [13]”, Federal Reserve Bank of Richmond, *Economic Brief* 15-10, October.

Orphanides, A and J C Williams (2002) “Robust monetary policy rules with unknown natural rates”, *Brookings Papers on Economic Activity*, 2002(2): 63–145.

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Summers, L H (2014) “US economic prospects: Secular stagnation, hysteresis, and the zero lower bound”, *Business Economics*, 49(2): 65–73.

Williams, J C (2003) “The natural rate of interest [14]”, *FRBSF Economic Letter*, 2003-32, October 31.

Williams, J C (2015) “The decline in the natural rate of interest”, *Business Economics*, 50(2): 57–60.