One of the most important, but difficult to measure, concepts in macroeconomics is the natural or equilibrium real interest rate. This is the rate of interest consistent with full employment and stable inflation. The last few weeks have seen bond yields tumble and a **rising cacophony of market participants questioning both the Fed's central tendency of terminal or natural rates (around 4%) and the market's perception of how fast we get there**. SF Fed Williams models see a 1.8% natural rate, BofA also believes it is between 1.5 and 2%; and now Citi admits, *"fair value of long-term rates may be lower than we and other market participants judged them to be."**As BofA explains,***The natural rate is unobservable and varies considerably over time. **In particular, it tends to be low during recessions and high during recoveries. However, over the long term, it tends to gravitate toward a slowly evolving normal level. Thus, it is useful to think of both a shortterm natural rate—the level needed to counter short term shocks — and the longterm natural rate—the level once the economy settles down. **Pin-pointing the natural rate is important because it helps us gauge how stimulative current monetary policy is, and it helps forecast how far the Fed will eventually hike rates.****Recently, a number of analysts have suggested that the natural rate is much lower today. **They point to the low average rates of the last decade. They note that the current period may be similar to the pre-Volcker years of low real rates. They also argue that the drop in trend growth in the economy may mean a lower natural rate. According to our rates team, this talk of a lower natural rate has helped push long-run market expectations for the nominal funds rate down to just 3%. Assuming the Fed hits its 2% inflation target, this implies just a 1% real rate. Here, we take a close look at the natural real rate in both theory and practice and argue that the market has probably overshot a bit. __Our tentative bottom-line: the real natural rate has dropped from an historic average of about 2% to 1 ½%.__

...**A common view among analysts is that “according to growth theory, in the longrun, the real rate of interest should equal trend growth in GDP.”**

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So much for the theory, what about practice?** The simplest way to measure the natural rate is to average interest rates over long periods of time, smoothing out short-term swings related to recessions and other shocks.** While we can get data on short-term interest rates going back into the 1800s, we focus our analysis on the period since 1960. Capital markets are very different today than in the pre-war period, and the earlier periods featured some huge swings in real short-term interest rates (Chart 7). Real rates surged in the Depression when inflation went deeply negative and then collapsed during and after World War II when inflation spiked but interest rates were fixed by the US Treasury. These extended outlier periods tell us little about the natural rate.

Chart 8 shows “ex post” real rates over the last 55 years.

Finally, there is also an active academic literature on the natural rate.** In the most commonly cited paper, Laubach and Williams (L&W) have estimated the natural funds rate in a simple macro model**. The model includes three equations and two “gap variables”: (1) GDP growth depends on its own lags and the deviation of the real funds rate from its natural level; (2) inflation is determined by the gap between actual and potential GDP (i.e. the output gap); and (3) potential GDP growth and the natural real funds rate both depend on growth in productivity.

In the original paper-back in 2003, L&W found that the natural rate varied from a high of about 4.5% in the mid-1960’s to a low of 1.25% in the early 1990s, but had rebounded to about 3% at the time of the writing. They also found the natural rate did vary roughly one-for-one with potential growth, but that most of the variation in the natural rate came from other factors in their model.

More recently, L&W have updated their estimates, and the results are eyepopping:__ the natural rate has tumbled to -0.2% in 4Q of last year (Chart 9). If true, this has big implications for the economy and bond markets.__

Before investors pour all of their money into the bond market, however, it is important to take these results with a grain of salt. As the authors admit, the uncertainty around their estimates is “sizable”.__ FOMC members are in the process of revising their own views of the natural rate.__ Four times a year, each member submits funds rate forecasts for the next few years and for the “longer run”. Presumably the “longer run” corresponds to their estimate of the nominal natural rate—the sum of the real natural rate and the Fed’s 2% inflation target. This “dot plot” has been drifting lower since it was introduced in January 2012 (Chart 10).

The debate at the Fed has shifted lower with “hawks” abandoning the 4.5% projection and “doves” moving down to 3.5%.** Recall that one of those dots is San Francisco Fed President John Williams—he’s the “W” in “L&W”. His model suggests a 1.8% nominal natural rate. **And yet the lowest “dot” is 3.5%, and he has not offered an estimate in his public speeches.

BofA's ominous conclusion...

Unless the US is going down the “Japan path” of chronic malaise, higher rates are just a matter of time.

That could never happen here.. right? Of course none of this should a surprise after **Ben Bernanke himself said interest rates would not normalize to those historicl levels in his lifetime...**