Friday, January 17, 2014

Has The Natural Interest Rate Been Negative for the Past Five Years?

In my last post I raised the question of whether the nominal natural interest rate has been negative since the crisis started. Many observers say yes and point to it as the reason why the economic slump has persisted for so long. For if this output market-clearing level of the interest rate has been negative while actual interest rates have been stuck near zero, then a general glut is the inevitable consequence. Others find this hard to believe. Even if the natural interest rate turned negative in 2008-2009, they question how it could remain negative for five years.

So is the nominal natural interest rate really negative five years after the crisis started? To answer this question we need to first recognize there is an entire term structure of natural interest rates. This means there is both a long-term and short-term nominal natural interest rate. The former is the determined by structural trends in the economy while the latter is driven by the business cycle.

More specifically, the long-term nominal natural interest rate is determined by trend changes in the expected productivity growth rate, the population growth rate, and household time preferences given well-anchored inflation expectations. Productivity matters because it affects the expected return to capital and expected household income. Faster productivity growth, for example, translates into a higher expected return on capital and higher expected household incomes. In turn, these developments should lead to less saving/more borrowing by firms and households and put upward pressure on the natural interest rate. The opposite would happen with slower productivity growth. Population growth matters because it too affects the expected return to capital. More people means more workers and output per unit of capital. For example, the opening up of China and India's labor supply to the global economy, meant a higher expected return to the global stock of capital over the past decade. That should put upward pressure on interest rates and vice versa. Finally, for a given level of expected income, a change in households time preferences means a change in their desire for present consumption over future consumption. This, in turn, affects households' decision to save and borrow. If households, say, start living more for the moment there would be less saving, more borrowing, and upward pressure on the natural interest rate.

Some like Paul Krugman and Larry Summers believe these determinants have changed enough such that the long-term nominal natural interest rate has been negative. I am not convinced and hope to explain why in a subsequent post (if you cannot wait, see my views in this twitter discussion). In my view, then, the important question is whether the short-run nominal natural interest rate has been negative since the crisis started.

So what do we know about the short-run nominal natural interest rate? It is shaped by aggregate demand shocks that create temporary deviations of the economy above or below its  full-employment level (i.e. output gaps). For example, a large negative aggregate demand shock that temporarily weakens the economy will put downward pressure on interest rates. This happens because firms do less investment spending and therefore less borrowing in anticipation of lower future profits. It also happens because households, particularly credit and liquidity constrained ones, save more and borrow less in anticipation of lower future incomes. In short, aggregate demand shocks that create output gaps will also push the short-run nominal natural interest rate in a procyclical direction. This is a natural process that allows the economy to heal itself. What is not natural is when interest rates are prevented from fully adjusting to their market-clearing levels. That happens when interest rates are pinned down at the ZLB. See this earlier post for a graphical representation of this ZLB problem.

So is this happening now? Is the short-term nominal natural interest rate negative after all these years, while actual short-term rates are at or near zero? We cannot directly observe the natural interest rate, but there is evidence of ongoing slack in the economy. And since slack--or a negative output gap--is a key determinant of the short-run natural interest rate, it is reasonable to believe the natural interest rate has been depressed over the past five years.

The figure below supports this view. It indicates that when the crisis broke there was a sharp increase in slack that is still unwinding. This figure shows the BIS ouput gap, the unemployment rate, and the NFIB's measure of small business concerns over weak sales. There is a striking correlation among these measures. The most straightforward interpretation of it is that if some shock causes firms to expect weaker (stronger) sales they decrease (increase)  production, employment, and begin operating below (above) capacity. Collectively, these firms are creating a negative (positive) output gap. Since these series all appear to be mean reverting to the lines, this suggest the shocks have only temporary effects. It seems, then, that the shocks driving this figure are largely aggregated demand shocks. 

Given the large amount of slack during the crisis, it seems reasonable that the market-clearing nominal interest rate could have turned negative during this time. This understanding is also consistent with the fact that the large run up in U.S. public debt was readily funded by investors at record low interest rates. Note that most of the investors buying the debt were individuals, their financial intermediaries, and foreigners. It was not the Fed as seen below:

The Fed was not the great enabler of the large budget deficits as some claim. In short, the large amount of economic slack and seemingly non-satiable, non-Fed appetite for safe U.S. treasuries all point to a depressed and maybe even negative short-term nominal natural interest rate. 

The next figure shows my crude attempt to estimate it. To do this, I first identified a period where it is generally believed that the Fed did a good job moving its target federal funds rate in line with changes in the short-run nominal natural interest rate. Following John Taylor, I chose 1984-2002 as that period. The assumption I make is that this period's ex-ante real federal funds rate is a good indicator of the short-run real natural federal funds rate. Consequently, I regressed the ex-ante real federal funds rate on measures of slack and the demand for safe assets for this period. I then plugged in more recent measures of slack and safe asset demand to estimate the current ex-ant real natural interest rate. I then added one-year inflation forecasts to this estimate to get the nominal natural interest rate that is graphed below. (More details are in footnote 1.)

This figure also includes Fed Chair Janet Yellen's "Balanced Growth Path" measure which can be viewed as another attempt to estimate the output market-clearing level of the nominal federal funds rate (HT Michael Darda of MKM Capital). Both measures show that the short-run nominal natural interest rate turned negative and remained there for many years. Only now does it appear to be getting close to the actual federal funds rate.

A more sophisticated attempt to measure the nominal natural interest rate was presented by Robert Barsky et al (2014) at the AEA meetings a few weeks ago.  Using a rich DSGE model, they produce the following figure. It too shows a protracted period of negative nominal natural rate values for the federal funds rate. (Note that they graph interest rates on a quarterly not annualized basis.)

Both approaches point to a sustained period of negative values for the natural nominal federal funds rate. Given the improved economic outlook, I suspect it has risen a lot over the past six months and may have even broached zero as seen in my figure above. Still, it remained negative for many years while the actual federal funds rate was pinned at zero percent. The long economic slump was the result. This begs the question of whether there was more the Fed could have done to avoid this gap between the natural and actual federal funds rate from emerging.

In my next post I will present two ways to eliminate this interest rate gap that were proposed by bloggers but never tried.   

P.S. Miles Kimball provides a nice discussion of the natural interest rate here. Also see this Bruegel Blog Review on previous blogosphere discussion of the natural interest rate.

Update: On twitter Miles Kimball mentions the importance of the risk premium on the natural interest rate. I did not discuss this explicitly in the post, but it alluded to it in my reference to safe asset demand. For a more on this issue see here.

1For the period 1984:Q1-2002:Q4 I estimated the following equation:
  Ex-Ante Real Federal Funds Ratet =B0+B1Output Gapt-1+B2Average Unemployment Rate Forecasted for Next Two Yearst + B3Risk Premiumt-1+ B4 Current Account Balance/GDP +ut  
The first two regressors are included to measure current and expected slack. The last two regressors are used to capture demand for U.S. safe assets. The risk premium measure is Moody's BAA yield minus 10-year treasury yield. All regressors were significant and the R2 was roughly 70%.


  1. David,
    I have some questions about the data.

    1) Are you using the BIS "Finance Neutral" estimate of the output gap? Where precisely did you get those figures?

    2) Where are you getting the forecasted unemployment (average for 2 years) and inflation (one year) figures?

    3) Is the Yellen "Balanced Growth Path" simply the path specified by the 1999 iteration of the Taylor Rule which places double the weight on the output gap as compared to the original 1993 Taylor Rule?

    1. Mark,

      Yes, I used the BIS "Finance Neutral" output gap and got via email from the authors. I used the 2-year unemployment forecast from the Philadelphia Fed's Survey of Professional Forecasters. And the Yellen measure is the 1999 version of the Taylor Rule as outlined in here April 2012 speech on page 16. I used core PCE in her model. Shoot me an email and I will share the data with you.

  2. David,
    Getting the sustainable output gap correct is the core issue. If there has been a shift in potential due to an uncommon shift in demand, we will know ex post. I realize the article you cite on the output gap says that real-time is not very different from ex post, but the data may not see a shift until the true sustainable level gets close.
    If it turns out that sustainable potential is much lower than expected, it will be interesting.
    Just saying...

    1. Quick post comparing my method for the output gap to the 4 methods described in the paper used above.

      My method did see in real-time that the economy was above potential before the crisis, while the IMF, OECD and HP filter did not. , and that the economy was below potential after the 2001 recession. The Finance-neutral method did not see that.
      My method is set up to see in real-time a fundamental shift in demand if one has occurred. My method is showing a shift downward in potential since the crisis.

  3. Great post! Question: If we are indeed finally back at a natural interest rate of zero and economic conditions allow for the interest rate to remain above zero, can we begin to expect catch-up growth if the Fed maintains the interest rate at the natural level? Or will the Fed have to maintain the interest rate below the natural level for catch-up growth to occur?

    1. Eric, I would take my estimates with some caution. The economy has improved, but I am cannot say with certainty the natural rate has hit zero. Note that the more sophisticated paper has it still negative. I do fell confident that it has risen.

      With that said, if the natural rate is at zero, then the Fed should keep its target rate at zero too. Ideally, the Fed would move its target in line with movements in the natural rate.

  4. Professor Beckworth,

    Please read Fed's recent research paper:

    The paper says that there is no apparent relation between investment and interest rates.

  5. Negative natural interest rates are a near meaningless concept. Reasons are thus.

    If the amount of money that savers want to lend grossly exceeds the amount that borrowers want to borrow for near risk free loans, then obviously the rate of interest will collapse to near nothing. But the moment it becomes negative, savers have an alternative, namely to store their savings in the form of gold, dollar bills etc in safe deposit boxes.

    Now if for the sake of argument the chances of losing everything when making a near risk free loan is 0.5% and the cost of hiring a safe deposit box is 0.5% of the wealth stored there, then interest rates will never go negative.

  6. So implication is that fed should soon move off zero? Market behind the curve a bit then?

    1. Anonymous, as noted to Eric above, I would take the estimates with some caution. I do think the natural rate has risen, but one can reasonably disagree how far it has gone. But even if my estimates are close to accurate, all they say is the Fed now has monetary policy roughly appropriate whereas before it was effectively too tight. If the natural were to rise above zero, then yes the Fed should follow.

  7. "how it could remain negative for five years"
    Because it takes 3 gosh darn years to foreclose on a house and resell it. If the rate of change of the natural rate of interest is related to supply side issues (i.e. speed which which the housing market clears), you should be able to tease out a clear differential in the judicial foreclosure vs. non-judicial foreclosure states.
    see here:

    Note that the judicial foreclosure inventory peaked around Q2 2012, more than 4 years after the recession.

  8. David,

    Two fundamental factors are ignored in these discussions: 1) tax effects, and 2) variability of returns.

    Briefly, returns on risky assets are asymmetric and have high variance. There is little variance in returns on safe assets. Thus changes in tax rates on capital will have a disproportionately large impact on the after-tax return on risky assets.

    Example: Assume risky assets with an 80% chance of a 100% loss and a 20% chance of a 500% gain. This will yield an average expected pre-tax return of 20%, and an expected after-tax return of 5% at a 15% tax rate. If you raise the tax rate from 15% to 25% the after-tax expected return drops from 5% to -5%.

  9. David, I think there's one too many "Has" in the title of this post. Did you mean to write:

    Has The Natural Interest Rate Been Negative for the Past Five Years?

  10. David:

    Like Kimball, I think the risk premium is important. The low risk short natural interest rate is negative.

    The productivity portion of the determination of the long term natural interest rate involves both duration and risk. Transforming this to a short and riskless rate involves someone bearing risk. How much do they charge? That lowers the short term natural interest rate below that long run rate.

  11. Bill, though I did not explicitly mention it in the post, I agree the risk premium is important. I should have said something about it (I did allude to it with my comments about the demand for treasuries and safe assets). With that said, I sense a lot of the risk premium is endogenous to the business cycle and therefore some of it is captured by the impact the output gap has on the natural interest rate.