Scott Sumner  

The Wicksellian Natural Rate of Interest

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The Richmond Fed has a new study of the natural rate of interest, by Thomas A. Lubik and Christian Matthes:

The natural rate of interest is one of the key concepts for understanding and interpreting macroeconomic relationships and the effects of monetary policy. Its modern usage dates back to the Swedish economist Knut Wicksell, who in 1898 defined it as the interest rate that is compatible with a stable price level. An increase in the interest rate above its natural rate contracts economic activity and leads to lower prices, while a decline relative to the natural rate has the opposite effect. In Wicksell's view, equality of a market interest rate with its natural counterpart therefore guarantees price and economic stability.

A century later, Columbia University economist Michael Woodford brought renewed attention to the concept of the natural rate and connected it with modern macroeconomic thought. He demonstrated how a modern New Keynesian framework, with intertemporally optimizing and forward-looking consumers and firms that constantly react to economic shocks, gives rise to a natural rate of interest akin to Wicksell's original concept. Woodford's innovation was to show how the natural rate relates to economic fundamentals such as productivity shocks or changes in consumers' preferences. Moreover, an inflation-targeting central bank can steer the economy toward the natural rate and price stability by conducting policy through the application of a Taylor rule, which links the policy rate to measures of economic activity and prices.

Naturally, monetary policymakers should have a deep interest in the level of the natural interest rate because it presents a guidepost as to whether policy is too tight or too loose, just as in Wicksell's original view. The problem is that the natural rate is fundamentally unobservable.


Of course the Fed defines "price stability" as 2% inflation. The authors estimate how the natural rate has evolved over time, and then compare their estimates to the actual interest rate. After doing so they reach this bizarre conclusion:

The most notable finding, however, is that our estimate of the natural interest rate never turns negative. In addition, the natural rate has been above the measured real rate throughout the post-2009 recovery, which suggests that monetary policy has been too loose in the Wicksellian sense. This finding is qualitatively in line with Laubach and Williams, who also find a positive gap between the two rates, albeit a smaller one on account of their lower natural rate estimate.
I must be missing something really basic, as I would have expected exactly the opposite result. Since 2008, the inflation rate has usually been below the Fed's 2% target, and if you add in employment (part of their dual mandate) they've consistently fallen short. This means that money has been too tight, i.e. the actual interest rate has clearly been above the Wicksellian equilibrium rate. But they find exactly the opposite result. Why? What am I missing?

PS. When I did my previous post on "Peoples QE" I had not noticed a similar one by Nick Rowe. Nick approaches the issue from a different angle, but reaches the same conclusion, indeed the only conclusion that seems to make any sense.


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CATEGORIES: Monetary Policy




COMMENTS (12 to date)
B Cole writes:

I try not to be cynical. But these Richmond Fed researchers seem, like so many economists of certain stripes, to badly want to show that interest rates should be higher, or that quantitative easing is bad, or that money should be tighter, or that 0% inflation or deflation is the ideal.

My guess is that central bankers and staffs will choose 0% inflation or deflation if left to their own devices.

Independent central banks?

l

LK Beland writes:

Their estimate of the natural rate uses a modified VAR, that seems to largely work like a moving average (with some lag).

They have huge error bars.

Their estimate suggests that, on average, the real Fed funds rate during the 1970s was about equal to the natural rate.

Capt. J Parker writes:

If you read the quote below it sounds (to me anyway) like the authors are saying that monetary policy is too loose if the real rate is below the natural rate even by a small (about 1%) amount. But doesn't the real rate need to be somewhat below the natural rate to achieve the Fed's 2% inflation target? So, yeah, what am I missing? Doesn't seem plausible that Fed economists would make the error I think they made.


From page 3 of the paper (here they are talking about the Laubach-Williams estimate of the natural rate which did go negative starting in 2011):

"However, what matters for this interpretation is not the absolute level of the natural rate, but its level relative to the corresponding real rate. Figure 2 therefore shows the real interest rate computed as the difference between the federal funds rate and the expected personal consumption expenditures (PCE) inflation rate. As can be seen, the real rate is lower than the natural rate by a full percentage point and has been that low or lower since 2009. Based on this metric, this finding suggests that policy is not tight enough—and has not been for a while."

Scott Sumner writes:

Ben, I also try not to be cynical. But sometimes I fail.

LK, OK, they used a VAR model. But then if the model is telling you that policy was too loose, and the actual inflation rate tells you that policy was definitely too tight, then the implication is that your VAR model overestimated the natural rate, not that policy was too loose. What am I missing here.

Captain, That was worded in a confusing way, but I have to assume that they meant the real natural rate was above the real actual interest rate.

Njnnja writes:

Clearly there is something wrong with this analysis or else we would have had inflation over the last few years greater than the 2% target.

If I read the paper correctly, they define their estimate for the natural rate of interest in the VAR approach as the 5 year projection (under the model, conditional to that point) of the real interest rate from the date of the estimate, under the theory that the real rate of interest will converge in the long run to the natural rate of interest.

But comparing that to a policy rate seems to be a problem. If you subtract a measure of expected inflation from the nominal policy rate, then you end up with a somewhat circular logic where higher expected inflation means that you are running too loose a policy, which tells you more about your expected inflation measure than it does about your policy rate (after all, if you had a perfect measure of expected inflation such that ex ante expected always equalled ex post reallized, then you don't need to compare the policy rate to the natural rate of interest, you just need to look at whether your measure of expected inflation is high or not).

But it's even worse if your measure of expected inflation isn't very accurate. If your measure of expected inflation is too high, then your real FF rate will look like monetary policy is even more loose that it actually is. But in fact, you are going to undershoot actual inflation just because your measure of expected inflation is (in this case, assumed to be) biased. They say in footnote 6 that they don't depend on expected PCE, and that their results are robust to various measures of real rates, but there is definitely an issue here that isn't fully fleshed out.

Mark A. Sadowski writes:

Scott,
"Since 2008, the inflation rate has usually been below the Fed's 2% target, and if you add in employment (part of their dual mandate) they've consistently fallen short. This means that money has been too tight, i.e. the actual interest rate has clearly been above the Wicksellian equilibrium rate."

Lubik and Matthes' VAR model includes three variables: the rate of RGDP growth, the PCEPI inflation rate and the ex ante real federal funds rate. Their measure of the natural rate of interest is the conditional long-horizon forecast (five year) of the observed real rate.

In other words they define the natural rate as that rate of interest which does not change the rate of RGDP growth or of the PCEPI inflation rate.

That is, even if RGDP growth is too slow to lower the unemployment rate (e.g. 1%), and if inflation is below the official target of 2% (e.g. 1%), the natural rate of interest may still be above the real rate of interest if it is simply sufficient to cause the RGDP growth rate and PCEPI inflation rate to both accelerate, no matter how small that rate of acceleration.

Also, on page 3 Lubik and Matthis say:

"Based on this metric, this finding suggests that policy is not tight enough and has not been for a while. This impression also is supported by the accompanying estimate of the output gap from the Laubach-Williams framework, which has been positive since the middle of 2014. This implies that economic output is running above its potential, indicating that any inflationary pressures could be reined in by a higher federal funds rate."

Because you know, um, inflationary pressures might actually lead to the Fed reaching its target, and that would be, eh, bad (or something).

Njnnja writes:

@Mark A. Sadowski

Let me preface this by saying that I don't have experience with the TVP-VAR method myself, but I'm not sure your explanation is correct. In the paper, they claim that it doesn't exhibit the mean reversion that a typical VAR model does. So why would the PCE and RGDP variables not change over time? It seems that would require some kind of (implicit) mean reversion. I'm not even sure you can guarantee that the model processes for PCE and RGDP are stationary.

In a standard VAR or VECM model all of the real rate, RGDP, and PCE projections would be dancing around in the future. Obviously the starting point of the projections matter but that's not where they would end up, so even if you had a low RGDP growth at the last data point before the projection, the RGDP in the projection could do just about anything.

Furthermore, if a TVP-VAR forces two out of three variables to be constant in the future I would say it is not a good model for them to be using at all.

But like I said, I'm not familiar with this variant so if you are I'd be interested in understanding its behavior better. Thanks.

Mike Rulle writes:

If the rate which is most important is not observable, it seems like the only comments one can make about it need only be consistent with our theory about it. But I am obviously out of my depth here.

I have to admit, the comments made by Yellen yesterday seem like non-sequiturs. I always thought that what mattered most regarding central policy and inflation was doing ones best to maintain a target and to communicate that target to the market regardless of the rate.I also cringe at the belief of central policy makers that that measurements of inflation---which seems very had to define precisely in the first place---- are taken seriously when concerns are measured in tenths of a percent. If we had a standard error estimate,it is hard to believe there would be a real difference between 1.8 and 2.

I also cannot believe that intelligent people think they predict trade offs years in the
future at such precise levels.

I sometimes think unless we are at Weimar inflation levels, this is all make believe theorizing.

I like NGDP targeting. We have inflation targeting. Fine. But when did economists start believing they can predict turning points,at absurdly precise levels no less. It is not as if I have a clue as to what the Fed should do, as I certainly do not. But the reasoning feels like "magical thinking".

As I said in a previous note, I think they just do not like zero interest rates, because, you know, its just too low. I know that is insulting and likely dumb coming from a lay person, but it seems it makes as much sense as what she said.


Scott Sumner writes:

Njnnja and Mark, I'm glad to hear that I didn't miss something obvious.

Mike, Yes, it does seem as if they just don't like low interest rates.

Mark A. Sadowski writes:

Njnnja,
"Let me preface this by saying that I don't have experience with the TVP-VAR method myself, but I'm not sure your explanation is correct."

In the interest of full disclosure, I haven't successfully estimated a TVP-VAR myself, but I have given it more than a little thought.

"In the paper, they claim that it doesn't exhibit the mean reversion that a typical VAR model does."

Well of course that's true, because the parameters are time varying.

"So why would the PCE and RGDP variables not change over time?"

I never said they wouldn't.

"In a standard VAR or VECM model all of the real rate, RGDP, and PCE projections would be dancing around in the future."

This is not at all true. Even with a stochastic simulation, you will see mean reversion with a properly specified VAR. If the variable projections in a VAR are "dancing around in the future", then the VAR you have estimated is almost certainly dynamically unstable, and hence is useless for forecasting.

And with a VECM, you will always see reversion to some kind of trend, depending on the nature of the cointegrating relationship.

However, my basic point is the following.

By the very nature of Lubik and Matthes' estimation method, they are defining the natural rate as that rate of interest which does not change the rate of RGDP growth or the PCEPI inflation rate (i.e. it is "neutral", but only in that particular sense). Hence it has no necessary relationship to the Fed's dual mandate of 2% inflation and maximum employment.

njnnja writes:

@ Mark A. Sadowski

When I say "dancing," I mean like a well choreographed ballet or the "dance of the planets," not my cousin Johnny doing the funky chicken at his wedding. Where the paths have a beautiful arc towards an asymptote or a smooth swooping hump. If your VAR projections make you think of something else then maybe you need new software ;)

But to your bigger point about not having a relationship to 2% inflation or the "maximum employment" rate of RGDP growth, I think that is a feature, not a bug. The implied assumption in their model is that the Fed knows what it is doing, and if it just wasn't for those pesky innovations, they would be able to manage the FF rate at a place of stable inflation and real growth. But the real world keeps throwing epsilons into their PCE and RGDP numbers every month! However, when you project those values into the future without innovations (or cancel them out in a simulation), then the pure relationship between the 3 variables (and their histories) plays itself out, and the FF rate that the Fed "should" be at, in particular, is revealed.

Furthermore, the problem is that there are times when the Fed doesn't really seem to care about it's 2% inflation or full employment mandates. In that case, a data-based historical model that reflects what the Fed actually did rather than what they say they should do seems to be the right approach. Given all that, I actually think that their methodology is a pretty clever "hack," and the problem, if any, isn't in their estimation of the natural rate.

Jeff writes:

One plot in Lubik and Matthes shows the realized real rate and the Laubach-Williams estimate of the Wicksellian real rate. In the 1970's, the realized rate jumps around a lot, but it's mean appears to be roughly the Wicksellian rate.

Another plot compares Lubik and Matthes estimated Wicksellian rate to the estimate of Laubach-Williams: this one shows that throughout the 1970's the Laubach estimate is higher than the Lubik estimate.

Put all of this together and it seems that:

(i) Laubach and Williams think money was neither too tight nor too loose during the 1970's, and

(ii) Lubik and Matthes think money was too tight during the 1970's.

Does anyone really believe this stuff?

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