Friday, December 13, 2013

Stochastic Dynamic Inefficiency, Secular Stagnation, and the Natural Discounted Growth Rate

(I could have put a "wonkish" warning at the top, but come on, just look at the title!)

Let's start with the concept of the natural real interest rate, which is already ubiquitous. The real interest-rate is the interest rate corrected for expected inflation, and the natural real interest rate is the real interest rate consistent with price stability.  (I leave the definition of price stability ambiguous because it depends on your theory of the price level and inflation, which is a whole 'nother blog post.)

Now market monetarists like Scott Sumner and Nick Rowe point to a deficiency in the natural real interest rate concept: the natural real interest rate depends on the expected real growth rate. And monetary policy affects the expected real growth rate, so if policymakers try to set the actual interest rate equal to the natural rate, they are chasing a moving target. To me, this criticism suggests that the appropriate approach is to adjust the nominal interest rate not for expected inflation but for expected nominal growth. (While we're at it, we can also replace "price stability" with "nominal growth stability" and be done with our futile attempts to measure the aggregate price level.)

Most economists think that the natural real interest rate is normally positive. I have my doubts, but never mind, because I'm ditching the whole concept. Once we start correcting for expected normal growth rather than expected inflation, we are clearly not dealing with a natural rate concept that can be presumed to be normally positive.  If we are talking about a risk-free interest rate, then the need for physical capital returns to compensate for risk would make it very hard to achieve a long-run growth rate [an equilibrium with the interest rate] as high as the [growth] interest rate, let alone higher. To come up with a number that's usually positive, I suggest that we reverse the sign. Instead of talking about a "natural growth-adjusted interest rate," let's talk about a "natural discounted growth rate."

We can also talk about an "actual discounted expected growth rate."  (The discount is "actual," determined by the observable interest rate, but the associated growth rate is only "expected" because it is not known with any confidence when the interest rate is set.) If the actual rate equals the natural rate, you get a normal employment level and nominal income growth stability (or price stability, if you insist). If the actual rate is higher, you get accelerating inflation. If the natural rate is higher, you get depressed economic conditions, with excess unemployment and deflationary pressure, if not actual deflation. (Wicksellians, please recall that I have reversed the signs compared to the usual natural rate theory.)

Now that I've defined the natural discounted growth rate, I can define "secular stagnation" in the context of an NGDP target. Secular stagnation means that the natural discounted growth rate exceeds the growth rate of the NGDP target path.  In other words, the target path would require a negative nominal interest rate.  Under a level targeting regime, an attempt to pursue such a path will result in either monetary instrument instability or a "zigzag" growth pattern in which recessions alternate with inflationary catch-up periods. Under a growth rate targeting regime, you'll just keep missing the target from below, much like most of the developed world's central banks today. 

But if you play with the numbers, you can probably convince yourself that secular stagnation, by my definition, seems unlikely. A reasonable NGDP target path growth rate is maybe 5%.  Do we really think that the potential growth rate exceeds the natural interest rate by more than five percentage points? It's remotely conceivable, but my guess would be that our problem today is not secular stagnation (in this sense) but a flawed monetary policy regime.

Now if the target nominal growth rate (and the associated possibility of secular stagnation) is one of our bookends for the natural discounted growth rate, the other bookend is pretty clear: it's zero. Some readers will immediately recognize zero as the criterion for dynamic efficiency. Ignoring the issue of risk for a moment, an economy with a strictly positive natural discounted growth rate would be dynamically inefficient. Overall welfare could be improved by instituting a stable Ponzi scheme that transfers consumption backward across generations.

Does my assertion that the natural discounted growth rate is almost certainly strictly positive imply that we actually live in a dynamically inefficient economy? In an important sense, I think it does.  The thorny issue here is risk, and some will argue that the relevant interest rate for dynamic inefficiency is not the risk-free rate.  But I disagree.  The US government can produce assets that are considered virtually risk free, and a stable Ponzi scheme operated by the US government could presumably produce such assets yielding any amount up to the growth rate.  At today’s Treasury interest rates, which are clearly less than expected growth rates, marginal investors are (we can presume, since the assets are freely traded) indifferent between these low-yielding Treasury securities and investments that represent newly created capital.  So, given the risk preferences of the marginal investor, the government could, by operating a stable Ponzi scheme, be producing assets that have a higher risk-adjusted return than newly created capital.  Given the risk preferences of the marginal investor, it’s inefficient for the government not to be producing such assets.

It’s important to recognize that, under a typical scenario, the marginal investor will end up worse off, in a material sense, from earning the growth rate, compared to earning the actual return on capital.  In a material sense, the economy is dynamically efficient.  But the concept of risk preferences models a subjective good – call it “security” – and we’re not producing enough of this good.  The history of interest rates and growth rates suggests that we have seldom produced enough security, but the deficiency today is clearly worse than usual.  

DISCLOSURE: Through my investment and management role in a Treasury directional pooled investment vehicle and through my role as Chief Economist at Atlantic Asset Management, which generally manages fixed income portfolios for its clients, I have direct or indirect interests in various fixed income instruments, which may be impacted by the issues discussed herein. The views expressed herein are entirely my own opinions and may not represent the views of Atlantic Asset Management. This article should not be construed as investment advice, and is not an offer to participate in any investment strategy or product. 


Nick Rowe said...

Andy: I think we are thinking along very similar lines. By coincidence, I've just done a closely-related post!

But while you introduce risk into the story, I introduce liquidity.

I think you are onto something. But there's something I'm not sure about. Is it costly for the government to produce a safe asset?

Frances Coppola said...


Gary Gorton argues that only government can produce a genuinely safe asset. Therefore you could argue that for government NOT to produce safe assets is costly, since it forces marginal investors to take risk they neither want nor can afford.

However, we have had some recent horror stories where government debt has been regarded as a safe asset but turned out not to be. Not all governments can produce safe assets. Indeed that is why I think the US government should accept its role as savings bank for the world. As Andy suggests, a sufficient quantity of safe assets is essential for economic stability. While we don't have enough, we will continue to see bubbles in other assets that are temporarily regarded as "safe" until it becomes apparent that they are not - property, for example.

I think the "cost" depends on what you do with the money. There is a risk of accelerating inflation if it all goes into consumption spending. So I think we should be regarding government-produced safe assets as a long-term investment scheme, partly replacing (or enhancing) private sector investment. Clearly there will be crowding-out concerns.

Nick Rowe said...

Frances: I think the risk might be the risk of the amount of taxes paid by future generations. If we start with Samuelson 58 (whch is where Andy is coming from), and then introduce uncertainty in (say) population size for future cohorts, the government might need to vary future taxes/transfers to make government debt a perfectly safe asset.

Frances Coppola said...


The Bank of International Settlements looked at this a while ago and concluded that the way to make government debt reliably safe was to commit to running a primary surplus for all future time periods to ensure that the debt can always be serviced. But that assumes that returns on debt are positive. BIS link is here:

As I understand it, what Andy is saying is that there is no reason to assume that the return on safe assets should necessarily be positive. Safety itself has a value, so the returns on genuinely safe assets should be lower than the long-run growth rate of the economy, the difference being the "safety discount" (if we can call it that). When growth is persistently low - as might be the case with a declining and/or ageing population - returns on safe assets would be negative. Under this scenario, there would be no need for taxes to rise to pay returns on safe assets. But there might be a problem convincing savers that it is reasonable for them to pay for safety through capital erosion.

Andy Harless said...

Nick has a point, but I would argue that government debt doesn't need to be perfectly safe to be a reasonable empirical counterpart of the theoretical safe asset. Anyone who has heard of the 1970's should know that nominal US government debt is not perfectly safe, and yet it still yields far less than any reasonable estimate of the nominal growth rate. So I would argue that the product demanded by the market is one that can be produced at very little cost, if not completely costlessly. I would argue for a system where the central bank targets NGDP, and government bondholders bear the risk that a greater than expected fraction of NGDP growth will be in the form of higher prices. That system is quite safe from the government's point of view (assuming it retains the ability to tax output at the same effective rate) and, I would argue, safe enough to satisfy the market from the private sector's point of view.

JOhn Williams said...

In the 1970s the UCLA School of Management hosted a monthly seminar series featuring talks by economists and theoretical economists. I attended because I was interested in theoretical ecology, and because my department (Geography) was in the building next door. The economists and theoretical ecologists used similar models, so the joint seminars made sense, but it seemed to me that the economists and theoretical ecologists had different relationships to data. I knew enough about ecology to know that theoretical ecologists had to deal with pesky field ecologists who collected actual data with which at least some of the theories could be tested, and these field ecologists could publish such tests in leading journals, but I wondered who the field eonomists were, and whether, if they existed, part of their job was publishing in academic journals.

I bring this up because Andy Harless's comment about government debt being a "reasonable empirical counterpart to the theoretical safe asset" reminds me of the economists' attitude toward data;
if something is sort of like the theoretical construct, that is good enough. Back in the 1950s, the Polish polymath J Bronowski wrote something about the "fatal reasonableness" of Adam Smith keeping economics from ever becoming a truly empirical science, and that seems still to be true.

Nick Rowe said...

Andy: OK. Maybe all you need is that the government has an advantage in diversifying risk, because it can operate over longer horizons.

Frances: Yep. If the economy is dynamically inefficient, so government bonds pay a rate of interest lower than the growth rate of the economy, you want the government to run a primary deficit. You actually need a primary deficit, so the debt/GDP ratio doesn't fall over time. said...

Andy, Am I correct in assuming that your claim is not just that the one year T-bill yield is less than the one year expected NGDP growth rate (which is obvious) but also that the 30 year T-bond rate is less than the 30 year expected NGDP growth rate (which may be true, but is far from obvious.)

Ralph Musgrave said...


What’s your definition of the “natural rate of interest”? I don’t see a definition in your opening paragraphs. There are actually any number of definitions. As Michael Sankowski put it, “There are lots of different meanings for the words natural rate of interest.” See:

Andy Harless said...


I guess my response to Nick doesn't make sense unless one takes it to refer to long-term bonds (although, when I wrote the post itself, I was thinking more of T-bills). I don't think it's very far from obvious that the 30 year yield is less than the 30 year expected NGDP growth rate, though I did overstate the case in the earlier comment. It's plausible that the ex post growth rate will turn out to be less than the 30 year yield, and it's also plausible that there are some people whose mean expectation for the growth rate is less than the 30 year yield, but it's just not plausible that the market's current best guess for the 30 year growth rate is less than the 30 year yield. It's also true historically that long-term yields tend to be less than the growth rate. See, for example, Darby (pdf)."


I defined it right at the top: "...the natural real interest rate is the real interest rate consistent with price stability." Certainly there are other ways to define it, and there are a lot of subtleties about this definition which I have swept under the rug, but I'm just trying to make some general points in this post.

John Smith said...


I think you touch very sensitive and broad topic about the nature of the interest.
The "secular stagnation" can be economically described as a time period when all the existing markets are so competitive that marginal efficiency of capital is equal to zero. An investor has either to create a new market or bite a competitor's share.
This real economic environment has direct impact onto the financial world: investors cannot share average yields of capital with rentiers because the yields do not exist.
The dispute over "natural" interest rate does not make economic sense because it is merely political, it's about a "fair share" of financial elite in the real growth.
Whilst safe assets are nothing but insurance from risks provided by government and therefore these assets should bear premium rather than generate interest. The natural level of the premium would be voluntarily determined by the market if risk assets like bank deposits were not be implicitly or explicitly insured by government.
This is the solution - consistent delimitation of safe assets produced by government (risk free and always cost bearing) and real investments (risky but potentially yielding).

Steve Roth said...

Maybe what we need is redistribution of economic security.

Lisa said...

After reading all this and many other economic books / theories, I'm quite sure that the economic system will have to change in the next years.

It has some good elements, but other things don't seem to work.

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Matt said...

Andy: OK. Maybe all you need is that the government has an advantage in diversifying risk, because it can operate over longer horizons.

Frances: Yep. If the economy is dynamically inefficient, so government bonds pay a rate of interest lower than the growth rate of the economy, you want the government to run a primary deficit. You actually need a primary deficit, so the debt/GDP ratio doesn't fall over time.

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