# Long run NGDP growth and long term nominal interest rates

If you had to write down a simple model of long-term nominal interest rates, you might start with long run expected NGDP growth, although as we’ll see it’s actually a lot more complicated. Here are some recent data on NGDP growth over the past 8 years, and 10-year bond yields:

Country NGDP growth rate 10-year yield

USA 2.75% 1.69%

Eurozone 1.17% 0.05% (German)

Britain 2.41% 1.28%

Japan -0.21% -0.15%

Australia 4.15% 2.15%

In the first three cases, bond yields are a bit over 1% below long-term NGDP growth. If we applied that to Japan, you’d expect negative 1.25% bond yields. Why are actual rates so much higher (less negative) in Japan?

1. Perhaps the zero lower bound prevents deeply negative nominal rates. This is the best argument for Abenomics–the Japanese Treasury has been paying excessive interest on its debt. They need at least Eurozone levels of NGDP growth, to get equilibrium bond yields up to zero.

2. Perhaps rates are not lower because NGDP growth has recently established a higher trend, under Abenomics. Bond yields are a forward-looking variable.

3. Perhaps what matters is NGDP/person growth, not NGDP growth. Thus Texas and Illinois have the same risk free rate, even though Texas’s population (and NGDP) are probably growing about 2 percentage points faster than Illinois. Japan has a falling population, and hence growth in its NGDP per person is closer to European levels.

I’d guess all three factors matter, and others as well.

Australia is sort of the opposite of Japan. In Australia, NGDP growth has recently slowed, not accelerated. And they have faster than average population growth. Those factors might help to explain why nominal bond yields are 2 percentage points behind NGDP growth.

Even so, there’s a very strong correlation between long run NGDP growth and long term interest rates. It’s up to each central bank to determine the long run NGDP growth rate, and by implication the long-term bond yield. If you want higher interest rates, ask for easier money.

PS. A few corrections on recent posts:

1. **Commenter BJ Terry** pointed out that in my recent Bullard post I misunderstood they way he used the term ‘regime’. I thought Bullard meant policy regime, but after reading **his paper** it’s clear he means macroeconomic regime (expansion or contraction).

2. When I wrote the recent post on the **Modi government**, I was unaware of a decision to liberalize foreign investment regulations, which was announced yesterday. I hope my post was wrong.

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21. June 2016 at 10:50

Yep! Bullard is content with the “Depression Regime”!

https://thefaintofheart.wordpress.com/2016/06/18/bullard-makes-sense-but-misses-the-vital-ingredient/

21. June 2016 at 11:32

This is why I read your blog.

21. June 2016 at 14:45

Scott, did you see that Bob Murphy wrote a review of The Midas Paradox?

http://consultingbyrpm.com/blog/2016/06/murphy-review-of-sumner.html

21. June 2016 at 14:49

Nice post.

Something is happening in central banking. The large central banks have not been able to successfully raise rates for years.

But in cutting rates, they reach zero bound, and maybe dabble with negative interest rates, but it is much like flogging a dead horse.

Japan escaped the Great Depression through money-financed fiscal programs.

Are some macroeconomic totems too hoary to be toppled? Why not money-financed fiscal programs?

21. June 2016 at 15:18

Low interest rates are deflationary lowering interest income to the economy. It also lowers inflation as the risk free rate in the forward pricing formula is lower.

21. June 2016 at 21:03

“In the first three cases, bond yields are a bit over 1% below long-term NGDP growth. If we applied that to Japan, you’d expect negative 1.25% bond yields. Why are actual rates so much higher (less negative) in Japan?”

One would not necessarily expect that. It depends on what theory you are presuming.

When I looked at those numbers, I used regular inflation premium theory. After looking at the first three countries in the list, and noticing that 10 year rates are somewhat less

in absolute values, but with the same sign, as compared to NGDP growth, then Japan makes perfect sense. In fact every example in your list would make sense.After looking at all of these examples, I would expect that the next example, if NGDP is 3.5%, then 10 year rate would be positive, and somewhat lower. If NGDP were -2.5%, then I would expect the 10 year rate to be somewhere between 0% and -2.5%, perhaps -1%. That could be wrong, but it makes more sense to me than to simply subtract 1% for both positive and negative NGDP.

22. June 2016 at 00:27

I wat foolishly hoping that someone would pose this question to the chair: your forecasts have consistently erred on the high side. Thus we know that they are biased. What are you doing to eliminate the bias and achieve an average error of 0? Do you really expect us to correct for your bias ourselves?

22. June 2016 at 04:04

Since you’re looking at nominal growth and nominal rates, we can subtract inflation from both and think about the relation between real growth and the real interest rate.

One way to think about what determines the real interest rate is that if it is higher than the inverse of people’s discount rate, consumption will fall and saving increase until the real rate matches the inverted discount rate. The opposite will happen if the real rate is too low. In a more sophisticated model, the real rate is the inverse of the discount rate plus the product of the growth rate of consumption and the intertemporal elasticity of substitution. If we assume the elasticity is 1, which is not implausible, then the real interest rate should equal the inverse of the discount rate plus the per capita consumption growth rate. If consumption grows as the same rate as income, we end up with a real rate that equals the sum of the inverted discount rate plus per capita income growth.

In nominal terms, I’m suggesting that you should be looking at nominal interest rates versus growth in

per capitaincome, rather than the growth rate of total income. Countries with slow or negative population growth rates should have lower interest rates.22. June 2016 at 05:53

I know correlation is not causation, but you seem to be making the point that there is at the least some common condition of fact that causes both to have some kind of relationship. I continue to have a problem with what actions the Fed should take to actually increase NGDP. You say easier money, but what creates easier money? Questions such as these probably bore you as they are so repetitive. But is it lowering rates and buying securities—-actions the Fed has done but has stopped? They could not get to 2% inflation (at least on average over the last 8 years). Is it try try again? I blame fiscal and regulatory policies for lack of growth—-it has to have an impact, doesn’t it? Is it really all about monetary policy?

22. June 2016 at 08:08

Brad DeLong praises Ryan Avent:

http://equitablegrowth.org/must-read-ryan-avent-3

22. June 2016 at 10:54

More interesting analysis by Brad DeLong:

http://equitablegrowth.org/must-read-paul-krugman-14

22. June 2016 at 11:13

“I hope my post was wrong.”

Bezos is obviously sold on India’s promise and Modi…

http://www.reuters.com/article/us-amazon-india-idUSKCN0YU01M

22. June 2016 at 14:17

Sumner; “Even so, there’s a very strong correlation between long run NGDP growth and long term interest rates” – WRONG.

The 19th century had very high real growth rates and low long term interest rates, meaning NGDP = Real GDP + interest rates/inflation, ex post was high. Hence high NGDP and low long term interest rates, the exact opposite of Sumner-speak.

22. June 2016 at 15:04

Ray, the 19th century did not have high NGDP growth rates. It had low NGDP growth rates (other than the inflation to finance the war of northern aggression).

The low interest rates during that period is consistent with the theory that NGDP and interest rates are correlated.

NGDP is not RGDP plus interest rates.

22. June 2016 at 22:24

@MF – check your facts, I’m talking about the western world. By “high” I mean no worse than today, see, for 1871 to 2011, this chart, note that logarithmic the growth back then is about the same as now: http://visualizingeconomics.com/2011/03/08/long-term-real-growth-in-us-gdp-per-capita-1871-2009/

Data before the late 19th century is hard to come by, but logic tells you it’s no worse than today.

23. June 2016 at 02:55

Scott, your post on India was right based on all the information you had upto the time of publishing:-)

Sure the move to liberalize foreign investment (FDI) norms was a bold move. But the timing wasn’t entirely coincidental. Last year after losing elections in a large State the government moved quickly to loosen some FDI norms to quell any doubts about their reform credentials. Now after the l’affiare Rajan they wanted to scotch doubts among investors. So one has to agree the govt is not tone deaf and wants to manage expectations.

The bigger issue is they don’t have a good plan to tackle the bad loan problem in banks. Latest noises suggest govt wants to consolidate 20+ govt owned banks into 5-6 large banks. Without governance or ownership reforms, this would just lead to 5-6 TBTF banks. Privatisation is still a dirty word around here.

23. June 2016 at 12:07

Marcus, You said:

“What’s missing is the acknowledgement that the “current (or any) regime” is the result of Fed decisions.”

That’s a good point.

Thanks James.

CA, Check out my new Econlog post.

Jeff, Keep in mind that those models make a lot of simplifying assumptions. For instance, the rate of return on capital is much higher than the rate of return on risk free government bonds.

Mike, Monetary policy determines long run growth in NGDP, not fiscal policy.

There are many ways to boost nominal growth—right now the best way might be level targeting. The Fed could also lower IOR.

Ray, No, the 19th century did not have very high growth rates.

Thanks for the info Athreya.

23. June 2016 at 12:09

Engineer, I agree that India has lots of promise. I few years ago I predicted that it would eventually become the world’s largest economy. I still believe that.

25. June 2016 at 11:34

Ray:

“By “high” I mean no worse than today, see, for 1871 to 2011, this chart, note that logarithmic the growth back then is about the same as now:”

Ray, that is real GDP, not NGDP.

Your facts are wrong.