Do people care about real interest rates, or nominal rates minus NGDP growth?

I frequently argue that inflation doesn’t matter, and that NGDP growth is usually a more appropriate variable to use when you need a nominal indicator.  One commenter recently argued that inflation is useful in calculating real interest rates, and that real interest rates determine whether people are motivated to borrow and lend.

I certainly understand that real interest rates are often better indicators of credit market conditions than nominal rates, but is the nominal rate minus inflation necessarily better than the nominal rate minus per capita NGDP growth?  To think about this issue, let’s consider an extreme case, where the rate of inflation is very very different from the rate of NGDP growth.  Then think about which variable seems more meaningful to people making decisions whether to borrow or lend.

In my example, I’ll assume a stable population, no inflation and 18% NGDP growth.  Let’s assume a 7.2% interest rate, although the exact number doesn’t matter.  I want the interest rate to be much higher than inflation and much lower than NGDP growth, to see which one seems to matter more.  Now consider someone who earns \$40/hour contemplating the decision to save \$40, by lending it to someone for 20 years.  What does this look transaction like in real terms?

Since the real interest rate is 7.2% (due to zero inflation) the money will double every 10 years, or quadruple over 20 years. That means you’ll get back 4 times more goods and services than you lent out.  Seems like a pretty good deal for savers, right?

But let’s think about this in terms of a loan of work effort.  At 18% NGDP growth, and no inflation, real GDP will double every 4 years, and increase 32-fold over 20 years.  In 20 years, you will be able to produce as much in 2 minutes as you now produce in one hour.  So that 4-fold real rate of return is actually just 8 minutes of output in the year 2036.  You are giving up one hour’s worth of output, and getting back 8 minutes of future output.  That doesn’t sound very appealing.  Your rate of return in terms of goods able to be purchased in an hour’s worth of work is negative 10.8%.  Instead of lending the money out, why not just work an hour less today and 8 minutes more in the future?  Or alternatively, work just as much today and don’t worry about 20 years from now, as you’ll be really rich by today’s standards.

What this example tries to illustrate is that the real interest rate that matters to savers is not the nominal rate minus price inflation, it’s the nominal rate minus wage inflation.  Which is roughly the nominal rate minus growth in NGDP per capita.

So once again we find that inflation doesn’t matter.

PS.  In about 30 minutes I’ll have a new post at Econlog, on the recent market gyrations.

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39 Responses to “Do people care about real interest rates, or nominal rates minus NGDP growth?”

1. Kevin Erdmann
7. January 2016 at 12:56

This is one thing I worry about regarding implementation. NGDPLT should create the sort of stability you are talking about, which should raise risk free real interest rates and reduce the equity risk premium. As in the late 60s and late 90s after previous periods of extended moderate growth when this was the case, labor share of income should be high and equity valuations will be healthy – not because of changing required yields on corporate assets, but because the change in risk perception will change the focus of at-risk investments, increasing real growth expectations. And partly, growth expectations will rise just because investors won’t have to factor in temporary sharp macro contractions. But if a regime shift to NGDPLT isn’t firm and persistent, people will react with fear, as if high labor income will be inflationary and high stock prices will be speculative.

2. E. Harding
7. January 2016 at 13:52

In this case, it’s clear real growth is good for everyone. Deflation is good for lenders and inflation is bad for lenders, but inflation is not necessarily good for debtors and deflation is not necessarily bad for debtors.

“What this example tries to illustrate is that the real interest rate that matters to savers is not the nominal rate minus price inflation, it’s the nominal rate minus wage inflation.”

-For some, wage inflation, for others, nominal income growth. Not all debtors earn their income primarily from wages. BTW, the nominal rate minus wage inflation soared during the Carter and first Reagan administrations. I still have no clue why. The 10 year Treasury and the rate of average nominal wage growth are often well-correlated.

3. A
7. January 2016 at 14:10

That’s a good point Kevin Erdmann. The more credible the policy makers, the more credible they have to be. You might also expect higher household debt/income, and wider asset-liability tenors. Perhaps a well communicated NGDPLT channel might help, where the borders are expected to be aggressively defended.

4. bill
7. January 2016 at 14:15

I never thought of it that way, but this makes a lot of sense.

Question: so much of the theory and discussion around real rates seems to focus mostly (exclusively?) on risk free real rates. But credit spreads are volatile and sometimes move with and other times against Treasury rates. Is there more literature on this? Most commercial real estate loans nowadays are around 5%+ for 10 year terms. Hardly a ZLB.

5. Benoit Essiambre
7. January 2016 at 14:56

This is a great point. I think real value is a very useful concept but I also like NGDP adjusted money because it represents a specified share of the future economic pie.

I would add that it works both way. If because of some catastrophe, the world’s economy was to shrink continuously instead of growing, asking a fixed real return would give you an unfair return above what the average person would likely be able to produce in a reasonable amount of time in this bleak future.

The borrower defaulting would become much more likely.

Better adjust to NGDP to get a compromise between complete defaults and economically oversized and unfair paybacks.

6. Ossi Saresoja
7. January 2016 at 15:28

What about a person who’s saving for retirement and trying to decide how much to save and how soon to retire? One would think that he would care more about consumer prices than NGDP.

7. Derivs
7. January 2016 at 15:49

Scott,
I remember when I once commented that Taylor just simply reverse engineered the bond market and shoved his name on it. Now I think he might be my best friend…

I am extraordinarily tired right now but will be happy to engage in this conversation to a rather lengthy extent, I’ll even drop my carefully crafted online persona for this one.

In order to frame it, do you accept if I use equities as an example of NGDP capture (long economy). I’m sure the correlation is not the best but short of NGDP futures I can’t offhand think of a better way to suggest to someone how best to be ‘long economy’.

….and I will paste my comment from the previous post, as my extreme example I think is quite a good representation of the opposite extreme of your example. And if you accept/tolerate the equities as =’ish long economy, I like my example of showing how you are comparing two completely different investments while simultaneously disregarding/neglecting the costs of synthetically equalizing the risk profile of of the 2 examples.

Also I assure you that I have never executed an interest rate transaction where NGDP, real rates, or inflation have been given so much as a second of consideration. What motivates the hoi polloi is not what motivates me.

OLD POST

“it’s not so much interest rates minus inflation that matters, it’s interest rates minus NGDP growth.”

…are you saying that if he were in Brazil right now, with negative NGDP growth, he should be happy to lend at flat to negative even with 10%+ inflation? That’s nuts!!!!

“Suppose inflation was zero and RGDP growth was 20% per year. How would you feel about lending money at 5% for 30 years?”

Scott, you are asking a question that is missing way too much information for anyone to properly answer.
What does the entire yld curve look like? Where are all the forward curves in commodities? Are they flat, backwardated, contango? How could they be flat at 5% (suggests contango) and how could they not be flat if there is no inflation (suggests flat)… Also getting long the economy leaves you short the put on that economy and at 20% you are implying a pretty high vol. What do you think that put will cost you to take off and make your play risk free as well????

..you are essentially implying that no one should lend Google/Alphabet a billion+ @ 3.375 since their 5yr ROE is over 20%. only an idiot wouldn’t buy the stock!! But the market gladly did fill them @3.375… Let’s see what an at the money 1 yr google put costs … \$82 vs \$740 or 11% of the underlying!!

and if Matt said he was eyeing that Enzo for 3mil. and a year later bought it for 3 mil and had 150k in cash for lap dances, did it all **risk free**… in my book, nothing at all to be embarrassed about.. I’d even congratulate him as he was driving us all to the club to blow the extra 150k…

8. Derivs
7. January 2016 at 16:11

…and one last thing, for now. I once asked someone here “what are you tring to do when you buy a bond”? I’ll now add, think of where you are putting your debits and credits along a time horizon, then tell me what it is you think you are entitled to have as a return on a risk free investment (skiers should get this one). Then apply that to a bond essentially being it’s own arb. Now here I am working into the reverse engineering of that Taylor Rule…

OK.. time to find a bad Spanish horror film and then get some sleep.

9. Benjamin Cole
7. January 2016 at 16:27

Excellent blogging. All the constant jibber-jabber about inflation, especially in central bank policy making circles, is truly annoying.

I suppose for practical and political reasons, inflation should be kept below 5%.

The Thai central bank now has an inflation band target of 1% to 4%. Not bad.

10. Doug M
7. January 2016 at 16:34

Lets look at this from the debtors perspective.

Since every borrower is competing for the same pool of money, the marginal borrow effectively sets the nominal interest rate.

In the supply of debt out there about 1/3 is corporate debt, 1/3 is mortgage debt, and 1/3 is government debt.

Corporate debtors:

I embark on a project when expected return of investment > cost of cost of capital (interest rate) + risk premium.

I think it is reasonable to assume that expected marginal ROI is something close to NGDP. Corporations will be bid up interest rate up to a point where the rate is a little below Expected NDGP growth.

Inflation is irrelevant.

Mortgage debt —
Do I buy or do I rent?
I buy the house, when the sum of future mortgage interest payments – appreciation > sum of future rent payments + risk premium.

both appreciation and future rent payments are sensitive to inflation.

Mortgage borrowers will bid up the interest rate up to a point where the mortgage rate is a little bit below 2*expected future inflation

GDP growth isn’t particularly relevant… Unless you think the marginal mortgage borrower borrows more than he can really afford and hopes that growth in real wages will bring his debt service costs under control.

I don’t think the government thinks to much about when to take on more debt. The budgeting process is strung out years ahead of time. The government borrows what it needs to borrow to get through the year.

Who is the more powerful player at the margin? The GDP influenced corporation, or the real-rate influenced mortgagor? Or, does it flip back and forth over time?

11. mbka
7. January 2016 at 16:35

Scott, your post got me thinking. Let’s take another example. Imagine a person with 0% wage inflation, inflation at 3.6% and interest rates at 1.8%. Is it rational for this person to save?

In 20 years time, an hour worked gets the same nominal output. It would take 40 years to double one saved dollar’s nominal value but it only takes 20 years to halve its real value. Subtracting gains from losses, saving still incurs real losses.

Clearly, saving loses less value than work effort, but it still loses value. How would you expect a person to behave in this situation?

12. E. Harding
7. January 2016 at 18:11

@mbka

-I’d expect that person to emigrate, since his country is rapidly becoming a third-world one.

13. Scott Sumner
7. January 2016 at 18:33

Kevin, I’m a bit skeptical of the idea that monetary policy impacts the labor share of national income.

E. Harding, Employment rose rapidly during the 1970s, so the growth in per capita NGDP was less than the growth rate of NGDP. It’s the per capita figures that matter.

Bill, You are right about the yields on riskier assets, but that doesn’t really impact the zero lower bound argument.

Benoit, George Selgin has written some good stuff on that very point.

Derivs, Sorry, you lost me somewhere.

Doug, If I understand you correctly, this also works from the lender side. I agree.

mbka, I’d save to avoid starving to death when I got old, as real wages would be below Bangladeshi levels. I exaggerate, but you see my point.

14. ssumner
7. January 2016 at 18:39

Ossi, Do they care about absolute levels of consumption? Or consumption relative to their neighbors? The British government built a pension scheme based on the former assumption, and had to abandon it when the old folks revolted.

15. Major.Freedom
7. January 2016 at 18:40

“But let’s think about this in terms of a loan of work effort. At 18% NGDP growth, and no inflation, real GDP will double every 4 years, and increase 32-fold over 20 years.”

This point is an excellent illustration of how confused one can become by thinking like an NGDP guy.

If you assume 0% (price) inflation, then by posing various “NGDP” rates, 1%, 5%, 10%, 18%, you are merely posing various real growth rates.

In other words, if NGDP growth is 18%, then real growth is 18% because price inflation is 0%.

If real growth is 18%, and price inflation is 0%, then a nominal interest rate of 7.2% means that the real interest rate is 7.2% PLUS 18%, or 25.2%. It is not -10.8%. You are getting both interest and your money is increasing in purchasing power (purchasing power in terms of goods, not prices!).

Now, if you don’t lend, and sit on your cash, then with 0% price inflation your total real return is 18%. Your money will not grow, but you will be able to buy quadruple the goods in 29 years.

If you lend at 7.2%, then your total real return will result in your wealth growing at 25.2%. Your purchasing power will rise by 9.5 times after 10 years, and 90 times after 20 years.

This statement:

“Since the real interest rate is 7.2% (due to zero inflation) the money will double every 10 years, or quadruple over 20 years”

is just wrong. Your money does not double or quadruple because of the real rate. It doubles or quadruples because of the nominal rate. It is just that the nominal rate happens to also be the real rate, since price inflation is 0%, that it is correct to conclude the money doubles or quadruples.

With 0% price inflation, and 18% real growth, you can gain 18% by doing nothing, or you can gain 25.2% by lending at the nominal rate of 7.2%.

THAT is the meaningful choice. What THIS scenario shows is that NGDP doesn’t matter. It is real growth and price inflation that matter.

Summer’s logical mistep was caused by deftly switching from a nominal rate to the corresponding real rate, calculated depending fully on price inflation mind you. He barely realize this dependency, and immediately forgot about it. With 0% price inflation, it is easy to switch back and forth between nominal rates and real rates and pretend that you did not even incorporate price inflation in your analysis that claims price inflation doesn’t matter!

Imagine instead 0% NGDP growth. Suppose the nominal interest rate is still 7.2%.

What is the real rate of interest? OMG we don’t know! We don’t know this because we don’t know both the rate of price inflation, and the real growth rate. Here we cannot deftly switch from a 7.2% nominal rate to a 7.2% real rate without realizing it. We can’t start with a 7.2% and then ask how many times our money will grow after 10 years or 20 years in real terms.

But why is that? We have the nominal rate, of 7.2%, and we have the NGDP growth rate, of 0%. Shouldn’t this be sufficient for a NGDP guy? What does it mean to calculate 7.2% minus 0% = 7.2%, or 0% – 7.2% = -7.2%? What is the number on the right hand side of the equation?

Why can’t we form any conception of how richer we will be in 10 or 20 years, in real terms, using only nominal interest rates and NGDP?

Oh I know! It’s because there is no way we can deftly switch either 7.2% or 0% to real terms, that’s why!

Therefore, it is indeed prices (and production) that matter, not spending. Prices matter more than NGDP because it is prices that individuals set. Individuals do not set or transact in NGDP. NGDP is an outcome of pricing and production actions of all individuals.

Never reason from a spending change. EVER.

16. Major.Freedom
7. January 2016 at 18:42

20 years.

17. E. Harding
7. January 2016 at 19:38

Scott, I wasn’t looking at NGDP when I commented on those rising “real” interest rates, I was looking at Average Hourly Earnings of Production and Nonsupervisory Workers.

18. Ray Lopez
7. January 2016 at 20:12

Wow, this post by Sumner is so full of mistakes that I could spend pages on it. Suffice to say E. Harding, Derivs, and MF make excellent points. Sumner’s biggest fallacy is that, as implied by the other posters, he assumes there is just one “representative agent” and that person is a worker. In fact, ‘people’ (including corporations as fictitious persons, as mentioned by Doug M) lend for a variety of reasons, and not just because they are considering their future earnings as workers. Some of them may be risk adverse, some of them many not feel like working, some of them, being corporations, cannot ‘work’ at all.

Sumner further makes a classic fallacy of compound interest: he assumes the time period too long. In fact, as any student of environmental economics knows, if you set the time period more than 1 generation (e.g., say 200 years) the accounting becomes unmanageable since the tiniest perturbation in interest rate makes a big difference. Example: did the Manhattan American Indians get a good deal for selling the entire island of Manhattan for \$25 in trinkets from the Dutch? It depends on the interest rate they invested their \$24 in. In general however, paper loans tend to rot over time, hence real estate is a better preserver of wealth (as is gold).

The biggest problem however with Sumner is the one MF highlights: if you assume real interest rates as over 7%, the nominal rates don’t matter if inflation is zero. Essentially Sumner is implicitly saying money is neutral (inflation does not matter). Even I would not go that far: I say inflation matters, but only severe hyperinflation (that even Brazil in post-WWII did not experience; think Bolivia or Greece or Weimer Germany).

BTW when the commentators to a blog make better comments that the host, that’s a sign of senility by the host. Then again, we have to thank Sumner as a useful idiot for making talking points for us.

19. Don Geddis
7. January 2016 at 21:50

@Major.Freedom: “In other words, if NGDP growth is 18%, then real growth is 18% because price inflation is 0%.

Yes, that was obvious to everyone (else), in the construction of the original example.

No, that would mean deflation. You are assuming that the same number of nominal dollars buys more goods. But Sumner’s example explicitly stated 0% inflation, not deflation. Real GDP (and NGDP) is growing 18% annually … but the price level stays fixed, so the same number of nominal dollars buys the same real goods throughout all time.

Now, if you don’t lend, and sit on your cash, then with 0% price inflation your total real return is 18%.

You’ve completely misunderstood the hypothetical example. In the example, if you sit on your cash, your real return is 0%, not 18%. Big difference.

20. Kevin Erdmann
7. January 2016 at 22:12

Scott, I don’t know if I ever sent you this:

http://idiosyncraticwhisk.blogspot.com/2015/03/the-huge-potential-value-of-ngdp-level.html

It’s a post where I think through NGDPLT from a CAPM perspective.

In the simplest terms I would say that wages would rise for basically the same reason that fixed income yields rise during periods of stability. There isn’t as much of a premium earned for taking the cyclically risky (equity) position.

21. Derivs
8. January 2016 at 03:15

MF.. D. Geddis is 100% correct. The shelves would have a lot more products, but your purchasing power would be the same.

Doug M.
The mortgage guy trades 10 units of volume.
The corporate debt guy trades 10 units of volume.
So where fits in all this, the guy that sells the 1 yr forward Google 750-800 call spread for 20, sells the Google 750-800 put spread for 29.5, and then since he synthetically created a bond, his hedge needs to sell 3700 units of volume in bonds? Interesting that with 2 puts and 2 calls in an equity I can perfectly synthetically create a bond without ever having traded a bond. Almost no one knew to look for it but Voldermort and Co. has always done this specific trade in ginormous volumes, across all equities, in order to take very large synthetic bond positions prior to them actually stepping into the the bond market and showing their hand there. The inter-relationships that exist between and within products are mind boggling and almost always unfamiliar to even people that would consider themselves VERY sophisticated in the area of markets/finance. This is what the HFT/algos are all trying to search for and force back into EMH. (and FYI, before someone corrects me…I incorrectly call all paper, regardless of term, bonds).

Now again can someone please tell me, without NGDP futures, and without saying “see this is why we need NGDP futures”, how one would recommend to a friend how to capture NGDP growth?

Scott, break it down one piece at a time, and I will gladly explain piece by piece… We can create a whole new field. Financenomics! A world where all the pieces connect logically and properly. As they must.

22. Ossi Saresoja
8. January 2016 at 06:30

Scott, the example was about someone saving for retirement on his own. Indexed pensions are another matter. It might be that the example is not that relevant in practice.

23. Todd Ramsey
8. January 2016 at 06:40

Honest questions seeking understanding: Is today’s save/consume decision based upon a belief that the real interest rate equals the nominal rate minus EXPECTED inflation? If so, do these analyses still hold true?

I have never understood the idea that today’s real interest rate equals today’s nominal rate minus TODAY’S inflation rate. Isn’t today’s inflation rate unimportant, except as one input toward an estimate of future inflation?

24. Ray Lopez
8. January 2016 at 07:13

@Todd Ramsey – you’re new here. This group takes magical significance in the accounting identity NGDP = RGDP + inflation. They think–wrongly–that inflation somehow adds to RGDP, via “sticky prices / sticky wages” and “money illusion”. Hence to them, NGDP = RGDP (inflation) + inflation, meaning real GDP is a function of inflation. Bizarre little group of fanatics we have here, and trying to convince them they’re wrong is about as futile as preaching common sense to the Scientologists.

25. Brian Donohue
8. January 2016 at 07:19

Great thought experiment, Scott. Like Ossi, I’m inclined to think of an individual/ life cycle view of this. There is an arc to the “value of future labor” for an individual that doesn’t overlay neatly onto NGDP growth… it feels like there is some combination of this plus Friedman’s permanent income hypothesis that could be really interesting…or trivial.

Anyway, very thought-provoking.

26. Ray Lopez
8. January 2016 at 08:29

@Don Geddis, @ Derivs – you misread both Sumner and Major Freedom.

Geddis says: ” Real GDP (and NGDP) is growing 18% annually … but the price level stays fixed, so the same number of nominal dollars buys the same real goods throughout all time.” – lol! What a foolish statement to make! In fact, after 20 years you’ll be able to buy 32-fold more real goods, according to Sumner’s example. Don’t you know how to read?

PS–another fallacy in Sumner’s post is that price inflation and wage inflation are assumed to be very different from one another, when in the real world they are never so far apart.

27. Njnnja
8. January 2016 at 08:29

Very interesting way to look at things. I think that the key question is whether on the margin, do people have more choice about when and how much to consume than they do about when and how much to work?

Or put another way, when talking about choices that individuals can make, is it better to say that people are naturally short a periodic basket of variable consumption goods than to say that people are long a periodic and variable share of National Income/NGDP? If people are more flexible with respect to when to buy consumer goods, it would be more natural to compare how much of a basket of goods one can buy today, versus the (1+i)x of that same basket they can buy at time T.

However, if people have more choice between working today and earning a share of NGDP and lending that out to get (1+i) at time T versus working at time T and earning (1+deltaY), then basing a real interest rate on NGDP makes more sense.

In the short run, I think people have more choice with respect to consumption than they do income. Most salaried people could work more or less with no impact on their income. But even though people have lots of fixed costs, there are definitely things at the margin that people can do (reduce going out, entertainment, kids activities), and do do in emergencies, to cut consumption. So in the short run, I think people have more choice about consumption.

But in the long run I think it switches. People can take a second job to make more money, or cut to a part time schedule to make less. In the very long run, people can decide when to retire and leave the workforce altogether (or only partially). But people’s consumption ironically seems to be pretty fixed in the long run. Barring unforeseen events, people who are determined to have a certain lifestyle, in a certain city, are going to have little leeway in the level of their consumption, and how much the save is really just a matter of how much more money they make than this fixed basket of consumption costs. Which goes back to, in the long run, people care about real interest rates with respect to them working more or less.

I’m still not convinced that real interest rates should be calculated off NGDP than inflation, and it would be interesting to see some analysis on real interest rates calculated both ways and seeing which is more consistent with savers’ choices. But it’s interesting that in all my theory of interest, I’ve never seen anybody propose this as a model.

28. Ray Lopez
8. January 2016 at 08:35

@myself-ah, I misread it…so my bad. I don’t know how to read… But anyway my PS stands. And BTW in the real world it’s a rare industry where output increases 32-fold but you have zero inflation nor any deflation, but that’s another point.

29. Derivs
8. January 2016 at 10:10

Ray the illustration is in no way supposed to be indicative of any sort of reality, it is just a stress test on a concept.

Now how forward wages got into a question of… If I have \$1 today and I AM going to lend it, do I use inflation or NGDP as my determinant. Wages in 20 years are forward earnings. We are discussing where to put an extra dollar that today, is lying on the table.

As for no one taking a punt on what that NGDP capture investment is, or even agreeing or disagreeing with equities, I do not know what to say other than if you can’t answer that you shouldn’t be talking about comparing the 2 as you are comparing something (a bond) vs. nothing.

Now back to inflation and interest rates….

I have a fictitious item that is 100% perfectly correlated to inflation. We will call this item ‘Enzo’. And we will say Enzo is a completely non essential item so that we remove any convenience yield of holding it. (As in I would not try and arb my TV on a timespread as I would then have to live a year without TV).

So our nonessential ‘Enzo’ is currently worth \$1,000, and inflation is 5%. If interest rates are 6%. I would sell my Enzo today in Jan ’16 and receive a credit of \$1,000 for this, I would then buy 1 yr paper which would debit me 1,000 in January ’16 and provide me a credit in Jan ’17 of \$1,060. Since inflation was 5%, the Enzo would now be worth \$1,050 so I would buy the Enzo for \$1,050 and have a credit remaining of \$10. I WIN!
If interest rates were 4%, I would hold my Enzo, knowing that if I sold it to buy 1yr paper, in 1 yr I would only have \$1,040 while the Enzo is now worth \$1,050. I LOSE!!! It was better for me to have held the Enzo and therefore………. I would refuse to transact at interest rates below inflation, and it would be beneficial for me to transact at interest rates above inflation.

30. BC
8. January 2016 at 15:34

“Instead of lending the money out, why not just work an hour less today and 8 minutes more in the future?”

Interesting perspective, but I don’t think it’s quite right. The opportunity cost of lending money is that one gives up consumption now. Lending money does not require that one give up the opportunity to work 8 minutes more in the future. One could still do so and get even more consumption.

Having said that, I think i minus inflation and i minus NGDP both should matter. In Scott’s example, i, inflation, and NGDP growth are all known. Inflation=0 for simplicity so that there is no difference between real and nominal interest rates and real and nominal income growth. Given known future prices and wages, a person can decide his future path of working hours and consumption subject to constraint that present value of lifetime income must equal or exceed present value of future consumption. Then, he can just borrow or lend (save) to match his income cash flow stream to his desired consumption stream. Holding income (NGDP) fixed, a higher interest rate makes future consumption cheaper relative to current consumption, so he will consume more in the future relative to present, i.e., higher interest rate minus inflation leads to more savings.

On the other hand, suppose we hold interest rates, lifetime income, and path of consumption fixed and raise NGDP growth. The effect of raising NGDP growth while holding lifetime income fixed is to push more of the person’s lifetime earnings into the future relative to now. Because consumption path is fixed, the person will need to borrow more or save less to match his income stream to his preferred consumption stream. Thus, higher NGDP growth or lower interest rate minus NGDP growth leads to less savings, same as for interest rate minus inflation.

The point here is that with borrowing and lending, one needs only match one’s *lifetime* income with *lifetime* consumption; the timing of the two don’t need to match. Interest rates determine the relative price of current vs. future consumption and, hence, affect one’s preferred consumption path. NGDP growth affects the timing of one’s income and, hence, affects the saving or borrowing needed to handle mismatches between income and consumption timing.

31. ssumner
8. January 2016 at 17:30

E. Harding, Sorry I misread that comment. I don’t know why that version of real rates was so high. Perhaps taxes played a role. The after tax real rate was far lower.

Ray, You said:

“BTW when the commentators to a blog make better comments that the host, that’s a sign of senility by the host.”

Don’t you have that backwards? Wouldn’t the commenters be senile in that case?

Kevin, I’m not saying your theory is wrong, I just wonder how important it is in terms of changes in labor’s share.

Todd, You’d want to use the expected future inflation rate.

Brian, Yes, I agree. It’s clearly incomplete, and other factors certainly play a role.

njnnja, I see my role as spurring others to create such models. So far I’m still waiting for good NGDP targeting models.

BC, Just to be clear, I was suggesting there are several trade-offs that are possible, those involving shifts in consumption but not work effort, or those involving shifts in work effort but not consumption.

32. Ray Lopez
8. January 2016 at 19:02

@Derivs, thanks, I think your point about “it would be beneficial for me to transact at interest rates above inflation” is sound. I think however Sumner’s point assumes that GDP is a large function of labor. That may have been true 75 years ago, but less true today I would say (Star Trek economy: machines do all the work).

33. BC
8. January 2016 at 20:05

I think I misstated the first part of my example, looking at the effect of higher i minus inflation. NGDP should be raised by the same amount as i to keep i minus NGDP constant, not NGDP constant as I originally stated. Since i-NGDP is constant, the present value of future income for a given work path remains unchanged. (Increase in future wages is offset by larger discount rate i.) Higher i-inflation though makes future consumption cheaper relative to current consumption so the conclusion is the same: both higher i-inflation keeping i-NGDP fixed and higher i-NGDP keeping i-inflation fixed increase savings.

34. BC
8. January 2016 at 20:20

Sorry, I still didn’t get the higher i-inflation, fixed i-NGDP, case quite right. The higher i-inflation leads one to favor more consumption in the future over current consumption. However, since NGDP is higher (to keep i-NGDP fixed), one will also have higher wages in the future, so it’s ambiguous as to whether one will need to *save* to support that higher future consumption. Maybe, Scott is right: higher i-NGDP unambiguously increases savings but higher i-inflation is ambiguous.

35. Major.Freedom
8. January 2016 at 23:04

Don Geddis

“No, that would mean deflation. You are assuming that the same number of nominal dollars buys more goods. But Sumner’s example explicitly stated 0% inflation, not deflation. Real GDP (and NGDP) is growing 18% annually … but the price level stays fixed, so the same number of nominal dollars buys the same real goods throughout all time.”

That is true, I misspoke. I was referring to the growth in purchasing power from lending, which means your cash balance is increasing. When I said “your cash” is not increasing, I should have said the aggregate money supply is not increasing. Society has no more dollars, but purchasing power is increasing, which yes, is about falling prices here.

If price inflation were 0%, and real growth was 18%, then the money supply and volume of spending must be increasing.

“Now, if you don’t lend, and sit on your cash, then with 0% price inflation your total real return is 18%.”

“You’ve completely misunderstood the hypothetical example. In the example, if you sit on your cash, your real return is 0%, not 18%. Big difference.”

No that is wrong. If you sit on your cash, and real growth is 18%, then your purchasing power is increasing, provided that prices are falling.

With 0% price inflation, total cash balances would be increasing with 18% real growth.

At the end of the day, we cannot infer from NGDP and nominal interest rates a real rate. They are incomplete. That is the key point you don’t seem to get. We need price inflation/deflation as a concept. Sumner used it in his own allegedly price inflation free example when he switched nominal rates to real rates due to the numbers being identical wih 0% price inflation.

36. Clayton
9. January 2016 at 07:33

BC hit on my cursory objections, but let me go in a different direction — what circumstances allow an 18% RGDP growth and only a 7% interest rate? I think this is where your example falls apart.

With a flat population, what are the sources of RGDP growth?

1) Capital accumulation (human or physical)
2) Technical change

First, let’s assume no technical change…

We’ve created a situation where RGDP growth encourages people to time-shift labor into the future. However, we’re using a representative agent so there’s no lending between agents. The only way an individual can work tomorrow and consume today is to reduce investment. But that reduction in investment **increases** interest rates and **reduced** RGDP growth.

I’m a little rusty, but I’m pretty sure a 7% interest rate means that the marginal investment produces a 7% risk-adjusted return. So the interest rate indicates that the representative agent is willing to pass on \$100 in consumption to make an investment that gives him \$107 in the next time period. This is a horrible way to increase current consumption. Does this match your intuition about the representative agent?

It would follow that the *only* way this happens is an agent that prefers a consumption path HEAVILY OVER-WEIGHTED into the future. In theory, this preference could/should exist for someone like a professional athlete. Even if they get 18% RGDP growth throughout their career, they must save since they’re forced to “retire” long before they die.

In a real economy, however, your example — high NGDP and low interest rates — just isn’t realistic.

===

I don’t think the addition of technology makes any difference. Technology is also the product of investment. The marginal investment in technology is only producing a 7% return or the interest rate would be higher. Thus it behaves exactly like capital.

===

I’m probably missing some subtleties, but long story short is:

– The gap between RGDP growth and real interest rates is — at least largely — *determined* by an individual’s preferred consumption path.
– The level of that consumption is determined by the supply of investment products (including technology) since these opportunities increase the clearing level of RGDP growth.

Since both are adjusted by the same inflation rate, all of this can also be said of NGDP and N-interest rates… but I don’t see how the N- helps us. Interest rate estimates can be horrible and the relevant gap (GDP vs interest rates) is unaffected.

37. ssumner
9. January 2016 at 16:53

Clayton, You said:

“BC hit on my cursory objections, but let me go in a different direction — what circumstances allow an 18% RGDP growth and only a 7% interest rate? I think this is where your example falls apart.”

I think you missed my point. It was just a thought experiment to think about which one is more important. In the real world there gap would probably be much smaller. The large gap would discourage saving and encourage borrowing, which would put upward pressure on interest rates.

38. Derivs
11. January 2016 at 04:27

“I think your point about “it would be beneficial for me to transact at interest rates above inflation” is sound.”

I was trying to be completely serious for one thread. It’s more than sound. It’s absolutely 100% correct.

It’s what I liked about the ridiculousness of the example, with all the logical components being so far apart. I can arb everything right to where it should be and illustrate how int connects to inflation. No theory, no behavior, simply EMH doing its thing.

If one were to bid interest rates towards to 15% based on NGDP growth of 18% with 0% inflation, everything not nailed down would be sold for cash, that cash would be invested at 15%, and then when the paper retired, considering the price of everything is the same, you would buy 1.15 times what you had before, the NGDP guy with his undefined investment that captures NGDP (a proposed free call nonetheless) would get his 3% on the investment he refuses to explain, and MF would be relatively correct as he would be getting a 15% gain in purchasing power. The market would keep doing this until the 2 merged. AS IT DOES ALREADY!!! simple. Taylor rule makes complete sense. Interest rate and inflation MUST be connected.

“The large gap would discourage saving and encourage borrowing”

Why would I borrow at near 18% to buy any asset that I know will be the same price at the time my paper expires? I buy a house for 1 million, pay 1 million in carrying costs over the next 5 years, to have a house still worth a million… No thanks!
But in the same respect, with a big smile on my face, I’d lend a million, wait 5 years, and have a house for free and my original 1 million left over that still buys me what a million did 5 years ago… it’s a WIN WIN WIN!!!

39. ssumner
11. January 2016 at 08:02

Derivs, How does any of that relate to my post?