A very simple macro model of the last few years

Here is a very simple model of interest rates, debt, asset prices, and recession. It seems to fit the facts of the last few years reasonably well.

There are two types of people: the A's and the B's. The A's have normal interest-elastic savings and investment functions. They save less and invest more if the (real) rate of interest falls. The B's have perfectly interest-inelastic savings and investment functions. The rate of interest has no effect on their savings and investment decisions. The A's also have normal wealth-elastic savings functions. They save more if their wealth declines, because of increasing debt for example. The B's have perfectly wealth-inelastic savings functions. Their wealth does not affect their desired level of savings.

In the beginning, the A's have savings equal investment, and the B's have savings equal investment. So total savings equal total investment and the economy is in equilibrium. Also, the A's are not borrowing from the B's, and the B's are not borrowing from the A's, so the stock of debt stays fixed (at zero).

Then the B's decide to save more of their income. Total desired savings now exceeds desired investment, so the central bank cuts the interest rate to prevent a recession. The A's respond to the lower interest rate by saving less and investing more, so total savings equals total investment at the new rate of interest.

The economy is once again in equilibrium, since total savings equals total investment. But the A's savings are less than their investment, and the B's savings are more than their investment. So the A's are borrowing from the B's. So the stock of debt (that the A's owe to the B's) is growing over time.

The stock of debt represents an asset to the B's and a liability to the A's. With their liability growing over time, the A's desired savings would be growing over time. (They want to reduce their consumption to prevent their debt rising any further). But that would mean that total savings would be growing while total investment stays the same, which would cause a recession. So the central bank slowly lowers the rate of interest over time, encouraging the A's to save less and invest more, so that total savings stays equal to total investment. But the stock of debt (that the A's owe the B's) continues to grow over time.

The central bank needs to continue to lower the rate of interest over time, so that the falling rate of interest is just sufficient to encourage investment and discourage savings and offset the effect of the rising level of debt on the A's savings.

As the rate of interest slowly falls over time, the price of assets rises over time. In the limit, as the rate of interest approaches zero, the fundamental value of very long-lived assets, like houses, stocks, and natural resources, approaches infinity.

But eventually the central bank will be unable to cut the real rate of interest any further, because the nominal rate will hit zero. So the central bank will be unable to prevent a recession. Savings will eventually exceed investment, and so recession is inevitable.

A recession will reduce the flow of income from assets, and lower the fundamental value of assets. When people realise that a recession is inevitable, asset prices fall. The fall in asset prices causes an increase in savings by the A's, and precipitates the recession, which was inevitable anyway.

If there is just one person in the world who is determined to save (and not invest) part of his income forever, regardless of the rate of interest, and regardless of how much he is owed by the rest of the world, then an eventual recession is inevitable. But any single individual, even one with a very high income, would die long before the recession he caused. The B's must have a big enough share of world income for this model to play out over a decade or two.

Who are the B's? The government and central bank of China are one example. But is China alone big enough?

Update: I found this on Brad Setser's blog: "China’s government provided — best that I can tell — close to $500 billion of financing to the US in 2008." That's new financing, a flow of loans, not a stock. That's around 4% of US GDP. That is very big. Maybe China alone is big enough?

Comments

[Mercure]

According to this model, the only ways to get out of this vicious circle are:

1) the recession is so bad that B will no longer save, and maybe begin to invest more. Then there's a new equilibrum.

2) In the long term, use, decay and obsolescence of capital and durable goods make people want to spend and invest more. See:
http://krugman.blogs.nytimes.com/2009/02/17/slumps-and-spontaneous-remission-wonkish/#more-1423

3)When the interest rate hit the zero lower bound, one way to avoid the recession is that the government "A" start to borrow and spend/invest. When the debt of government "A" becomes too big, the government stops to play the game and we have a recession big enought to get 1) and/or long enough to get 2)

It's scary.

The only optimistic scenario is that the government is able and willing to keeps making deficit until 2) begin and then the government gradually lower the stimulus as 2) pick-up the slack. As the stimulus will not be big enough to completely avoid the recession, we will have a bit of 1) too.

[Nick Rowe]

Thanks Mercure. You clearly understand the model. Which pleases me, because it means I explained it OK.

I hadn't thought much about the exit strategy, or policy implications, as you have. I think your 3. is what is happening now, but my hope is that 1. is also happening. I don't know enough about China to say for sure. But 1. is the only permanent way out (2 only gives a temporary boost to investment). Or maybe:
4) higher target inflation, so real interest rates can continue to fall further and further below zero.

[Alex Plante]

What happens when A defaults on their debt to B?

[Nick Rowe]

Hmmm. Dunno. If we assume this does not affect expectations of future default (not a good assumption) then the model just rewinds a few years, to when the debt was lower, and then starts running forward again.

If we assume that one default increases the expectation of future default, then...dunno. I will have to try to think about it.

[calmo]

I feel compelled to shower Nick with Nobels whenever he disarms us with "dunno"...how do people maintain composure with this...teacher?
Nick, you said it was a simple and reasonable model:

It seems to fit the facts of the last few years reasonably well.

There are two types of people: the A's and the B's.

God if only I could turn the clock back a few decades and B smart or even in equilibrium part time...even partially "elastic" --I could pray for that.

I know you are wanting to say something about "investing" and "saving", in the Pure...making Recessions necessary. [Some (ok it is BDL) have a fondness for some philosphers (Hume, not typically cited in Economics, yes?) and this [A & B -> Recession] reminds me of synthetic a priori propostions associated with that sock-suspender Kant...enlightening us about each component and the "->" not so much, but intended to light what remains between our ears (fuzzy notions about investing, saving and deterioration cycles ending in recessions)...pretty much guaranteed to heat what remains there as we debate the nays and yays of that connection, ->.]
Robert D Feinman (rdf), a frequent and serious! (not like some) commenter at Economisty, has been especially bothered by this distinction (A vs B). I B but a small flickering candle compared to his furnace on "investing". I remain somewhat distracted that you should light on this distinction as characterizing this recession, but rdf might B facinated...possibly helpful...gloriously scientific...I don't know how he puts up with me.
From where I sit, the essential character is not the investing vs saving (but I am mullin it over), but the fraud perpetrated by low wages...making it necessary to "invest" in houses, rather than rent like the poor folk who would never be able to save enough.

[Declan]

You're almost there Nick, now just forget about China (this process has been at work far longer than China has been a factor) and consider that 'B' is for Bank.

The rate of interest indeed does not matter to the bank because they make money on the spread (unless the rate gets too close to zero of course). And their supply of loanable funds is not constrained by low interest rates because they can just print (credit) the money they want to lend. Similarly their wealth level does not affect their desire to lend out more money.

[kharris]

Declan,

Banks lend other people's money, so we still have to figure out who the B's are. If China is the B, then banks are lending China's money, which is in fact the case.

Mercure,

I think China has announced a bit domestic welfare and investment effort this week, on top of earlier plans. So we may be seeing your case 1 getting underway.

[kharris]

"Big" not "bit". Ugh.

[Raging Ranter]

Hey Calmo, can you repeat that in Enlgish? Thanks.

[Nick Rowe]

Curses! I thought I had posted a comment, and now it's not here. Maybe I forgot to click "post"?

Trying to remember what I said..

calmo: I like David Hume, both his philosophy and his economics (he wrote a few short very good economics essays). Most economists think highly of Hume, at least his economics.

Declan: what kharris said. Let me restate it my way: commercial banks are owned by people, their shareholders. If commercial banks save a large part of their income, then their shares become more valuable. If the shareholders are A's, their spending and saving will adjust to the value of those bank shares, so it's as if the banks were A's.

I was also reading Brad Setser's blog on how big a fiscal stimulus China was planning, to see whether Mercure's 1.) was coming true. But they don't seem to think they have a good estimate yet.

[Mark]

Yes, China's holdings of US debt have increased at quick pace, but until recently Japan was the largest holder of US debt as this document from the US Treasury Department clearly indicates http://www.treas.gov/tic/mfh.txt Based on an article I read this morning, Japan may be poised to buy up more US debt http://www.telegraph.co.uk/finance/financetopics/financialcrisis/4782755/Hillary-Clinton-pleads-with-China-to-buy-US-Treasuries-as-Japan-looks-on.html

There is something about the model I don't understand. With interest rates at zero percent, and an increasing money supply with expansionary fiscal policy isn't an increae in inflation inevitable if the Federal Reserve doesn't raise interest rates? If so, shouldn't China and Japan be afraid of US just inflating their debt away? Are they simply placing their trust in the US government to not pull a fast one on them?

[Nick Rowe]

Mark: yes, I think perhaps Japan's savings play a role. But if they are mostly private savings, the interest rate ought to affect their savings. Of course, the model is oversimplified, with just 2 types of people.

The model is almost a real (non-monetary) model. I say "almost", because you don't get the zero nominal bound without money; and you can't have a standard recession in a barter economy (in a barter economy, aggregate supply IS aggregate demand). So the inflation rate doesn't really matter (except for how the zero nominal interest rate bound translates into a real rate of interest).

We certainly _hope_ the increasing money supply plus expansionary fiscal policy has an inflationary impact, to offset the deflationary forces of the recession. And I _hope_ that China and Japan become afraid of inflation. The proximate cause of the crisis is that everyone wants to hold USS cash and bonds, and doesn't want to buy anything else. If we can get everyone scared of inflation, they will have to start buying real assets and real goods, which is just what we want.

Put it another way: It would be good for the US, and the world, if Hillary fails. I just can't understand why she's doing that.

Hmmm. I feel another blog post welling up.

[reason]

OK,
I see a couple of flaws.
1. When A borrows from B he does so to invest. No? So surely he is gaining an asset as well as liability so the direction of the change in his net wealth is uncertain.
2. The interest rate effects are dependent of real interest rates, but the liquity trap on nominal interest rates. So why isn't inflation a solution?

[pointbite]

But with fractional reserve banking, the debts (investments?) are much larger than the savings. So if I understood your model, bailouts require money printing. China isn't big enough, nobody is big enough -- right now, China can just get away with printing more money.

[pointbite]

I like this blog you make me think... I guess everybody's debt is somebody's asset, so if the investment drops in value and the principal on the debt stays the same, it's actually the exact opposite of my previous comment, the assets become larger than the debts... however, if the debtor subsequently defaults or the lender is forced to write down some of those assets, then everyone loses except the people who never lend and never borrow.... which I guess you would call the savers, unless their money is in a bank that goes bankrupt.

Time to stock up on supplies and precious metals?

[reason]

Pointbite
No savings always equal investment, it is an identity. Savings is just that part of income that isn't consumed and (ignoring for the moment the foreign and government sectors) realising that one mans expense is anothers income : income = consumption + investment.

[reason]

Pointbite
debt doesn't change that, even when it creates more money. It either encourages more to be produced or creates inflation.

[pointbite]

reason,
I don't understand your comment, debt changes everything. If the supply of money is stable or growing slowly, asset prices generally can't rise faster than interest forever, if prices somewhere are rising prices elsewhere must be dropping (there is only so much demand to go around). But as Marc Faber says, for the first time in the history of capitalism during this past decade the Federal Reserve managed to create a bubble in everything. That's debt at work.

[Declan]

So I write, "And their [the banks] supply of loanable funds is not
constrained by low interest rates because they can just print (credit) the
money they want to lend."

and the response is "Banks lend other people's money"

Am I not typing in English? :)

The banks don't lend other people's money, they create other people's money
by lending, that is the whole point. Where do you think all the (credit)
money comes from? Sure they need (a little) capital, but the capital is tiny compared to the lending.

Nick, I agree with you about the behaviour of the shareholders of the
banks, but the shareholders are not the bank. Banks don't stop lending
because they are successful at it (they should, but they don't).

[reason]

pointbite
First I never said the debt phenomenon is not important - it is crucial, it is just that we shouldn't confuse the financial economy (the score keeping) with the real economy (the actual ability to produce things and distribute them). A disfunction in the financial economy doesn't necessarily mean that that the real economy is disfunctional (although it may be eventually distorted).
As for asset prices, I agree that excessive debt creation has fueled the bubbles but it is not necessarily true that you need a lot of debt to blow up asset prices. Asset prices can change a lot on relatively low turnover.