Why I=S is a bad place to start doing macro, again

I was reading Philip Cross's article "The Limits of Economic 'Stimulus': How monetary and fiscal policy have sown the seeds of the next crisis". I came to this bit in the Executive Summary:

"Low interest rates also depress savings and therefore investment."

It is clear from the context that he is talking about the Bank of Canada setting low rates.

Most macroeconomists will freak out when they read that sentence. I freaked out too, initially. But let me try something that might be more constructive. Let me tell you about a world where what Philip Cross said is precisely correct.

Just to clear the decks of everything that is not essential to this argument, let us assume a closed economy (no exports and imports), and assume that "saving" and "investment" mean "national saving" and "national investment" (i.e. we make no distinction between private vs government saving and investment). [Or just ignore government spending and taxes if you can't get your head around that.]

National Income Accounting identities then tell us:

C + S = Y = C + I, and therefore S=I

Actual saving and actual investment are just two different ways of looking at the same thing. So if something did cause actual saving to fall, then that same thing must indeed cause actual investment to fall too.

Now suppose that output (Y) is supply-constrained. Firms are already selling as much output as they want to sell, at existing prices. There is a queue of buyers trying to buy more output, but firms don't want to sell them any more, and since exchange is voluntary, the Short Side Rule tells us that Y = min{Yd,Ys}, so if Yd > Ys then Y = Ys.

And further suppose that customers wanting to buy consumer goods are always at the front of the line, and customers wanting to buy investment goods are always at the back of the line. Production of consumer goods takes priority in the allocation of scarce resources, and production of investment goods takes whatever is left over. So C = Cd, but I < Id.

What Philip Cross said makes perfect sense in that world. If the Bank of Canada cuts interest rates, and that causes desired saving to fall, and so desired consumption to rise, then actual investment must fall too, even if desired investment rises.

But if the world did look like that, with firms facing a queue of customers wanting to buy more goods than firms wanted to sell, each firm would have an incentive to raise its price relative to the amount it expects other firms to raise their prices. Actual inflation would exceed expected inflation, and would soon rise above the Bank of Canada's 2% target. So the Bank of Canada would be setting interest rates too low, even if judged by its own standards of doing what's right.

And that does not seem to be happening. Instead, the exact opposite seems to be happening. Canadian inflation has averaged below the Bank's 2% target since the recession. (Though it depends a bit on which measure of inflation you use.)

Plus, anecdotes where buyers of goods are rationed, and unable to buy as much as they want to buy at announced prices, seem to be rare. Everything I see or hear or read tells me that sellers are hungrier to sell more goods than buyers are hungrier to buy more goods. (That seems to be the normal case, in market economies without price controls, and is probably due to monopolistic competition, and you sure notice the difference when you spend time in Cuba.)

So I think Philip Cross is wrong, because the only sort of world that I can think of where he would be right is very different from Canada since the recession. His proposed cure would make things worse, because lower demand for consumer goods would likely lower the demand for the investment goods needed to produce those consumer goods.

That said though, the fact that there have been no fundamental changes to the monetary policy framework since the 2009 recession (either in Canada or other advanced economies) leads me to despair. Things are not good. Things might get worse, and the existing monetary policy framework is inadequate to deal with the things that might get worse. Mr Micawber's monetary policy tactics are not good enough.

But to improve the monetary policy framework, we must first think clearly about how monetary policy works. And seeing monetary policy as interest rate policy, and thinking about how it affects I=S, is a very bad place to start.

And when Philip Cross says that interest rates affect only the timing of demand, and not the average level of demand over time, he does have a point. And the New Keynesian models that ignore that point get around it by just assuming, without any valid justification, that the economy eventually returns to full employment.

God it's a mess.

Comments

[Market Fiscalist]

If the CB said something like "we're going to target interest rates of 5% and we're going to keep increasing the money supply until we hit that target", then I can imagine that this would indeed boost both S and I relative to now.

This would not be an optimal policy as if 5% was not the optimal level for interest rates then we may get inflation higher or lower than its optimal level, but it would probably be better that what we have now.

[JKH]

“And that does not seem to be happening. Instead, the exact opposite seems to be happening”

What about – that at some (zero bound related inflection) point, low interest rates by reducing the return on the stock of outstanding savings may cause people to save more rather than less (other things equal)?

[Too Much Fed]

Nick, is there any way to reopen the comments to:

http://worthwhile.typepad.com/worthwhile_canadian_initi/2016/11/my-cunning-plan-to-reform-new-keynesian-macro.html

Thanks!

[Nick Rowe]

MF: that policy would work. Trouble is, when the Bank of Canada hears "target 5% interest rate" (i.e. higher than current interest rate) it interprets that to mean *cut* the money supply until interest rates rise to 5%.

JKH: I decided not to go there, since Philip Cross was saying that lower interest rates would lower saving. I think you would need some sort of OLG model, with just the right distribution effects, to get your result, and then it would also depend on investment's response.

TMF: There's 324 comments on that month-old post, and I think the discussion has wandered quite a bit from NK macro models. I can't keep watching it.

[Benoit Essiambre]

Also in a society that is trying to smooth out consumption over an upcoming period where it will be more difficult to produce (maybe less labor will be available, maybe less resources), would lower rates really depress desired total savings?

In other words, does a community of squirrels facing a wet winter that will spoil a greater proportion of their cache than usual build a bigger nut cache to make sure to be able to survive the winter despite the larger loss or a smaller one because they don't want to put too much resources into something with a high rate of loss?

[Henry]

Cross' argument seems perverse. His is worried about the next recession and economic management authorities' abilities to deal with it, because, he argues, fiscal and monetary policy are being over used. He presumably wants fiscal and monetary policy to be wound back. So we should bring on the next recession earlier than it might occur so as to avoid the next recession later on?

He also talks about Japan's 15 fiscal stimulus packages, arguing they have failed. David Andolfatto argues that Japan's fiscal policy has been inadequate and focused on mitigating Japanese public debt and borders on "austerity":

http://andolfatto.blogspot.com.au/2016/11/the-failure-to-inflate-japan.html

And arguably, austerity has been practiced around the globe. I would argue that fiscal policy has been largely underutilized. Rather than back off the fiscal accelerator (or perhaps applying more fiscal brake), we should work fiscal policy harder.

[Henry]

http://andolfatto.blogspot.com.au/2016/11/the-failure-to-inflate-japan.html

Who would have thought this from David Andolfatto- I had to check I wasn't reading Paul Krugman's blog!

:-)

[Henry]

It's monetary policy that's been an abject failure.

[Majromax]

In the meantime, David Dodge argues for higher interest rates via coordinated global action combined with higher levels of deficit spending.

At least this one has some backing from classical economics, since it's compatible with shifting savings from the government sector to the private sector. It also works from a classical crowding-out argument: nominal rates can go up if the real rate increases from crowding out. On the other hand, governments don't have much patience for being policy-followers, and the possibility of an unlimited deficit commitment must be disconcerting.

[Majromax]

@Benoit:

> Also in a society that is trying to smooth out consumption over an upcoming period where it will be more difficult to produce (maybe less labor will be available, maybe less resources), would lower rates really depress desired total savings?

If we anticipate that society, then the best investment vehicle might be warehouses full of Twinkies. Individuals, faced with a real future consumption target (even if their own discount rate is zero or negative!) will find building a Twinkie warehouse attractive over a financial instrument if the latter's rate is negative enough.

Remember that for conventional monetary policy to be ineffective, we need lower rates to increase the demand for money, not real goods.

If I thought that half of my wallet would vaporize overnight, no circumstances would convince me to put more money in it rather than invest in canned goods.

[Benoit Essiambre]

Majromax, right. In the National Income Accounting identities, (I) is things like Twinkie stockpiles, not financial instruments (the later net to zero on the aggregate).

[Ralph Musgrave]

"Low interest rates also depress savings and therefore investment." Er…banks don’t need to attract savings in order to lend: they create money out of thin air and lend it.

[Ralph Musgrave]

On second thoughts, my above "thin air" point isn't too clever. Apologies. Must try to remember to think before I speak.

[Nick Rowe]

On the squirrels and stuff: words don't cut it. Draw an Irving Fisher diagram, like the second picture in my old post here, then swivel the budget line around the point where the PPF and Indifference curve kiss. With a representative squirrel, you get regular results. You need OLG squirrels, or some sort of distribution effect.

[rsj]

I'm with JKH here. I can very easily see a situation in which lower rates drives up savings demands, and I don't think you need OLG to do it. It's enough to not take the euler consumption equation so seriously, and I don't think it deserves to be taken seriously. But even if you do take it seriously, there are buffer stock savings models due to, say, credit constraints, that lead people to target a fixed level of precautionary savings that increases as rates fall.

[rsj]

Suppose, for example, that we take some radical view such as people saving for their retirement. They will retire and need to be able to pay for, say, 20 years of living without working. In a low rate environment, they will need to save more while they work.

Take another radical example, such as needing to save for a house. As rates fall, house prices go up, but you need a downpayment of 10% of the price of the house, so the downpayment amount increases as rates fall, so people have to save up more for the downpayment and they need to save more because of lower rates.

To take a third radical example, suppose people need to save for college tuition for their kids. As rates fall, they need to save more in order to afford the same tuition.

I think the null hypothesis has to be that to the degree that people are credit constrained and so need some kind of savings up front in order to make a purchase, lower rates mean higher savings demands. Retirement is the obvious example of needing the money up front, but there are other examples as well.

[Nick Rowe]

rsj: the retirement savings motive is part of an OLG model.
But you could be right on the precautionary savings stock.

[rsj]

Yes, but you don't to get an OLG model to be "just right". You just need to not allow people to borrow for their retirement. Since people can't pay back after death, the crucial issue is any model with a finite life, not a special kind of OLG model per se. I prefer to think of this as a credit constraint.

[Majromax]

@rsj:
> I think the null hypothesis has to be that to the degree that people are credit constrained and so need some kind of savings up front in order to make a purchase, lower rates mean higher savings demands.

The effect there is marginal at best. Assume that people can hold savings in either cash or one-year GICs. With a cash-in-advance constraint, individuals have to weigh the risk of insufficient liquidity against the foregone gains of interest. As the interest rate falls, the portion of desired savings in cash rises because the opportunity cost is lower.

In the meantime, however, we have to look at every agent that isn't credit-constrained – and there have to be some of these agents in order to make any credit model work. These agents can borrow nominal funds at the nominal rate and invest in real goods at a presumed real rate, and as the nominal rate falls they have every incentive to take on more debt and increase investment.

@rsj:

> Yes, but you don't to get an OLG model to be "just right". You just need to not allow people to borrow for their retirement.

You're looking at the wrong rate here. People want to consume less in the present period and save more (via investment) for future periods because of a low real rate, in terms of the actual marginal return of building a new factory or warehousing Twinkies.

This is not a story about money or liquidity, so no central bank rate-setting can affect it. People don't need liquidity to save for retirement, they need real return.

[rsj]

@Majormax,

You are assuming that there is no income risk. But that is incoherent: credit constraints exist because of income risk -- you may go one period without any income, which is why banks wont lend to you. If you can go a period without income, the disutility is very high, so regardless of the interest rate, you will want to save 1 period worth of income. Cash in advance is not a model of credit constraints. You have to add the possibility of earning zero income in some periods to justify having credit constraints and to motivate people to care. Otherwise it's just a mathematical fiat to add some characteristic to the model but has no micro foundations.

If people have income risk, which is the same as saying if people are credit constrained, then they will hold a buffer stock of savings regardless of the interest rate. That target is determined by how many periods they will go without income and is not determined by the rate. The amount you have to save each period to achieve that target buffer is determined by the rate. But we know that people end their lives by retiring in which they receive very little income. This is a large, known quantity. so there is a huge demand for retirement savings regardless of the interest rate. This is not negligible! It's dominates all discussions of household savings. The demand for downpayments is also significant, as is having a cushion for unexpected expenses and unemployment. The above are the main reasons why people save. If you remove retirement, major purchases, and unexpected expenses, then you are left with your cash-in-advance model in which there is some little trade off between holding money for 1 period and earning interest. That is a bad model, as the trade off is living in your car as you lose your home when your company lays you off and you may spend a year looking for new work versus keeping your home.

So if households are striving to save 10-20 periods of income by the time they retire, and 1 periods of income before they buy a house, and another 1-2 period of income at all times in case they lose their job or encounter an unexpected expense, then that creates a huge demand for buffer stock savings that completely dominates all other savings considerations for the vast majority of households. When interest rates are low, although the target buffer stock doesn't change, the amount they have to save each period goes up a lot.

In terms of people who are not credit constrained, there are very few such people, given our unequal distribution of wealth. Most people worry about money and about how they will retire or pay for their retirement and for housing/college.

The financial system does very little unsecured lending to households. Almost all household lending is secured with collateral.

In terms of real/nominal, I'm not sure why you thought I was talking about nominal rates or how this affects the argument at all.

[Majromax]

@rsj:

> In terms of real/nominal, I'm not sure why you thought I was talking about nominal rates or how this affects the argument at all.

Because the original basis for discussion here is how the Bank of Canada sets interest rates. I think we all agree that the central bank cannot affect the supply-side, such that the spectrum of investment opportunities is left unchanged regardless of the bank rate.

I agree with you that low real interest rates can cause an increase in real savings demand from individuals via the income effect (but are retirement savings really a Giffen good as you argue?), but I don't see where the central bank rate (and hence Phillip Cross's statement) comes into play. In particular, if the Bank of Canada exogenously raised the rate, I would expect consumers would shift more of their income towards financial savings while firms (facing a higher cost of capital) would scale back their investment plans. The long-term real rate would not increase, and we would not escape from your proposed cycle of excess savings.