Theory does not say that equilibrium interest rates cannot be below growth rates (Part 1)

First I need to tell you why I am writing this post.

I got two emails from Canadian economists saying they agreed with my post against "normalising" interest rates.

The first email was from an academic macroeconomist. He asked me if I thought that calls for normalisation from bank economists were motivated by bank profitability. I said I didn't know, but that if the Bank of Canada raised the actual interest rate r above the equilibrium natural rate of interest r* this would probably be bad for bank profitability in the long run. Because the Bank of Canada would eventually need to cut r below r* to prevent inflation falling below the 2% target. Plus it would likely cause r* to fall, relative to counterfactual, because it would reduce confidence that future aggregate demand would be strong enough to make current investment profitable. But if something caused r* to rise, and the Bank of Canada responded by raising r to keep inflation from rising above the 2% target, this might be good for bank profitability, and those hoping for normalisation needed to distinguish the two cases. (But even here it is not obvious to me what the effect on bank profits would be, because banks make profits off interest rate spreads, between borrowing and lending rates, and not on the level of interest rates, so you need to argue that a higher level of interest rates would prevent spreads being squeezed.)

The second email, ironically, was from a bank economist, Avery Shenfeld from CIBC (quoted with permission).

" I’ve been trying to articulate that same message [as your blog post] since 2008, and oddly enough, the greatest resistance has come from academic economists, or those with equivalent training, who believe that some model somewhere “proves” that the real natural rate always has to be the equal to the real potential growth rate, or has to be a real rate of 2%, or at least has to be positive given a positive marginal product of capital. What I’ve always said is that, at least for an open economy, since interest rates also interact with the exchange rate and both matter for growth/inflation, there’s no simple rule of thumb like that."

This blog post is in support of Avery Shenfeld.

Avery is right to make that point about the interest rate and the exchange rate. For example, under perfect capital mobility where the domestic interest rate (adjusted for expected appreciation/depreciation of the exchange rate) equals the world interest rate, it is perfectly possible for the domestic growth rate to exceed the world growth rate and world rate of interest. But I'm not sure whether that argument can be made for Canada. So I want to set it aside for now, and say that the academic economists Avery is arguing with are wrong, even for a closed economy, like the world.

First off, there is no one theory of the rate of interest. If you want to see just how numerous and diverse the theories are, I recommend you skim down this hilariously long recent Twitter thread by Jo Michell. Now we might say that a lot of those theories are false, and that some of them are different versions of each other. But I think it's more like the blind men and the elephant; each gets part of the truth, but none of them gets the whole truth

Second, here's a really simple and obvious counterexample to the claim that theory says that the Canadian equilibrium real interest rate cannot be below the growth rate and cannot be negative. And it's one where we all know for certain what that equilibrium real interest rate must be. Hint: it's minus 2%, and all of us willingly hold that financial asset despite its negative real yield. That counterexample is currency, given the Bank of Canada's 2% inflation target, and the fact that the nominal rate on currency is stuck at 0%.

Now you might say I'm cheating, because the real interest rate on currency is not what we are talking about when we talk about the Bank of Canada normalising interest rates. But currency is just an extreme example to illustrate a more general point: there are lots of different interest rates, because there are lots of different financial assets, and they are not all perfect substitutes for each other, and the yield spreads between those financial assets can vary over time, depending both on how their differences vary over time and on how people's valuations of those differences vary over time. Yield spreads depend on liquidity, term, and safety. And even safety is not a simple thing, since different people are concerned about different sorts of risk.

And the three interest rates set by the Bank of Canada (the deposit rate, the bank rate, and the overnight rate) are very peculiar, and cannot be assumed to be representative of the whole spectrum of interest rates, even if we restrict our attention to Canadian interest rates. And "the" interest rate, to which a particular theory of interest rate applies, might be better proxied by an anticipated rate of return on equities, or even a rental yield on houses or farmland, than by an interest rate on promises to pay a fixed number of Canadian dollars.

And, even if we do pick one Canadian dollar nominal interest rate, what real interest rate we get depends on what price index we use to define "inflation". Sraffa was right to say it doesn't make sense to tell the central bank to set the nominal interest rate equal to the natural rate, because there is a different natural rate for every price index. This does not mean a Neo-Wicksellian central bank cannot set a nominal interest rate equal to a natural rate plus a target rate of inflation (where both are defined using the same price index). But it does mean that any economic theorist who tells the Bank of Canada what the natural rate can or cannot be must make sure that the price index implicit in his theory matches the price index the Bank of Canada targets, or else make an adjustment so both are talking about the same real rate. And some such adjustment will almost certainly be needed, because the Bank of Canada targets a Consumer Price Index, and the prices of capital goods can vary relative to the prices of consumer goods, and any theory of interest rates in which investment is endogenous should include that relative price change. Lower interest rates mean higher house prices relative to rents, for example.

The Theory of Capital and Interest is difficult, even if we ignore money and other complications. It is perfectly possible to have the real interest rate, defined by the price index of capital goods, equal to the Marginal Product of those Capital goods (defined using that same price index), and the latter being positive, but the real interest rate defined by the price index of consumption goods, being negative. All you need is the relative price of capital goods falling faster (or being expected to fall faster) than the own rate of return on capital goods. If robots can reproduce themselves at 10% per year then the robot rate of interest will be 10%. But if the price of robots is falling at 15% per year relative to consumption goods, the consumption rate of interest will be minus 5%.

The rate of return on investment that matters for the consumption rate of interest is the Marginal Rate of Transformation between present consumption goods and future consumption goods. The simplest of such technologies is simple storage. If we can store consumption goods costlessly and safely then the consumption rate of interest cannot be negative, because if it were negative there would be arbitrage profits from storage. All forms of investment are just like storing apples, except that we first transform the apples into trees, and then back into apples. Or use the resources that could have produced apples for current consumption to produce something else to help us produce apples for future consumption. And we can sometimes get "negative wastage" of apples when we "store" them using those more "roundabout" methods. But if technology is improving in those roundabout methods, or if supply increases as we invest more, we will tend to see the relative prices of those goods falling over time. And if our consumption basket includes a rising proportion of services that cannot easily be stored, even metaphorically, the consumption basket interest rate will be less than the return on investment on goods that can be "stored", and will be falling over time. We end up singing each other songs, with all the other goods free. Which isn't so bad really, provided there are enough young people around to sing songs for us old retired folks. See my other post for an example.

Which brings me to demographics.

Most macroeconomic theories of interest rates are variations on the theme of productivity and thrift, with a bit of liquidity preference thrown into the mix though usually only for the short run. So let me talk about demographics and thrift, because saving for our retirement is a big motive.

The textbook representative agent macroeconomic models do not have demographics. In the simplest case of a representative agent with log preferences, so the Marginal Utility of consumption equals 1/consumption, the real interest rate (measured in consumption goods) equals the growth rate of consumption, plus an allowance for innate impatience ("pure" time-preference "proper"). You can get an interest rate higher or lower than this if the Marginal Utlity of Consumption falls more or less quickly than 1% per 1% rise in consumption. But the real interest rate will not go negative unless consumption has negative growth or people have negative impatience (they prefer consuming 99 today and 101 tomorrow than 100 on both days).

But that is growth rate in consumption per capita. Which will be less than growth rate in aggregate consumption, if the population is growing.

But the biggest problem with this way of looking at thrift is that the representative agent lives forever, and never retires. The only way we can translate that model into a model of finite lives is to think of the representative agent as an infinitely-lived dynasty of parents, kids, grandkids, etc., each of whom is perfectly altruistic towards older and younger generations of the same family (and let's not even think about sex, which brings in the in-laws to mess things up). So parents care about their kids' and grandkids' consumption as much as they care about their own, and kids support their retired parents, and "saving" means all generations of the dynasty who are currently alive not collectively consuming part of their collective income. And even if we accept all this, if the representative parent has less than one kid (don't think about sex, or integer constraints), the dynasty might want to save, even at negative interest rates, to take the burden off the kid in supporting the parent's retirement.

Overlapping generations (OLG) models, like Samuelson 1958, do explicitly incorporate demographics. And one interesting result of those models is that an economy with an interest rate below the growth rate is "dynamically inefficient". It means that the government (or someone) could set up an unfunded pension plan that pays a rate of return equal to the growth rate, and make all generations better off. It's like a Ponzi scheme, except it can run forever, because the liability grows at the same rate as GDP, so the implied debt/GDP ratio can stay constant and sustainable.

But that deserves a post of its own, because this post is already too long. So I'm going to stop there, for now.

Comments

[Max]

On average banks pay about 2% less on bank accounts than they receive on riskless assets. When rates go to zero, this revenue goes to zero (without reducing costs). They don't cut customer rates below 0%. So they are right to dislike low rates, though maybe not right to lobby for premature central bank rate increases.

[Nick Rowe]

Max: I think that's roughly right. But one way that banks can implicitly adjust the interest rate they pay on chequing accounts is by varying service fees, in particular by varying fees according to the average or minimum balance in your account. (If they waive fees when you have a larger balance, it's like paying interest.) So I'm not sure if it's exactly right. But I don't see them implicitly paying negative interest this way, because that would be like cutting fees if you have *below* a minimum balance.

[Matthew Young]

Interest is what we pay when our assets diverge from liabilities. It is he surplus needed to cover planning error. Interest over time is the rate of divergence between assets and liabilities. Positive rate.

OK, with that, we get bankruptcy. In bankruptcy the assets already have a large divergence from liabilities. The bankruptcy judge goes through a sequence of trades that cause assets to converge to liabilities. Negative rate.

Elsewhere, returning an item to the store, recalling automobiles to the factory.

[JKH]

“banks make profits off interest rate spreads, between borrowing and lending rates, and not on the level of interest rates”

Not quite, Nick.

Not too related to the main theme of your post - but visualize a bank balance sheet and think of the common equity (book) position down in the right hand corner of the balance sheet. That position has a zero interest cost for purposes of determining profit. So the total net interest margin of the bank includes not only the asset/liability spread portion (calculated on the basis of matching some chunk of interest earning assets to the remaining (non-common-equity) interest-paying liabilities), but that ‘slice’ of the balance sheet that includes an ‘interest rate mismatch’ between some chunk of interest earning assets and a (permanently) zero interest cost book equity position. This is a non-trivial contribution to the total net interest margin of the bank, and it means that the contribution of this portion does indeed benefit from a higher level of interest rates. The exact nature of that contribution in turn depends on how the treasury function manages the interest rate sensitivity of that part of the balance sheet (along with the rest of the balance sheet). This is all part of interest rate risk management for the bank as a whole.

Another type of zero bound to consider in banking.

:)

[Nick Rowe]

JKH: I think I see your point. I had missed that. I think it's the same as the distinction between what we economists call "accounting profits" vs "economic profits". The difference is that economic profits consider the opportunity cost of the firm's own assets ("equity"). Like if I quit my job to start a business, I should include my foregone salary as a cost of that business when calculating profits. Not sure which definition of profit applies here (though, naturally, I'm biased).

[Nick Rowe]

(If I quit my job to start a business, and can't get my old job back if my business fails, then my foregone salary becomes a sunk cost, and no longer an opportunity cost, so the two concepts of profit line up again. Might be the case for banks.)

[JKH]

I think you’re referring to a separate issue Nick. Whatever you do with asset values in the calculation of profit – ‘economic’ or ‘accounting’ – the net interest margin must be a component of the fully calculated profit. You can choose to fluctuate asset values (and liability values for that matter), or not, in the calculation of profit. In fact, standard bank accounting includes both types of asset value accounting, depending on the nature of the asset business. (For example, trading positions are marked to market; residential mortgage positions are not.)

My point relates purely to the calculation of that net interest margin, which must always be a component of the fully calculated bank profit. And you can split the interest margin into two different sections of the balance sheet that originate it – the common equity position and the rest. There is no interest cost on the common equity position. So profits go up when the general level of rates goes up, other things equal.

[louis]

"(If I quit my job to start a business, and can't get my old job back if my business fails, then my foregone salary becomes a sunk cost, and no longer an opportunity cost, so the two concepts of profit line up again. Might be the case for banks.)"
I think JKH's point WAS that the bank's equity capitalization is a sunk cost. In the extreme where a bank is fully equity capitalized and employs no leverage, changes in rates would flow directly to profits. To extent you substitute in (floating rate) liabilities for equity finance, the bank is less exposed to rates, but is still long.
The capital isn't truly sunk - a bank can always liquidate all or part of its portfolio to return capital to shareholders - but in the short-term it is clear that bank managers want to be able to earn higher returns on their equity capital base.
In medium to longer term, this shouldn't matter, as the interest rate spreads banks charge are set competitively, not fixed. In a lower-rate, lower-profitability environment, banks will be less willing to extend loans at previous customary spreads and demand higher spreads to justify their equity cost of capital. Example - 3:1 leverage, 4% funding rate, 2% spread - $1000 loan generates $30 in profits on $250 in equity, or 12% ROE. If funding rate falls to 2%, profits fall to $25, or a 10% ROE. But if the fall in rates is seen as permanent, and the 12% remains the cost of equity, then new loans will be done at a 2.5% spread to restore previous profitability.

[JKH]

" If robots can reproduce themselves at 10% per year then the robot rate of interest will be 10%. But if the price of robots is falling at 15% per year relative to consumption goods, the consumption rate of interest will be minus 5%. "

Just wondering if you personally relate this area at all to the General Theory Chapter 17.

I've spend some time on that chapter from time to time - seems super brilliant to me.

[Market Fiscalist]

I have a question on 'And if our consumption basket includes a rising proportion of services that cannot easily be stored, even metaphorically,'.

I really liked your earlier description of investment: 'All forms of investment are just like storing apples, except that we first transform the apples into trees, and then back into apples. Or use the resources that could have produced apples for current consumption to produce something else to help us produce apples for future consumption." Why can't this be applied to the production of services ? Rather than producing haircuts in the present I can instead invest in human and physical capital to increase the productivity of haircuts in the future (more skilled hairdressers who can cut faster using electric, lazer-controlled scissors or whatever) and in this way transport haircuts into the future with "negative wastage". Are you saying that it is just an empirical fact that services have less potential for roundabout production methods than physical consumption goods or that there is something about services that makes this necessarily true ?

[Jacques René Giguère]

MF: We can also invest in non-haircut sector productivity so that we can transfer the economised resouces back to haircut. Which is a good part of what happened in manufacturing to service transition in the 20th century.

[Nick Rowe]

JKH: "Just wondering if you personally relate this area at all to the General Theory Chapter 17."

I hadn't thought of that connection until you mentioned it, but yes I think it's there.

MF: I agree with what you say there. Yes, by training future hairdressers we can invest in services. But the investment opportunities (plus possibility for big technological improvement) seem, empirically, to be rather limited. I don't think it's necessarily true about all services.

[Tristan Hanson]

Great post, Nick. The last paragraph effectively sums up what Eric and I argue for UK policy: https://ftalphaville.ft.com/2017/11/23/2196091/guest-post-time-for-a-uk-sovereign-wealth-fund/ and https://www.philosophyofmoney.net/safe-asset-issuance-discovery-oil/

[Nick Rowe]

Tristan: Thanks! I'm still collecting my thoughts for my next post, following up on that last paragraph.