Rowe v Glasner... round 33!

It's the Roe v Wade of the blogosphere, a battle that never quite gets resolved. Nick Rowe and David Glasner have been having one of their bi-annual debates over the ability of private bankers to create excess deposits. See here, here, and here.

The nub of their conflict seems to resolve revolve around the following points: if we assume that 1) bank deposits and cash are imperfect substitutes for each other, and that 2) bankers simultaneously raise the rate on deposits and increase the quantity of deposits, then 3) an excess supply of deposits and cash will emerge. Nick argues for the last point while David argues against it.

At the risk of only adding noise to what is always an interesting debate, I'm going to chime in. I'm going to focus on the step-by-step process by which events play themselves out, the bricks & mortar if you will. Given the complexity of this process there will no doubt be errors in this post, hopefully readers will flag them.

The thought experiment that Nick and David have been debating involves a simultaneous increase in deposit rates and the quantity of deposits via loans. But I'm going to focus on just an increase in deposit rates first, then bring in the quantity adjustment later.

Let's start out with a full spectrum of assets, including central bank liabilities (cash and reserves), bank deposits, durable assets (i.e. gold, houses, stocks, and bonds) and perishable assets (apples, soap, jeans). All provide varying expected pecuniary returns (i.e. dividends, interest, and capital appreciation) as well as expected non-pecuniary returns (consumption and liquidity), the sum of which adds up to an asset's total return. In equilibrium, every asset offers the same total expected return.

What do we mean when we say that cash and deposits are imperfect substitutes for each other? Like cash, deposits are useful in a wide range of transactions. However, unlike 0% banknotes, deposits yield interest. Given that deposits provide both interest income and broad marketability, people will prefer to only hold the bare minimum of cash that they deem necessary.

What dictates this bare minimum? The marginal unit of cash that an individual holds in their wallet has been specifically accumulated to deal with a unique set of transactions in which deposits simply cannot participate. This unique set of transactions occurs in markets where digital payments are not allowed, say laundromats, farmers' markets, or cash-only diners; or where fees are levied on card payments, like gas stations; or in places where payments must be anonymous, like in the back alley behind city hall.

On the margin, people try to anticipate the chances of engaging in these sorts of cash-only transactions and accumulate what they deem to be an appropriately sized cash inventory. So while an individual's inventory of 0% cash does not provide a pecuniary return, it does provide a non-pecuniary liquidity return arising from its ability to be used in both a broad set of transactions in which it competes with deposits, and a narrower set of transactions in which only it is useful.

Now say that banks have figured out a way to cut costs. Their profits grow, but this only lasts a short time as competition forces them to increase the interest rate they offer on deposits. Given stationary pecuniary yields and non-pecuniary yields on cash, durables, and perishable assets, deposits now offer the best return. An excess demand for superior-yielding deposits and an excess supply of inferior-yielding durable assets, perishable assets, and cash emerges.

A number of adjustments need to occur in order to restore equilibrium. Along the margin of deposits-to- durables and perishables, an effort to simultaneously sell these assets for deposits will result in a fall in the their relative price. Their prices will fall until they stabilize at a low enough level that they are now expected to appreciate at a rate sufficient to equal the return provided by deposits. This resolves the excess demand for deposits along both the deposit-to-durable asset margin and the deposit-to-perishable asset margin.

Things are a little trickier along the deposit-to-cash margin. Given the superior return on deposits, people will now want to hold more deposits. An excess supply of cash develops. Unlike the durable and perishable asset markets, the cash-to-deposit market is inflexible; the price of cash cannot fall relative to deposits in order to restore equilibrium.

What happens instead is a quantity adjustment; people begin to sell cash for deposits at a fixed rate of one-to-one. The market where they go to do this is at a bank. They don't "sell" cash. Rather, they deposit cash at the bank in return for higher-yielding deposits. They continue to deposit cash until the benefits of adding one more unit of deposits to their portfolio, namely the marginal enjoyment provided by their higher pecuniary return, no longer exceeds the foregone benefit of one less unit of cash, namely their ability to participate in prospective cash-only transactions.

Once people have reduced their cash balances to a point at which they are once again indifferent between cash and deposits, equilibrium has once again been restored along the cash-to-deposit margin.

So in short, an increase in deposit rates causes a temporary excess demand for deposits in the deposit-to-cash market as well as the deposit-to-durable and perishable asset markets. These excesses are quickly removed by a fall in the prices of durable and perishable assets, and a quantity substitution of cash for deposits.

I'll bring this back to Rowe v Glasner in a moment, but as an aside it's worth noting that the process doesn't halt here. Having sold deposits for cash, the banks now have more cash than they desire. Their excess balances are trucked over to the central bank where they are converted into reserves, or clearing balances. But banks don't really want these either. Instead, they will all try to spend away their reserves simultaneously on durable assets, or try to lend them in vain to other banks in the interbank market. This pushes prices of durable and perishable assets higher and the interbank rate lower. At this point the central bank, noticing that its target for the interbank interest rate has deviated from its target, steps in and mops up all the excess reserves by conducting open market sales. This pushes the interbank rate back up to target. Voilà, the excess quantity of cash (and reserves) has been removed, first by depositors forcing cash back on banks, and then banks forcing the cash back on the central bank.

Let's circle back to Nick and David's argument. They were considering not just an increase in deposit rates, but a simultaneous increase in deposit rates and the issuance of new deposits. I'd argue that the same process that I've just described applies to this second scenario.

The rise in deposit rates causes durable and perishable asset prices to fall. At the same time, the new deposits are spent into the economy by borrowers. Individuals now hold more deposits than before, but they still own the same quantity of cash, an undesirable situation for them since cash is providing an inferior return relative to deposits. How can they rid themselves of this unwanted cash? If one person sells their horde, the next person will only try to sell it to someone else, and someone else. The cash never leaves the economy.

But here's an out. At some point an individual who is in debt to a bank will come into possession of that cash and will use it to reduce the amount owing. That cash will take the same route back to the central bank described earlier, ultimately meeting its demise in the blades of a paper shredder.

So given an increase in deposit rates and the emission of more deposits, the final resting point is a fall in durable and perishable asset prices, and an increase in the amount of deposits at the expense of the quantity of cash. That leaves us in the same spot as an increase in deposit rates alone.

Where does that place me relative to Nick and David? If it takes a while for unwanted cash to find a debtor who will reflux that cash back to the banks, then we can see the sort of effects that Nick describes. But on the whole, I think I'm more on David's side here. But that's hardly surprising. As Nick usually says, he's arguing against the mainstream view. The odds always were that I'd land in the same bucket as the majority. Anyways, for what it's worth, those were my two-cents.

Before I sign off, let's follow one final tangent. Thanks to higher deposit rates, one of the features of my final resting point is lower durable and perishable asset prices. But after a few months, our central bank will notice that the incoming data is showing that the price of perishable assets has ticked down. The perishable asset category, which includes things like jeans, apples, and soap, is the category of assets the prices of which a modern central banker targets. In an effort to right deflation in the perishable goods market, our central banker will counter by reducing the return on reserves. (He/she can do so by conducting open market purchases and/or by reducing the interest rate corridor). Banks will react by simultaneously trying to offload their inferior-yielding reserves in favour of durable and perishable assets. Prices will rise back to the central bank's target.

So a fall in prices that was kicked off by commercial banks sweetening the return on deposits is ultimately reversed by a central bank reducing the return on central bank liabilities. Tit-for-tat. Here I definitely agree with Nick Rowe—central banks are alpha banks. Commercial banks can only have a passing influence on the price level if a central banker decides to have his or her way.