Pushing on a String (Supply-Demand Version)

In response to a query about the “Pushing-On-A-String” post, I thought it would be helpful to post some pictures clarifying the elasticity argument.

Recall that we are discussing supply and demand for bonds. The central question is whether CB bond purchases can force households to hold more deposits.  My contention was that this would be ineffectual, as households would push the (bulk of the) excess deposits back onto the financial sector. There is no “hot potato” effect with deposits in a modern economy.

Essentially this is an elasticity argument — recall that anyone who holds a bond is a potential supplier, and anyone who may want to purchase a bond is a potential demander.

Imagine three sectors: “FG” = (non-financial) firms + government. “F” = finance. “H” = households. All three sectors are both potential suppliers and demanders of bonds, although generally speaking FG will be a net supplier, H will be a net demander, and “F” will be somewhere in between.

We can make this more precise by picturing the excess demand function for all three sectors, the sum of which is the total excess demand function for bonds:

As pictured, the household sector ends up being a net consumer of bonds in equilibrium, firms + government are net suppliers of bonds in equilibrium, and the financial sector is a small net consumer. The sum of all positions is zero.

What is meant by the elasticity argument is that the slope of the Finance excess demand function is much more steep than the slope of the other functions (in this diagram, quantity is on the vertical axis, so this corresponds to a “highly elastic” excess demand curve with respect to the interest rate). The reason for this is leverage — a small change in yields creates a much greater return opportunity for the financial sector than the corresponding increase in consumption or investment opportunities of the non-financial sector. The financial sector is more sensitive to changes in interest rates.

As a result of this steepness, what happens when the Central Bank intervenes, to buy up bonds? Effectively, the excess demand function for the “FG” sector in our model shifts upward, but this creates a much smaller shift in the total excess demand function:

The new excess demand function shifts only slightly. The household sector’s equilibrium bond holdings are basically unchanged (they do change slightly), and the financial sector’s equilibrium bond holdings swings to a near zero position to offset the change in bond supply coming from the central bank (“FG”).

In this sense, transactions between the central bank and the rest of the economy are effectively transactions between the central bank and the financial sector. That is, on the margin, the financial sector is the one making almost all of the adjustments.

This follows because of the increased sensitivity of interest rates of this sector, which follows because this sector is leveraged whereas the other sectors are not. And the more the financial sector is leveraged, the more ineffective central bank bond purchases are at forcing households to hold more than the level of deposits that they demand.

Pushing on a String (Supply-Demand Version)

10 thoughts on “Pushing on a String (Supply-Demand Version)

  1. Anders says:

    Wow – this is crystal clear, and even more compellingly expressed than previously. Thanks! Hope this manages to reach a wide audience.

  2. Anders says:

    Actually playing around with numbers, the ‘elasticity ratio’ seems to be key. For any given quantum of CB bond purchases, the ratio between the decrease in the non-financial sector’s bond holdings and the decrease in the financial sector’s bond holdings is the same as the ratio between the two elasticities. So if the financial sector’s elasticity of excess demand is 4x that of the non-financial sector, then CB purchases of 10 will increase non-financial sector deposits by 2 and financial sector deposits by 8. (Of course, this is before circuitists effects kick in, where those 10 of ‘excess’ deposits find their way to repay their or someone else’s bank debt.)

    Whilst agreeing with the argument that leverage ought to increase relative elasticity, I’d be interested in how one would try to estimate the elasticity ratio.

    1. Yes, the relative elasticity is the key. If you think about it for a moment — it has to be this way, otherwise the bond adjustment would be evenly distributed among all the sectors.

      In terms of numerical estimates, you could look at historical data of adjustments, but as (I believe) this is a function of leverage, things like changing capital requirements are going to influence the underlying in historical time series.

  3. Anders says:

    rsj, I agree, but whilst we can say that the financial sector will do more adjusting than the non-financial sector because it is more levered, can we go further and say that <10% of any increase in deposits from QE (again, ignoring second-order effects) will go to households? It would be good to be a bit more specific.

  4. Sergei says:

    I think it would be better to separate (non-financial) firms because their supply function is downward sloping. While it might make the graphs more complex, it will also make them much more real 🙂

    1. Well, it’s a pedagogical device, not a model. I’m hoping that it gets the point across about how the elasticities matter. One system — say in which banks are constrained from performing arbitrage will yield a very different response to an increase in high powered money versus another system — in which banks are less constrained. In a stylized case with infinite leverage, there is zero effect on the quantity of non-financial deposits as a result of an increase in outside money. The truth is somewhere in between, but generally QE has been a rounding error on influencing the quantity of deposits held by the non-financial sector. It is lost in the seasonal adjustments. And trying to compare the response of prices in a system such as ours to the experience of nations like Zimbabwe is idiotic. The institutions are different and therefore the elasticities are different.

  5. Winslow R. says:

    RSJ thanks for links….

    I may be putting words in your mouth but your idea seems to align to….

    1) ‘bank loans create bank deposits’
    2) ‘government spending creates bank deposits and reserves’
    3) ‘government taxes destroys bank deposits and reserves’
    4) ‘government bond sales to banks destroy reserves’
    5) ‘government bond sales to public destroys deposits and reserves’

    Next step QE

    When the Fed purchases bonds from banks, bank reserves increase and bonds decrease but deposits don’t change.
    When the Fed purchases bonds from the public, reserves increase and deposits increase.

    Hmmmmm so who the Fed buys bonds from and the government sells bonds to may matter if the quantity of deposits matters? Need to think about more.

    1. No, the argument is that it *doesn’t* matter who the government sells bonds to. The easiest way to see that is to understand that households will demand a premium when selling their bonds to the government, and that premium is exactly the same premium as the financial sector requires before it will sell an additional bond to the household sector.

  6. Winslow R. says:

    If the government sells $10 in bonds to banks, $10 decrease in reserves and no decrease in deposits.

    If the government sells $10 in bonds to public, $10 decrease in reserves and $10 decrease in deposits.

    The premium from selling to banks vs public would be equal to the $10 of deposits not destroyed?

    If the Fed buys $10 in bonds from banks, $10 increase in reserves and no increase in deposits.

    If the Fed buys $10 in bonds from the public, $10 increase in reserves and $10 increase in deposits.

    The premium from buying bonds from the public vs. banks would be equal to $10 increase in deposits?

    The key is In order for government to be able to sell to banks and Fed to buy from public, a transaction between banks and public needs to occur. As banks sell a $10 bond to public(bond is moved outside the banking aystem), deposits decrease $10.

    In regards to QE, net transaction is same whether government bonds are sold to public or banks and then purchased by the Fed.

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