Wednesday, 11 September 2013

Banks, Non-Banks and the Interest Rate Effect

In my last post, I used the balance sheet framework of a simple imaginary economy to look at the relationship between bank lending, non-bank lending and payments money.  I thought it would be useful to use this framework to construct a little model.  I particularly wanted to look at the way non-bank lending and bank lending differ, even though both are expansionary.

A full list of the equations, variables and parameters for what follows is set out at the end of this post.

Many of the equations simply set up the accounting relationships shown in the balance sheet matrix.  This is the same as before and set out below:


Time deposits


Savings accounts



The financial sector is represented by two types of lender: banks and non-bank financial institutions (NBFIs).  Both entities make loans to firms (households are assumed not to borrow).  Banks offer time deposits to households and NBFIs offer something similar which we will call savings accounts.  The key difference between banks and NBFIs is that only banks can offer checking accounts.  As we are going to assume that only checking accounts can be used for payments, we're going to define money as the balance of such accounts.  Because they cannot offer checking accounts, NBFIs have to attract funds into their savings accounts before they can make loans.  As the timing of new loans does not necessarily coincide with the timing of new savings, they also hold some money balances as a float.

I am assuming that households behave as follows:
- they hold money in a fixed ratio to income;
- they have a long term target ratio of total financial assets to income, but move towards this incrementally; and
- they allocate their non-money assets between deposits and savings accounts on the basis of the rates paid on each.

Investment is driven by loans.  I am assuming the demand for loans exceeds supply, so the quantity of loans is determined by credit constraints imposed by banks and NBFIs.  The amount of lending by each can therefore be treated as exogenous.  As we are assuming firms do not retain any money, their spending must be equal to the change in loans.  

I am assuming here that neither consumer spending, nor investment depends on interest rates.  This makes it easier to isolate the effects we want to observe.  We could easily relax this assumption if we wanted.

This set up now means we can compare the effect of an increase in bank lending to an increase in NBFI lending.  The charts below show this for the same absolute increase in the value of loans made by each.

The first thing to note is that the effect on GDP is the same for bank lending as for NBFI lending (this depends on my assumption that spending is not affected by the change in interest rates described below).  New loans have a temporary effect on investment when they are made and a permanent, but lesser impact on consumption due to the increase in overall financial assets.

The difference between the two is in what happens to interest rates.  As we can see from the charts below, an increase in NBFI lending tends to push up rates offered to savers, compared with an increase in bank lending.

If they want to increase lending, NBFIs need to attract more savings.  To do this they will have to raise their savings rates.  This will tend to pull funds away from banks.  The total funds placed with banks cannot fall because it must always be equal to the total of bank loans, but what will happen is that banks will find the ratio of deposits to money falling.  Banks will react to this by raising their own deposit rates to try to attract more longer term funds.

Bank lending will tend to have the reverse effect.  Initially, bank lending adds to checking account balances and banks will need to raise their rates to try to attract savers into longer term deposits.  NBFIs will need to follow suit if they are not to lose funds themselves.  However,  once the initial boost from the new loans has worn off and income falls, household demand for money holdings also falls and they try to invest more into term deposits and savings accounts.  However, banks and NBFIs do not at this stage need more funds and so they can cut their savings rates.

To illustrate further what is going on, the graphs below show the deviations in the balances of household money holdings, deposits and savings accounts.

So we can see that even though bank lending and non-bank lending might both be expansionary, they are not equivalent.  The difference reflects their relative position in the hierarchy of money.  NBFIs need bank money to make payments.  Banks do not need NBFI claims.  In addition to facilitating debt funded expenditure, bank lending will also increase liquidity in a way that NBFI lending will not.  Banks and NBFIs are therefore different.  But this does not mean that NBFI lending does not matter.  


GDP is consumer spending plus investment by firms.

Y = C + I

Consumer spending and investment are defined by accounting identities.  Consumer spending is income less increase in assets (i.e. saving).

C = Y - ( V - Vt-1 )

Investment is equal to the increase in loans.

I = L - Lt-1

Households holdings of money are in a fixed ratio to GDP.

Mh = αm . Y

Households also wish to hold total financial assets in an fixed ratio to GDP, but this is achieved by a gradual adjustment based on the difference between a target and actual value.

V = Vt-1 + εv . ( V* - Vt-1 )

V* = αv . Y

The proportion of non-money assets that households wish to hold as savings accounts is a function of the interest rate differential between deposits and savings accounts.

S = ( V - M) . ( λh0 + λh1 . ( rs - rd ) )

Deposits are then the balancing item.

D = V - Mh - S

The amount of loans by banks and NBFIs adjust incrementally towards a target level.

Lf = Lft-1 + εf . ( Lf* - Lft-1 )

Lb = Lbt-1 + εb . ( Lb* - Lbt-1 )

Banks and NBFIs each have to make a portfolio decision based on rates.  The proportion of loans that banks would prefer to finance with money, as opposed to deposits depends on the deposit rate. 

M = Lb . ( λb0 + λb1 . rd )

The amount of money that NBFIs wish to hold depends inversely on the savings rate.

Mf = Lf . ( λf0 - λf1 . rs )

The above two equations are re-arranged as equations in the interest rate.  In addition to enabling solution, this reflects the idea that banks and NBFIs set the rates they offer and then take all money at those rates.

Lastly, some accounting identities.

M = Mf + Mh

L = Lf + Lb

Mf = S -Lf


Start Value
Consumer spending
Time deposits
Investment by firms
Loans by banks
Target loans by banks
Loans by NBFIs
Target loans by NBFIs
Total balance in checking accounts
NBFIs' balance in checking accounts
Households' balance in checking accounts
Savings accounts with NBFIs
Total household financial assets
Target household financial assets
Rate on deposit accounts
Rate on savings accounts


Household money holding ratio
Household wealth ratio
Bank loan adjustment rate
NBFI loan adjustment rate
Household wealth adjustment rate
Bank portfolio parameter
Bank portfolio parameter
NBFI portfolio parameter
NBFI portfolio parameter
Household portfolio parameter
Household portfolio parameter

The graphs show the result of an increase of 10 in the value of either Lf* or Lb*.


  1. Nick,

    This is a carefully crafted post. I need to compare basic assumptions before delving too far into it.

    1. Do NBFIs guarantee deposits? To my thinking, that is a far more important precondition for money supply expansion than is the speed or ease of money movement.

    2. Do NBFIs have bank accounts? They must if all payments go through bank checking.

    3. Is there an unwritten assumption that banks can make low cost loans based on deposits as "free capital"? This would be the reason that banks could make loans at lower interest rates.

    4. In the graphs, "deposits" are charted. Are these "Time deposits"? It does not look like checking deposits are on any graph.

    This post is an excellent platform for serious consideration. Thanks again for making it available.

    1. Roger,

      1. Not sure what you mean, here. The savings accounts would be debt obligations of the NBFIs. They would be expected to pay out on them regardless of performance on their loans (although, as I haven't modeled capital, there is no first loss position to protect savers, so savers would suffer the loss on loans anyway).

      2. Yes. Household and NBFIs both hold checking accounts. Money is the measure of the balance on those accounts.

      3. I haven't said anything about lending rates, purely because it would confuse the issue I wanted to highlight. The banks are funding their loans with checking account balances (money) and time deposits. The time deposits pay interest, the checking accounts don't. In practice there are more admin costs involved in operating checking accounts and I'm implicitly assuming that is why they pay no interest. That would have to be seen as a cost of raising that type of funding. There's a lot more that could be said here, but again I've avoided it as I don't think it matters to what I wanted to look at.

      4. Yes. In the graph, deposits means time deposits. Money is checking account balances.

  2. Nick,

    Thanks for the clarifications. They helped bridge the gaps in linguistic form.

    I am short of time right now, but in the future, I would like to put your model into Minsky.

    My intuitive reaction to the graph "Variation of Account Balances with NBIF Lending" was that the scale of saving account increase was much too high. I expected the sum of all the forms of money to be a constant after NBIF lending.

    My intuitive reaction to the graph "Variation of Account Balances with Bank Lending" was that both deposits and savings accounts should have always been positive, eliminating any negative points. (I can't think of any reason that a bank loan would cause a draw down of either deposits or savings accounts although a change in relative savings rates could change the relative quantities of account value.) Intuitively, I also expected the sum of the three forms of money to always equal the initial loan amount.

    Thanks again for the post.

    1. I'd be very interested to know how you get on putting it into Minsky. I have still been unable to download it. I don't need it because I like using excel, but I'd still like to look at it.

      In the graphs, savings accounts is just the funding of NBFIs, i.e it doesn't include banks. Money is just household money - it doesn't include NBFI money holdings. So you'd still need NBFI money holdings to deduce the increase in loans (although that doesn't change much).

  3. Hi Nick, are Lf* and Lb* constant? There are no equations for them. Thanks.

    1. HJC,

      Lf* and Lb* are exogenous. They are the variables I vary to look at the effect. I should have said though, that the graphs show the result of increasing either Lf* or Lb* by 10. Thanks for your question - I'll edit the post.

  4. Wow, this seems to connect well with the discussion I was having with JKH at, specifically on the issue of what should happen to interest rates on deposits if banks want to loan more.

    Could you share more intuition as to why the banks need to change their interest rate on deposits when they make loans in your model? In what scenarios would they not have to? Is this reflective of what plausibly happens in the real world?

    I probably need to just study your model more.

    1. Thank ATR,

      I'm assuming here that banks just spontaneously decide to lend more. Assume perhaps that their risk perception changes, so that they expect fewer defaults.

      The long term effect is a slight reduction in rates. This is because some of the extra savings pool generated by the new bank lending is going to the NBFIs. Because I am assuming in this scenario that NBFIs lending is staying constant, they don't really want this money. It just sits as un-invested cash earning little return. Faced with more savings than they want, they will tend to lower rates. Bank deposit rates can then also come down.

      In the short term, however, there is a rise in rates. This is because the initial lending creates an imbalance for banks, giving them too many short dated liabilities. To redress the balance, they need to raise deposit rates to get people to make longer term deposits. NBFI rates must then go up as well, or they will lose funds themselves.

      You do have to be careful with results like these. I have deliberately ignored certain reaction functions in order to illustrate the points I wanted to make. For example, a reduction in NBFI funding costs might well lead to them wanting to lend more, but I have ignored that because I wanted to keep NBFI loans constant.

      But overall, I think this does reflect something true about the way the real world works. Both lending by banks and lending by non-banks can be expansionary. But lending by banks has the additional effect of adding to overall liquidity.

      There is a parallel here with IS/LM. Both types of lending push the IS curve out, because they facilitate additional expenditure. But by increasing the money supply, bank lending also pushes the LM curve out. That's why NBFI lending involves higher interest rates than bank lending.

      Hope this helps. I think this stuff is often really hard to just imagine in your head. The only way I can see it is to make the models.

    2. Thank you for the response. I think I'll ultimately have to closely examine the model, as you suggest.

      However, maybe if I more directly aim at what’s bugging me, you can see where I’m getting stuck.

      My starting place is the central bank fixing short-term bank cost of funds at some level, via the interbank market and its standing facilities. This sets an anchor to the interest rate on banking lending, with of course various forms of premia impacting the end interest rate offered. How does this relate, if at all, to the interest rate offered on deposits?

      I view deposits ultimately as a source of funding for banks, but one among the alternatives mentioned above. As such, in a simple model, if the interest rate on deposits rises following an expansion of bank lending, is it safe to say it shouldn’t rise beyond the cost of these other sources of funding for banks? Otherwise, why would they continue to borrow at a more expensive rate? Where do these other sources of funding come into play in your model?

      Also, as a friendly suggestion, if you could make the comment box larger, it would make it easier to type responses :). Right now, we only get 4 lines of visible spaces at any one time.

  5. ATR,

    It's a good question and really the answer really goes beyond the scope of what this model is doing.

    In this model, I've sort of lumped commercial banks and the central bank in together but, in reality, there is a sort of tier structure from the central bank to commercial banks to non-banks. Just as non-banks have to use commercial bank money, commercial banks have to use central bank money. Thus in the same way, if commercial banks try to expand and the central bank does not want to facilitate that with an increase in base money, that implies rising rates. In practice, of course, it's done the other way round - they set the rate and then supply base money as needed. But the central bank is holding the strongest position. Commercial bank expansion can only have the effect I've described if the central bank plays ball.

    At least, that's how I think it works. I might have do an expanded model to check that really makes sense.

    Thanks for your point on the comment box as well. I'll see what I can do about that.

    1. Good stuff. To make sure I understand your comment, you said: "Thus in the same way, if commercial banks try to expand and the central bank does not want to facilitate that with an increase in base money, that implies rising rates."

      Does "rising rates" refer to rising rates on loans and/or rising rates on deposits? If the latter, I would think your sentence suggests that the rising rates on deposits in your model are coming from the central bank not facilitating the increase in base money.

      However, as you note, in practice, the central bank does accommodate. When you write “commercial bank expansion can only have the effect I've described if the central bank plays ball,” which effect are you referring to? The 'central bank playing ball' to me means holding rates constant; so do you mean the effect in which banks expand loans but deposit rates don't change?

    2. ATR,

      By rising rates, I was thinking of both deposit rates and loan rates and yes that would involve an increase in the policy rate, which would be in response to the increased demand for base money.

      And yes, by "playing ball", I meant keeping the policy rate constant and supplying reserves on demand.

      Adding central bank funding into the mix provides three possible liabilities for banks: central bank loans (or repo), transactions accounts (what I'm calling money) and time deposits. Banks will want to manage the balance between these - they need a certain amount of term funding, but there's no point paying for more than they need. The proportion of term deposits they want will vary negatively with the rate on term deposits and positively with the policy rate.

      Therefore, the way I think this works with a three tier structure (central bank, commercial bank, non-banks) is as follows:

      The central bank sets the policy rate. This forms the anchor for all the other rates and is the most important factor for end user rates.

      Expansion by banks but not NBFIs will then tend to push down deposit rates relative to the policy rate. This will also tend to lower loan rates, as banks' overall funding cost has come down. This reflects changes in bank liability portfolios. The extend of rate movements depends on how sensitive the banks are to different ratios, but it will not generally have as much impact as a change in policy rate.

      Expansion by NBFIs but not banks will tend to push up end user rates relative to the policy rate, both savings rates and lending rates. Again the policy rate provides a strong anchor.

      This is my gut sense, but I think I'd probably need to work through a three tiered model to get comfortable with that - perhaps a topic for another post.