Saturday, 25 May 2013

The Real Money Multiplier

Conventional economic theory states that banks are bounded by their reserve requirements when it comes to creating new money. In the conventional way, if just one bank exists in the economy, the money multiplier roughly equals the inverse of the reserve ratio. For example, if banks are required to hold a 10% reserve ratio, then the value of the multiplier is roughly 10. Thus if money introduced in the economy via the government is M then with the banks' assistance they will reach 10M. (for a more detailed analysis and some examples, Wikipedia provides an excellent introduction)

Nevertheless, the idea that the money multiplier is a myth, in its conventional estimation at least, has been promoted by a number of academics and non-academics. Notably, a 2010 paper by the Washington Federal Reserve questions its existence while a recent article by Scott Fullwiler does an excellent work in explaining the endogenous money theory (which basically states that banks are not constrained by deposits but by regulatory capital requirements) as well as the interactions between the economy and monetary and fiscal policies. What has been left unanswered, however, has been whether a money multiplier exists in the endogenous money theory and whether this may be calculated up to any degree. It is this author's belief that both of the above questions can be solved and the answer is affirmative in both case.

Consider an economy with just one bank. The bank chooses to invest the money it receives in one of the following types of assets, depending on its risk appetite and the risk-return relationship. Each asset has its own specific risk weight which is as defined by the Basel II capital adequacy rules (in the case where the asset types could have more than just 1 risk-weight value, I have assumed for simplicity the lowest)

1. Government bonds (0%)
2. Loans to corporates or securities companies (20%)
3. Retail Loans (75%)
4. Secured residential property loans (35%)
5. Secured commercial real estate loans (100%)
6. Other loans (100%)
7. Cash (0%)

Now suppose that at time 0 we witness an influx of  €X of new money in the economy (again for simplicity we assume that no cash in circulation exist. The reader may find it easier to understand this as an economy where every transaction is carried out via a credit/debit card and subsequently when an account is debited another is credited). The money, (which as we have seen here is basically a transfer from the government to the people) is subsequently deposited in a bank. Then, it is up to the bank's discretion to select one of the 7 asset choices mentioned above. Through the analysis, the assumption is that the bank holds 0.1X in equity and the minimum capital requirement is 10%.

If, for example, the bank chooses to invest in option 7, then the currency available in the economy does not change at all. Using the broad definition of M2 (can be found here) if the money deposited in the bank stays in the bank as cash, then the money stock is exactly equal to €X. In this case, it is more than obvious that the money multiplier value is exactly 0.

Now suppose that the bank decides to invest fully in loans secured by residential property. Then, the first time these funds are lent out the bank has a risk weight of 0.35*€X. Thus, the bank's capital ratio will be:
Thus, the bank after producing the aforementioned loans, still has a margin of 18% which is to its best interest to use; which means that the bank will choose to lend again and again until the ratio equals 10%.
The value of the multiplier here is essentially based on the amount of money lent out. Thus, since the money supply in the economy has been increased by 285%, the money multiplier is 2.85, or exactly 1/0.35. In other words, if the initial money supply was 1bn, then the bank was able to raise the amount of money in the economy to €3.85bn with just €100m of equity. 

Money Multiplier Using Reserves
While in the previous example we have not used the notion of bank reserves at all, we will now show that these do not matter at all to the money multiplier (i.e. they do not affect the multiplier value). Suppose now that the bank has to save 10% of its existing deposits each time, or in other words it can only lend 90% of its existing deposits. Now, the capital requirement ratio for the first round of lending will become 
Continuing with our substitutions, we find that the multiplier value which will again make the regulatory capital equal 10% will be 2.85, yet it will be reach in an additional round of lending

Thus, any change in the reserves ratio does not have any affect whatsoever on the multiplier value. All it does is make the rounds of lending until the final value is reached more. In addition, what can also be inferred from the above analysis is that a Y% increase in equity will mean a similar Y% increase in the multiplier value. The following graph indicates the multiplier values for 0.1X equity (solid line) and the effect a 20% increase on the equity value (dashed line).

What is considered as a fact (regardless of the approach) is that approximately 90% of the money supply in the economy comes as a result of the banking sector. Nevertheless, as we have seen above, the multiplier appears to be very small to accommodate such an increase in the money supply. In fact, the banks in this model represent about 75% of the money supply under the 35% risk weight assumption; if the weight is at the low of 20% then the banks represent up to 83% of the supply of money. What the reader should note is that these values are much larger than real-life ones, as it is customary that a bank would choose a combination of the above assets and not just focus on a specific asset category. 

An issue which would further increase the amount of money in the economy would be the introduction of a new bank. If a new bank enters the market then the maximum value of the multiplier given the asset selection has been reached, then money supply may be increased, again up to the point where capital regulations allow it. If, for example, bank 2 has an equity value of 0.05X then the money supply in the economy can be increased by 1.425, making bank-created money supply reach 82% of the total money in the economy. Thus, after many more banks are considered in the economy, with each bank contributing to the total money supply (yet, not all banks having the same equity values) the bank-created money would reach approximately 90% (or even higher) of the total money stock. The same would occur if 2 (or more) banks were in the economy at time 0.

The above model presents what the author understands to be a much better representation of the money multiplier values. As we have seen, these values are heavily determined by the bank's equity and (most importantly) the investment decisions each bank chooses to make. Although we cannot pinpoint the exact value of the money multiplier, we can be sure that this has no relation to the reserve ratio. In addition, the number of banks in the economy plays an important role to the total money stock, although their individual multiplier values are constrained just by their equity.

The policy implications of the money multiplier will be duly discussed in a follow-up post.


  1. Very interesting reconciliation of classical money multiplier theory with endogenous money theory.

    Banks' investment choices are driven by their risk appetite. The trouble is that banks are rubbish asset managers, because they don't see themselves as "investing" on behalf of depositors but as "funding" their lending. In other words, banks are driven much more by their asset side and tend to treat liabilities as residuals.

    I think banks should regard themselves much more as asset managers and develop proper portfolio management skills. They would then be able to create properly diversified portfolios of assets, which would significantly reduce the risks to depositors. One of the major drivers of bank fragility is over-concentration of assets in particular asset classes - especially mortgages and related products, whose risks are also often misunderstood.

    1. Thanks for the comment. Coming from you it's even more flattering.

      You are right on risk appetite, and that is what I was trying to do with the graph. Basically, all multiplier values cannot exceed the maximum ones, yet the real values should be much lower. The graph should basically look like a Markowitz efficient portfolio, with equity replacing risk.

      You make an interesting point on banks as asset managers. Recent experience (e.g. Greek Government Bonds, sub-prime lending, etc) indicates that many banks are making a lousy job in allocating assets. Training bankers for that would probably make the risk of bank crises lower.

      Unfortunately, the risk of banking products cannot be properly evaluated: residential property has a risk weight of just 35% compared to the 75% of other loan products. Thus, the incentive to invest more in "low" risk products is much higher, which in turn helps in creating bubbles.

  2. OK the commersial banks create money.
    The quantity of money created depends on special rules and calcualations.
    But who is the owner of the new money? Obviously it is not the credit taker because he must return these money + interest added

    Is owner of the new money the bank owner?
    Or he gives them in some way to the government and get's only the inerest paid?
    The bank decides how much to produce, but who decides about the ownership?

    1. The new owner has to be the person where the money goes to. For example if I obtain a loan purchase a house, the money goes to the house developer. Yet, this distribution of new money will eventually affect most of the society as the developer will spend most of that money, or that money will be lent out by a bank if they are simply used as a deposit (or even for loan repayment).

      The bank decides how much to produce but the loan taker decides who the money is going to.

  3. I have tried to understand the concept of the money multiplier for such a long time but i can't get it.In my own opinion I believe the money multiplier is beyond what we all literally take it to be.
    Taking a scenario of a given economy for example,if banks lend out money to its clients, this clients have to repay the loan plus some interest.In real sense, we can not rely on the fact that the money in an economy has double or tripled for instance.Why ? its because, the interest paid out creates a deficit in some sector of the economy and an equal surplus in another sector of the same economy.My point is, money in an economy is only multiplied through channels such as printing,foreign remittances and lets say foreign grants just but to name a few...Therefore i fail to agree on how banks through lending contribute to the economy's money multiplier.
    Please do feel free to correct me if am wrong.

    1. Hello and apologies for the late response, I didn't check the blog for a while.

      I think what you are missing in your story is the fact that money increases just when banks create a new loan. For example, say we have 100k in the economy and the bank hands out an additional loan for 10k. Now the money in the economy is 110k right?

      I think what confuses you (correct me if I am wrong here) is that when you think of money you think of cash. But most money nowadays is just a number on a computer and that is the money I am saying increases with bank loans.

      And as you correctly mentioned the interest one has to pay for the loan does not really make a difference as it is just a redistribution of the money across the economy.

      Let me know if this is not clear enough,.