The Banking System Made Simple

One of the most popular discussions on the web is banking. Numerous commentators have been commenting on how banks work or how we perceive that they work. These views are occasionally correct while they are also occasionally wrong. In addition, a relative confusion on how bank loans are created or why deposits are needed by the banks appears to exist. What follows are three simple examples intending to indicate how banking really works, how deposits and loans are created and how the Central Bank functions in a financial system.

In all examples, we assume (for simplicity) a closed economy where banks face a mandatory reserve requirement of 10% and a Tier 1 ratio which cannot fall under 10%. It is also assumed that the money needed in the economy for transactions is on average a fixed amount M (already existing in the economy) and all loans have a fixed risk weight of 40%. 

Note: all of the above assumptions can be altered with no change to the conclusions reached.

Example 1:One-Bank Economy

In this economy we have a bank which has in its balance sheet deposits of 100 units of currency with its equity being 10. In period 1 it decides, according to the regulations imposed above, to lend out 90 units. These units, we have just one bank in the economy will be deposited in the banks' accounts. A simple balance sheet would indicate the following:

Then, the bank would continue to operate under the same way until it reached the limit of 10%. This limit is nevertheless not the one imposed by the reserve requirements but by the Tier 1 needs. The reserve requirements would, under these assumptions, allow the amount of loans available in the economy to reach 1000 units had there not been for the Tier 1 ratio which essentially forces the bank to stop at 250 (for more details about the money multiplier see this). The "final" balance sheet would look like this:

Example 2: Two-Bank Economy

Now let's suppose that 2 banks exist in the economy, both having a 50% share of the market. Their equity values would be 5 each and their starting deposits would be 50.

In the first period of time, each bank will lend 45 units to the public. Each bank knows that it controls only 50% of the market thus it makes sense to expect 22.5 of those units to be deposited in its rival. Yet, the total amount of loans in the economy has not been altered even though the banks are now more and lending less individually. Total loans will still be 90 and they will be divided equally between each bank. Thus, each bank now knows that if the other bank lends as much as it will they will both get back in the form of deposits as much currency as they have provided as loans. In addition, the number of banks is irrelevant to the conclusion, as is their market share. If we had 10 or 200 banks in the economy total loans would still be 90 and the market share would have been the same after the lending as it was before. More still, the situation would not have been altered even if market shares were unequal. 

With some frictions, this is what most commonly occurs in real life: as banks do not have the same amount of loan applications or do not grant the same amount of loans in each period of time, market shares are continuously changing. Thus, although banks (usually) want to lend until their Tier 1 limit is reached, they cannot do this as easily (either because of lower demand or because applications do not match the perceived risk-reward profile needed) thus making market shares and loans growing at different paces in every bank. In addition, reputation makes a great difference; banks who were leading the market once are now mere followers as clients view others as better alternatives.

Example 3: Two-Bank Economy with a Central Bank Providing Liquidity

Assuming that the previous initial conditions hold, the situation should theoretically be the same. Yet, reality is different. Since the Central Bank can provide liquidity (what is called ELA in the Eurozone) for banking needs then it means that the banks can allocate their loans based on demand and not based on their liquidity constraints; what the Central Bank essentially does is eliminate the liquidity constraints in the short-run by lending banks. 

The situation would unfold as following: In period 1, banks face increased demand and decide that they should lend 60 units each instead of the 45 they are allowed by their liquidity constraints. This means that the Central Bank has agreed to lend an additional 21 units of currency (additional 10 to cover for the difference from 50 to 60 and another 11 so that they can have their regulatory minimum and not fact trouble in their day-to-day operations) to each bank with the banks promising to return it at a later date. The banks' balance sheets would now look like:

Notice that the Tier 1 ratio was 28% in Example 1's first period while it is 21% now. The reason is simple: more loans can be generated in less time using the Central Banks' available liquidity. 

A question is how the Central Bank will get its money back; after all this funding is nothing but a loan to the bank. Notice now that the bank who received the funding still has received 60 units of capital as deposits back. Now, according to the rules, the bank only has to maintain 11 units (10% of total deposits, i.e. 110) for liquidity. This means that it can afford to give the liquidity back to the Central Bank, hold the regulatory minimum for liquidity and still have 28 units (60-21-11) at hand which it will be able to lend in the next period.  That is if the bank does not get any more funding from the Central Bank to boost its loans.

As with example 2, in reality things are a little different. Banks not only borrow from the Central Bank but from each other as well, since their liquidity is changed every day (as stated before loan grants and demand is unequal between banks) and they may find themselves in need of some extra cash or have some extra liquidity which they prefer to lend out in order to get some interest instead of having it idle.

From the above examples we can derive the following conclusions:

• Deposits matter with regards to liquidity. Yet, they do not matter to the amount of loans to be given. As the balance sheets have indicated loans cancel out since their creation is a simultaneous creation of an asset and a liability. Thus, the bank has no limitation to the amount of loans it can create other than the regulatory capital requirements (e.g. Tier 1)
• The amount of money given by the Central Bank will be returned to it, yet its effect will be permanent. If the Central Bank agrees to give X units of currency to the banks then the money supply will be increased by more than X permanently even if banks return it to the Central Bank. This happens because that money is created by the banks and even if the extra liquidity is returned the amount of loans in the economy would have still been increased.
• The starting value of deposits is irrelevant. It does not matter whether initial deposits were 10 units of 10 million units. The amount of loans to be granted will be exactly equal to the amount allowed by the regulatory requirements and not by the initial state of deposits (obviously, deposits have to be greater than 0 for this to work since the bank cannot print money).
• The more cash at hand and the more government bonds banks purchase the more money supply they can create since both instruments are of zero risk weight and are thus excluded from the calculation.
• Increased regulatory requirements at a given amount of equity, means that less loans can be created, thus making money supply will in general be less; an increase in the regulatory requirement (e.g. from 10% to 11%) means that ceteris paribus less new loans will be created in the future. This situation is evident in the EU at the moment.
• The only way for money supply to be increased is for banks to raise more equity. If it is raised then more money can be created in the economy.

As the reader has seen through this analysis, the way banking works is not as complicated as we usually think it is. Nevertheless, understanding how the banking system works is paramount to the economy and has been an issue which had received much less attention than it should have. As stated above, the examples can be very easily extended to include more complexity; yet understanding the larger image can most of the times provide us with more knowledge than by narrowing our focus to the specifics of banking.

Inflation and the Long Run

Milton Friedman is known for the famous monetarist aphorism "inflation is everywhere and always a monetary phenomenon", a doctrine which has been fed to a whole generation of economists, especially in the US. Monetarists believed that in any case, inflation is, in the long-run, determined by the rate of change of the money supply. Nevertheless, this has not been the case even in Friedman's time, and it will never be so in ours.

First of all, let us determine what we mean by money supply. Usually, depending on what measure we use, we either mean the monetary base (i.e. the amount of money circulated by the government) or the monetary base plus the amount of money held at banks, depending on the measure we wish to employ. The amount held by banks is usually the result of bank credit, i.e. bank-created money through the process of the money multiplier. Although during Friedman's time, money supply usually meant the monetary base, the case holds even if we use the broader measures.

As stated in the last article, money supply and bank credit make up for much of the inflation in a country. Nevertheless, they do not make up for all of it, neither do they determine the final rate. The famous "in the long run" statement does not hold for such issues. The long run is always determined by the short- and medium-run. For example, let us assume that we raise the money stock in the economy by 1% per year over the next 30 years and we expect that to be the long-term inflation rate. Even if we use the average of those years, then we would not end up with just a 1% inflation rate. 

The reason is relatively simple: the long-run has the short- and medium-run embedded in them. Using our previous example, we would expect that in 2043, our average 30-year inflation rate would be 1%. Yet, in the past 10 years, i.e. the medium term, we might have experienced a recession or a depression, which lowered the velocity of money, the inflation rate would have been significantly lower than what we expect. Data for the United States, obtained via the St. Louis Federal Reserve, indicate something similar for the 29 years from March 1984 until April 2013.

The simple average of the monthly change in inflation over the past 29 years was approximately 0.23%, while the monetary base grew by an average 0.56% and the broad M2 money measure by 0.46%. As the data indicate, the change in inflation is about half the change in all other measures. Not even the MZM measure, which is supposedly better in predicting inflationary powers, fares any better: it's average is 0.61%, far greater than the rest and about 2.5 greater than the actual inflation rate. 

Many readers, on observing the spikes on the monetary base, may be inclined to treat them as outliers and comment that without them, the situation might have been just like Friedman described it. I beg to differ. Those outliers are exactly the outcome of a world without a steady state, with large deviations from a stable equilibrium (if one exists), forcing economists to realize that their predictions and remedies might not work in the real world. If, in the case of the monetary base, we excluded all observations which are in excess of 1% as being outliers, we would effectively eliminate approximately 30% of the observations. Thus, one may safely conclude that either our sample is erroneous (which is not the case here) or that the "outliers" are an important part of our world.

Concluding, although money supply can assist us in explaining inflation rate, it does not tell us the whole story, as data indicate. A simple explanation is that money needs to be spent in order for inflation to be affected. Even  if the government prints money or if banks create more credit, if people are still afraid to spend because they feel the need to save more for the future then inflation is not affected. Policy-wise, it is not enough to make people not willing to keep their money in a bank. In order to move from depression to growth you have to persuade them to spend as well.

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.

Model:

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.