No Such Thing as a Free Lunch: Principles of Economics (Part 125)

It's all about the money.

Joe Jackson

 Money Demand, the Equilibrium Interest Rate, and Monetary Policy

(Part E)

by

Charles Lamson

Having discussed the supply of money in the last several posts, we now turn to the demand for money. One goal of the next several posts and the previous posts is to provide a theory of how the interest rate is determined in the macroeconomy. Once we have seen how the interest rate is determined, we can turn to how the Federal Reserve (Fed) affects the interest rate through monetary policy.

It is important that you understand exactly what the interest rate is. Interest is the fee borrowers pay to lenders for the use of their funds. Firms and the government borrow funds by issuing bonds, and they pay interest to the firms and households (the lenders) that purchase those bonds. Households and firms that have borrowed from a bank must pay interest on those loans to the bank.

The interest rate is the annual interest payment on a loan expressed as a percentage of the loan. A $1,000 bond (representing a $1,000 loan from a household to a firm) that pays $100 in interest per year has an interest rate of 10 percent. The interest rate is expressed as an annual rate. It is the amount of interest received per year divided by the amount of the loan.

While there are many different interest rates, we will assume that there is only one. This simplifies our analysis yet provides a valuable tool for us to understand how the parts of the macroeconomy relate to one another.

The Demand for Money

What factors and what forces determine the demand for money are central issues in macroeconomics. As we shall see, the interest rate and the level of national income (Y) influence how much money households and firms wish to hold.

Before we proceed we must stress one point people find troublesome. When we speak of the demand for money, we are not asking these questions: "How much cash do you wish you could have?" "How much income would you like to earn?" "How much wealth would you like?" (The answer to these questions is presumably "as much as possible.") Instead, we are concerned with how much of your financial assets you want to hold in the form of money, which does not earn interest, versus how much you want to hold in interest-bearing securities, such as bonds. We take it as given the total amount of financial assets; our concern here is with how these assets are divided between money and interest-bearing securities.

The Transaction Motive

How much money to hold involves a trade-off between the liquidity of money and the interest income offered by other kinds of assets. The main reason for holding money instead of interest-bearing assets is that money is useful for buying things. Economists call this the transaction motive. This rationale for holding money is at the heart of the discussion that follows.

Assumptions To keep our analysis of the demand for money clear, we need a few simplifying assumptions. First, we assume there are only two kinds of assets available to households: bonds and money. By "bonds" we mean interest bearing-securities of all kinds. By "money" we mean currency in circulation and in deposits, neither of which is assumed to pay interest.

Second, we assume that income for the typical household is "bunched up." It arrives once a month, at the beginning of the month. Spending, by contrast is spread out over time; we assume that spending occurs at a completely uniform rate throughout the month---that is, that the same amount is spent each day (Figure 1). The mismatch between the timing of money inflow and the timing of money outflow is sometimes called the nonsynchronization of income and spending. 

FIGURE 1

Finally, we assume that spending for the month is exactly equal to income for the month. Because we are focusing on the transactions demand for money and not on its use as a store of value, this assumption is perfectly reasonable.

Money Management and the Optimal Balance

Given these assumptions, how would a rational person (household) decide how much of monthly income to hold as money and how much to hold as interest-bearing bonds? Suppose Jim decides to deposit his entire paycheck in his checking account. Let us say Jim earns $1,200 per month. The pattern of Jim's bank account balance is illustrated in Figure 2. At the beginning of the month Jim's balance is $1,200. As the month rolls by, Jim draws down his balance, writing checks or withdrawing cash to pay for the things he buys. At the end of the month, Jim's bank account balance is down to 0. Just in time, he receives his next month's pay check, deposits it, and the process begins again.

One useful statistic we will need to calculate is the average balance in Jim's account. Jim spends his money at a constant $40 per day ($40 per day * 30 days per month equals $1,200). His average balance is just his starting balance ($1,200) plus his ending balance (0) divided by 2, or ($1,200 + 0) divided by 2 equals $600. For the first half of the month Jim has more than his average of $600 on deposit, and for the second half of the month he has less than his average.

Is anything wrong with Jim's strategy? Yes. If he follows the plan described, Jim is giving up interest on his funds, interest he could be earning if he held some of his funds in interest-bearing bonds instead of in his checking account. How could he manage his funds to give himself more interest?

Instead of depositing his entire paycheck in his checking account at the beginning of the month, Jim could put half his paycheck into his checking account and buy a bond with the other half. By doing this, he would run out of money in his checking account halfway through the month. At a spending rate of $40 per day, his initial deposit of $600 would last only 15 days. Jim would have to sell his bond halfway through the month and deposit the $600 from the sale of the bond in his checking account to pay his bills during the second half of the month.

Jim's money holdings (checking account balances) if he follows this strategy are shown in Figure 3. When he follows the buy-a-$600-bond strategy, Jim reduces the average amount of money in his checking account. Comparing the dashed lines (bold strategy) with the solid green lines (buy-$600-bond strategy), his average bank balance is exactly half of what it was with the first strategy. 

The buy-a-$600-bond strategy seems sensible. The object of this strategy was to keep some funds in bonds, where they could earn interest, instead of as "idol" money. Why should he stop there? Another possibility would be for Jim to put only $400 into his checking account on the first of the month and buy two $400 bonds. The $400 in his account will last only 10 days if he spends $40 per day, so after 10 days he must sell one of the bonds and deposit the $400 from the sale in his checking account. This will last through the twentieth of the month, at which point he must sell the second bond and deposit the other $400. This strategy lowers Jim's average money holding (checking account balance) even further, reducing his money holdings to an average of only $200 per month, with correspondingly higher average holdings of interest-earning bonds. 

You can imagine Jim going even further. Why not hold all wealth in the form of bonds (where it earns interest) and make transfers from bonds to money every time he makes a purchase? If selling bonds, transferring funds to checking accounts, and making trips to the bank are without cost, Jim would never hold money for more than an instant. Each time he needed to pay cash for something or write a check, he would go to the bank (online or in person) or call the bank, transfer the exact amount of the transaction to his checking account, and either withdraw the cash or write the check to complete the transaction. If he did this constantly, he would squeeze the most interest possible out of his funds because he would never hold assets that did not earn interest.

In practice, money management of this kind is costly. There are brokerage fees and other costs to buy or sell bonds. At the same time, it is costly to hold assets in non-interest-bearing form, because they lose potential interest revenue.

We have a trade-off problem of the type that pervades economics. Switching more often from bonds to money raises the interest revenue Jim earns (because the more times he switches, the less, on average, he has to hold in his checking account and the more he can keep in bonds), but this increases the money management costs. Less switching means more interest revenue lost (because average money and holdings are higher) but lower money management costs (fewer purchases and sales of bonds).

The Optimal Balance There is a level of average money balances that earns Jim the most profit, taking into account both the interest earned on bonds and the costs paid for switching from bonds to money. This level is his optimal balance.

How does the interest rate affect the number of switches that Jim makes and thus the average money balance he chooses to hold? It is easy to see why an increase in the interest rate lowers the optimal money balance. If the interest rate were only 2 percent, it would not be worthwhile to give up much liquidity by holding bonds instead of cash or checking balances. However, if the interest rate were 30 percent, the opportunity cost of holding money instead of bonds would be quite high, and we would expect people to keep most of their funds in bonds and to spend considerable time managing their money balances. The interest rate represents the opportunity cost of holding money (and therefore not holding bonds, which pay interest). The higher the interest rate is, the higher the opportunity cost of holding money, and the less money people will want to hold. This leads us to conclude:

 

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 499-503)

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Graham Hancock Q&A - Part 2/2 - in Peru!

Graham Hancock Q&A - in Peru! Part 1/2

No Such Thing as a Free Lunch: Principles of Economics (Part 124)

The ultimate purpose of economics, of course, is to understand and promote the enhancement of well-being.

Ben Bernanke

The Money Supply and the Federal Reserve System

(Part G)

by

Charles Lamson

The Discount Rate

Banks may borrow from the Fed. The interest rate they pay the Fed is the discount rate. When banks increase their borrowing, the money supply increases. To see why this is true, assume there is only one bank in the country and the required reserve ratio is 20 percent. The initial position of the bank and the Fed appear in panel 1 of Table 3, where the money supply (currency + deposits) is $480. In panel 2, the bank has borrowed $20 from the Fed. By using this $20 as a reserve, the bank can increase its loans by $100, from $320 to $420. (Remember from part 121, the money multiplier = 1/required reserve ratio. So, a required reserve ratio of 20 percent gives a money multiplier of 5; having excess reserves of $20 allows the bank to create an additional $20 * 5, or $100, in deposits.) The money supply has thus increased from $480 to $580. Therefore:

Bank borrowing from the Fed leads to an increase in the money supply.

TABLE 3

The Fed can influence bank borrowing, and thus the money supply, through the discount rate: The higher the discount rate, the higher the cost of borrowing, and the less borrowing banks will want to do.

If the Fed wants to curtail the growth of the money supply, for example, it raises the discount rate and discourages banks from borrowing from it, restricting the growth of reserves (and ultimately deposits).

Historically, the Fed has not used the discount rate to control the money supply. Prior to 2003 it usually set the discount rate lower than the rate that banks had to pay to borrow money in the private market. Although this obviously provided an incentive for banks to borrow from the Fed, the Fed discouraged borrowing by putting pressure in various ways on the banks not to borrow. This pressure was sometimes called moral suasion.

On January 9th, 2003, the Fed announced a new procedure. Henceforth the discount rate would be set above the rate that banks pay to borrow money in the private market, and moral suasion would no longer be used. Although banks can now borrow from the Fed if they wish to, they are unlikely to do so except in unusual circumstances because borrowing is cheaper in the private market. It is thus clear that the Fed is not using the discount rate as a tool to try to change the money supply on a regular basis.

Open Market Operations

By far the most significant of the Fed's tools for controlling the supply of money is open market operations. Congress has authorized the Fed to buy and sell U.S. government securities in the open market. When the Fed purchases a security, it pays for it by writing a check that, when cleared, expands the quantity of reserves in the system, increasing the money supply. When the Fed sells a bond, private citizens or institutions pay for it with a check that, when cleared, reduces the quantity of reserves in the system.

To see how open market transactions and reserve controls work, we need to review several key ideas.

Two Branches of Government Deal in Government Securities The fact that the Fed is able to buy and sell government securities---bills and bonds---may be confusing. In fact, two branches of government deal in financial markets for different reasons, and you must keep the two separate in your mind.

First, keep in mind that the Treasury Department is responsible for collecting taxes and paying the federal government's bills. Salary checks paid to government workers, payments to General Dynamics for a new Navy ship, Social Security checks to retirees and so forth are all written on accounts maintained by the Treasury. Tax receipts collected by the Internal Revenue Service, a Treasury branch, are deposited to these accounts.

If total government spending exceeds tax receipts, the law requires the treasury to borrow the difference. Recall that the government deficit is (G - T), or government purchases minus net taxes. (G - T) is the amount the treasury must borrow each year to finance the deficit.

The Fed is not the treasury. Instead, it is a quasi-independent agency authorized by Congress to buy and sell outstanding (preexisting) U.S. government securities on the open market. The bonds and bills initially sold by the treasury to finance the deficit are continuously resold and traded among ordinary citizens, firms, banks, pension funds, and so forth. The Fed's participation in that trading affects the quantity of reserves in the system, as we will see. 

Because the Fed owns some government securities, some of what the government owes, it owes to itself. The Federal Reserve System's largest single asset is government securities. These securities are nothing more than bills and bonds initially issued by the treasury to finance the deficit. They were acquired by the Fed over time through direct open-market purchases that the Fed made to expand the money supply as the economy expanded.

The Mechanics of Open Market Operations How do open market operations affect the money supply? Most of the fed's assets consist of the government securities we have just been talking about.

Suppose the Fed wants to decrease the supply of money. If it can reduce the volume of bank reserves on the liability side of its balance sheet, it will force banks in turn to reduce their own deposits (to meet the required reserve ratio). Since these deposits are part of the supply of money, the supply of money will contract.

What will happen if the Fed sells some of its holdings of government securities to the General Public? The Fed's holdings of government securities must decrease, because the securities it sold will now be owned by someone else. How do the purchasers of securities pay for what they would have bought? By writing checks drawn on their banks and payable to the Fed.

Let us look more carefully at how this works, with the help of Table 4. In panel 1, the Fed initially has $100 billion of government securities. Its liabilities consist of $20 billion of deposits (which are the reserves of commercial banks) and $80 billion of currency. With the required reserve ratio at 20 percent, the $20 billion of reserves can support $100 billion of deposits in the commercial banks. The commercial banking system is fully loaned up (actual reserves are equal to required reserves). Panel 1 also shows the financial position of a private citizen, Jane Q. Public. Jane has assets of $5 billion (a large checking account deposit in the bank) and no debts, so her net worth is $5 billion.

Now imagine that the Fed sells $5 billion in government securities to Jane. Jane pays for the securities by writing a check to the Fed, drawn on her bank. The Fed then reduces the reserve account of her bank by $5 billion. The balance sheets of all the participants after this transaction are shown in panel 2. Note that the supply of money (currency plus deposits) has fallen from $180 billion to $175 billion.

This is not the end of the story. As a result of the Fed sale of securities, the amount of reserves has fallen from $20 billion to $15 billion, while deposits have fallen from $100 billion to $95 billion. With a required reserve ratio of 20 percent, banks must have .20 * 95 billion, or $19 billion in reserves. Banks are under their required reserve ratio by $4 billion [$19 billion (the amount they should have) minus $15 billion (the amount they do have)]. To comply with the federal regulations, banks must decrease their loans and their deposits.

The final equilibrium position is shown in panel 3, where commercial banks have reduced their loans by $20 billion. Notice that the change in deposits from panel 1 to panel 3 is $25 billion, which is 5 times the size of the change in reserves that the Fed brought about through its $5 billion open-market sale of securities. This corresponds exactly to our earlier analysis of the money multiplier. The change in money (-$25 billion) is equal to the money multiplier (5) times the change in reserves (-$5 billion).

Now consider what happens when the Fed purchases a government security. Suppose I hold $100 in Treasury bills, which the Fed buys from me. The Fed writes me a check for $100, and I turn in my Treasury bills. I then take the $100 check and deposit it in my local bank. This increases the reserves of my bank by $100 and begins a new episode in the money expansion story. With a reserve requirement of 20 percent, my bank can now lend out $80. If that $80 is spent and ends up back in a bank, that bank can lend $64, and so forth. The Fed can expand the money supply by buying government securities from people who own them, just the way it reduces the money supply by selling these securities.

Each business day, the open market desk in the New York Federal Reserve Bank buys or sells millions of dollars' worth of securities, usually to large security dealers who act as intermediaries between the fed and the private markets. We can sum up the effect of these open market operations this way:

• An open market purchase of Securities by the Fed results in an increase in reserves and an increase in the supply of money by an amount equal to the money multiplier times the change in reserves.

•  An open market sale of securities by the Fed results in a decrease in reserves and a decrease in the supply of money by an amount equal to the money multiplier times the change in reserves.

Open market operations are the Fed's preferred means of controlling the money supply for several reasons. First, open market operations can be used with some precision. If the Fed needs to change the money supply by just a small amount, it can buy or sell a small volume of government securities. If it wants a larger change in the money supply, it can buy or sell a large amount. Second, open market operations are extremely flexible. If the Fed decides to reverse course, it can easily switch from buying securities to selling them. Finally, open market operations have a fairly predictable effect on the supply of money. Because banks are obliged to meet their reserve requirements, an open-market sale of $100 in government securities will reduce reserves by $100, which will reduce the supply of money by $100 times the money multiplier.

Where does the Fed get the money to buy government securities when it wants to expand the money supply? The Fed creates it. In effect, it tells the bank from which it has bought a $100 security that its reserve account (deposit) at the Fed now contains $100 more than it did previously. This is where the power of the Fed, or any central bank, lies. The Fed has the ability to create money at will. In the United States, the Fed exercises this power when it creates money to buy government securities.

The Supply Curve for Money

Thus far we know how the Fed can control the money supply by controlling the amount of reserves in the economy. If the Fed wants the quantity of money to be $1,200 billion on a given date, it can aim for this target by changing the discount rate, by changing the required reserve ratio, or by engaging in open market operations. In this sense, the supply of money is completely determined by the Fed, and the money supply curve in Figure 5 is a vertical line.

Because the Fed, through open market operations, can choose whatever value of the money supply that it wants, it is useful to begin with the case in which the Fed picks a value independent of anything in the economy. In other words, we are assuming for now that the Fed's choice of the value of the money supply does not depend on things like inflation, unemployment, and aggregate output. This assumption is released in upcoming posts. We will see in these upcoming posts that in practice the Fed chooses a value of the money supply to hit a particular value of the interest rate, where the Fed's choice for the target interest rate depends on things like inflation and unemployment. But this is jumping ahead of the story. 

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 492-495*

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No Such Thing as a Free Lunch: Principles of Economics (Part 123)

The Federal Reserve ranks among the most transparent central banks. We publish a summary of our balance sheet every week. Our financial statements are audited annually by an outside auditor and made public. Every security we hold is listed on the website of the Federal Reserve Bank of New York.

Janet Yellen

The Money Supply and the Federal Reserve System

(Part F)

by

Charles Lamson

How the Federal Reserve Controls the Money Supply

To see how the Fed controls the money supply in the U.S. economy we need to understand the role of reserves. As we have said, the required reserve ratio (a central bank regulation that sets the minimum amount of reserves that must be held by a commercial bank) establishes a link between the reserves of the commercial banks and the deposits (money) that commercial banks are allowed to create.

The reserve requirement effectively determines how much a bank has available to lend. If the required reserve ratio is 20 percent, each $1 of reserves can support $5 in deposits. A bank that has reserves of $100,000 cannot have more than $500,000 in deposits. If it did it would fail to meet the required reserve ratio.

The money supply is equal to the sum of deposits inside banks and the currency in circulation outside of banks. Reserves provide the leverage that the Fed needs to control the money supply.

If the Fed wants to increase the supply of money, it creates more reserves, thereby freeing banks to create additional deposits by making more loans. If it wants to decrease the money supply, it reduces reserves.

These three tools are available to the Fed for changing the money supply: (1) changing the required reserve ratio; (2) changing the discount rate; and (3) engaging in open market operations. Although (3) is almost exclusively used it to change the money supply, an understanding of how (1) and (2) work is useful in understanding how (3) works. We thus begin our discussion with the first two tools.

The Required Reserve Ratio

One way for the Fed to alter the supply of money is to change the required reserve ratio. This process is shown in Table 2. Let us assume the initial required reserve ratio is 20 percent.

TABLE 2

In panel 1, a simplified version of the Fed's balance sheet (in billions of dollars) shows that reserves are $100 billion and currency outstanding is $100 billion. The total value of the Fed's assets is $200 billion, which we assume to be all in government securities. Assuming there are no excess reserves---banks stay fully loaned up (actual reserves are equal to required reserves)---the 100 billion dollars in reserves supports $500 billion in deposits at the commercial banks. [Remember from part 121, the money multiplier = 1/required reserve ratio = 1/20 = 5. Thus, $100 billion in reserves can support $500 billion dollars ($100 billion * 5) in deposits when the required reserve ratio is 20 percent]. The supply of money [M1, or transactions money (physical currency, demand deposit, traveler's checks, and other checkable deposits] is therefore $600 billion: $100 billion in currency and $500 billion in (checking account) deposits at the commercial banks.

Now suppose the Fed wants to increase the supply of money to $900 billion. If it lowers the required reserve ratio from 20 percent to 12.5 percent (as in panel 2 of Table 2), then the same $100 billion of reserves could support $800 billion in deposits instead of only $500 billion dollars. In this case, the money multiplier is 1/.125, or 8. At a required reserve ratio of 12.5 percent, $100 billion in reserves can support $800 billion in deposits. The total money supply would be $800 billion in deposits plus $100 billion in currency, for a total of $900 billion.

Put another way, with the new lower reserve ratio, banks have excess reserves of $37.5 billion. At a required reserve ratio of 20 percent, they needed $100 billion in reserves to back their $500 billion in deposits. At the lower required reserve ratio of 12.5 percent, they need only $62.5 billion of reserves to back their $500 billion of deposit, so the remaining $37.5 billion of the existing $100 billion in reserves are "extra." With that $37.5 billion of excess reserves, banks can lend out more money. If we assume the system loans money and creates deposits to the maximum extent possible, the $37.5 billion of reserves will support an additional $300 billion of deposits ($37.5 billion * the money multiplier of 8 = $300 billion). The change in the required reserve ratio has injected an additional $300 billion into the banking system, at which point the banks will be fully loaned up and unable to increase their deposits further:

For many reasons, the Fed has tended not to use changes in the reserve requirement to control the money supply. In part, this reluctance stems from the era when only some banks were members of the Fed and, therefore, subject to reserve requirements. The Fed reasoned that if it raised the reserve requirement to contract the money supply, banks might choose to stop being members. (Because reserves pay no interest, the higher the reserve requirement, the more the penalty imposed on those banks holding reserves.) This argument no longer applies. Since the passage of the Depository Institutions Deregulation and Monetary Control Act in 1980, all depository institutions are subject to federal requirements.

It is also true that changing the reserve requirement ratio is a crude tool. Because of lags in banks' reporting to the Fed on their reserve and deposit positions, a change in the requirement today does not affect banks for about 2 weeks. (However, the fact that changing the reserve requirement expands or reduces credit in every bank in the country makes it a very powerful tool when the Fed does use it.) 

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 489-491*

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