Interest rate

When you borrow money, you usually have to pay a fee for the loan. This fee is often called interest, particularly if the fee is proportional to the amount you borrow. The interest rate is commonly expressed as a percentage of the size of the loan per unit of time, typically per year.

If the interest rate is 10% per year, you must, for example, pay 1,000 per year if you borrow 10,000. The interest rate may be fixed or floating. If it is fixed, you will pay the same percentage for the entire duration of the loan. With a floating interest rate, the interest rate will change regularly depending on market conditions.

The Interest rate for a specific loan depends on the general level of interest rates as well as the specifics of the loan. Factors such as risk (the probability that the loan will not be repaid), duration of the loan and whether you select a fixed or a floating rate will influence the interest rate.

Market interest rates

The most important interest rates from a macroeconomic perspective are interest rates that the government pays on the loans they use to finance the national debt. The government borrows money by issuing government bonds. All such bonds have a fixed nominal amount and a given maturity date.

The government promises to pay exactly the nominal amount (also called the principal or the face amount) to the holder at the maturity date. Some bonds also promise regular payments, so-called coupon payments, at regular intervals, the coupon dates.

In most countries, you will find many types of government bonds. An important distinction is the duration of the bond, that is, the difference between the maturity date and the date when the bond was issued. For example, in the United States, government bonds maturing in one year or less are called Treasury bills.

Typically, bonds with a maturity of a year or shorter have no coupons. Instead, they are sold below the nominal amount at what is called the issue price. The issue price for a bond without coupons must be below the nominal amount. For example, if you pay 23,500 for a bond with a nominal amount of 25,000 maturing in one year, your interest rate is (25 000 − 23 500)/23 500 = 6.38%.

In most countries, you also find government bonds with longer maturity. For example, in the United States you have Treasury notes (two to ten years) and Treasury bonds (10 years or longer). Government bonds with longer maturity typically make coupon payments. You will also find other types of bonds

Relationship between the interest rate and the bond price

Note that the higher the issue price, the lower the interest rate. In the same way, when the price of a government bond increases, the interest rate falls and vice versa. The price of a government bond is normally determined by supply and demand which means that you can understand movements in these interest rates by analyzing the market. For example, if the government needs to borrow more money, supply increases, bond prices fall and interest rates increase.

Calculating interest rates on a yearly basis

If the maturity is different from one year, the interest rate is usually recalculated to a corresponding one year rate. For example, consider a bond that matures in six months, has a nominal amount of 25,000 and a current price of 24,200 (no coupons). The six month interest rate is then 800/24,200 = 3.3%. If we want to express this rate as a yearly rate we imagine that we make this investment twice.

Our return would then be 1.033*1.033 = 1.067 or 6.7%. Note that if the interest rate is fairly low, then the yearly interest rate is approximately two times the six month interest rate. In the same way, the monthly interest rate is approximately one-twelfth of the yearly interest rate.

Keep in mind that the six month interest rate, recalculated to a yearly rate, will typically not be equal to the one year interest rate. For example, suppose that we expect interest rates to increase. In such a case, the yearly interest rate would be an average of the current six month rate and the six month rate six months from now, which is expected to be higher. Hence, the one year rate would be higher than the current six month rate. In the same way, if we expect interest rates to fall, then shorter interest rates will be higher than longer interest rates.

This means that we have many different market rates in a country – rates depending on maturity. Even though rates with different maturity (all recalculated to a yearly rate) need not be exactly equal, they cannot be too different either. This is particularly true for rates with a similar maturity. The seven month rate cannot deviate far from the six month rate since they are fairly close substitutes.

The yield curve

The yield curve is a graph of interest rates of different maturity (recalculated to yearly rates) at a particular point in time. It is common for the yield curve to slope upwards (interest rates with longer maturity are generally higher than those with a shorter maturity). The reason for this is that there is a higher demand for loans with longer maturity due to the reduced uncertainty. Many borrowers are prepared to pay a premium to avoid fluctuations in the interest rates.

As discussed above, if the market expects higher interest rates, then the slope of the yield curve will increase. Although not very common, the slope may be negative if the market expects the interest rates to fall more than the premium on longer rates.

Other interest rates

There are many other interest rates in society. For example, you will earn interest when you deposit money in a bank account and you will pay interest when you borrow money. These interest rates will depend on the specifics of the deposit and the perceived risk when you borrow money. However, all interest rates are correlated with market interest rates. When you borrow money, you typically pay a higher interest rate compared to government bonds, and when you lend money, you will receive a lower rate.

Overnight interest rates

The market for overnight loans

Overnight interest rates are rates for loans over a single night – these are the shortest of all interest rates. During the day, banks normally have access to interest-free loans from the central bank. At the end of the day, all such loans must be cleared with the central bank. For this reason, there is a market for loans overnight between banks and the overnight interest rate is determined by supply and demand in this market.

Central bank overnight interest rate

The overnight interest rate is an important interest rate for a central bank and it has methods of influencing this rate. In most countries, the central bank signals what it would like the overnight rate to be. For example, in the United States, this rate is the federal funds rate. If the overnight rate steers away from the federal funds rate, the Federal Reserve will take action to steer it back towards the federal funds rate.

In addition to signaling a desired overnight interest rate, most central banks have “standing facilities” for overnight loans. For example, the ECB has a “deposit facility” and a “marginal lending facility” that member banks can use for deposits and for lending overnight. The overnight interest rate must therefore be in between the deposit rate and the marginal lending rate. Typically, the overnight rate is far from the deposit and lending rates and standing facilities are rarely used.

Monetary policy

The central bank and monetary policy

By monetary policy, we mean the policy directed at controlling the money supply and the interest rates. In most countries, the central bank is responsible for monetary policy. It usually has complete or nearly complete control over:

• Overnight interest rates
• The monetary base

It also has some control over:

• Interest rates with longer maturity. Since loans with longer maturities are substitutes for overnight loans, the central bank also has some control over longer interest rates. The control is larger for shorter rates. This relationship is discussed further in overnight rates and interest rates with longer maturity.
• Money supply. The monetary base is only a small part of the total money supply but, through the multiplier effect, the central bank’s control over the money supply is magnified. This is examined in the monetary base and the supply of money.
• Inflation. For many central banks, this is the variable they are most interested in controlling.

For all central banks, it is an important variable. Exactly how the central bank affects inflation by controlling the overnight interest rate and monetary base is one of the most important issues in macroeconomic theory and will be discussed throughout the book.

As we shall see in the next section, it is not possible to choose the overnight interest rate and monetary base independently of each other. In most countries, the main focus of the central bank is on controlling the overnight interest rate rather than the monetary base. The next section shows that the central bank must increase the monetary base if it wants to lower the overnight interest rate. When it increases the monetary base, the money supply will increase and we will see a negative correlation between the overnight rate and money supply.

When the overnight interest rate decreases, the money supply increases

When the overnight interest rate increases, the money supply decreases

The rest of this section describes:

• How the monetary base affects the money supply through the multiplier effect.
• How changes in the overnight rate cause changes in the money supply.
• How the central bank’s control over the overnight interest rate affects longer interest rates.
• How the central bank can affect inflation by controlling the overnight interest rate.

Monetary base and the supply of money

It is not possible for the central bank to print and distribute money - that would increase their debt without increasing their assets. Instead, they change the monetary base by buying and selling financial assets (usually government bonds) in so-called open market operations. Let us say that the central bank buys government securities for 100 million. They can pay for these bonds simply by printing new bills to the amount of 100 million. At first, this may seem suspicious and "too simple". But remember that outstanding notes count as a liability for the central bank. When it buys government securities, its assets will increase by exactly the same amount as its liabilities.

Typically, the central bank will not pay cash when it buys government securities. Instead, it will ask the seller’s bank to credit the individual’s account and will then credit the bank’s central bank account.

This procedure is equivalent to paying in cash – the monetary base will increase by the same amount in both cases (remember that the banks' assets in the central bank are included in the monetary base). Since this will lead to an increase in deposits in the banks, the money supply will increase. By the multiplier effect, the increases in the money supply will be more than 100 million. This way, the central bank can influence the money supply several-fold by changing the monetary base.

Overnight interest rates targets and money supply

There are many ways to explain the important connection between the overnight interest rate target and the money supply. We will use an example to demonstrate why a decrease in the overnight rate target increases the money supply.

Imagine that the central bank changes the target from 6% to 4%. Before lowering their target, overnight interest rates were at around 6%, say between 5.6% and 6.4%. When the central bank cuts the target to 4%, it signals that it wants to see an overnight rate around 4%.

Remember that central banks normally have standing facilities allowing banks to borrow from the central bank at a rate slightly above the target rate (and to lend at a rate slightly below). If the central bank does nothing except to change the target rate, the banks would immediately use the standing facilities and borrow from the central bank.

They were used to borrowing at rates around 6% overnight but can now borrow from the central bank at slightly above 4%. But the central bank does not want the standing facilities to be used – it wants the overnight rate to be close to the target such that the banks lend and borrow from each other in the market. The question then is, how can they influence the overnight market so that banks will want to borrow/lend at around 4%? The answer is by increasing the monetary base and thus the money supply.

When the central bank buys government securities, it purchases from many individuals, companies and institutions. Deposits and reserves in most banks will increase as described in the previous section.

Therefore, most banks will want to lend overnight and this will drive down the overnight interest rate. To summarize: When the Central Bank cuts the target rate, they must simultaneously increase the monetary base by buying government securities. The growth of the monetary base creates a surplus in the banks, the supply of funds overnight increases, the demand falls and the overnight rate falls.

Although the monetary base represents a small portion of the money supply, a change in the monetary base is magnified by the multiplier effect.

Overnight rates and interest rates with longer maturity

By controlling overnight interest rates, the central bank will affect the interest rates with longer maturity. The reason for this is that interest rates with similar maturity cannot be too different. If, for example, the central bank increases the target rate (move intercept on the yield curve upwards), then interest rates with short maturity will very likely increase but longer interest rates may also increase.

Let’s say that the central bank increases the target rate. When the target rate increases, the central bank needs to raise the overnight interest rate which may be accomplished by selling government securities.

The central bank will then debit the commercial banks’ central bank accounts and the banks will debit the accounts of the buyers of the securities. The reserves will now be too small, and this will create upward pressure on the overnight interest rate. To create a long-term balance, banks will want to increase their deposits and reduce their lending. They can achieve this by raising bank interest rates.

Another way to explain why banks raise their interest rates is as follows. With higher overnight interest rates, it is more expensive for banks to end the day with a deficit. To reduce the risk of having to borrow overnight, they can increase their reserves by increasing deposits and reducing loans, which they again accomplish by raising the interest rates.

Market interest rates are affected as well. First, when the central bank sells government securities, the price of these securities will fall and the interest rate will increase. Second, government securities are close substitutes for bank deposits, and when one of these rates changes, the other follows suit.

Overnight target rates and inflation

One of the main targets of every central bank is low and stable inflation. Its main control variable is the overnight interest rate target, and the mechanism that allows the target to affect inflation is called the transmission mechanism. A brief description of the transmission mechanism looks like this:

• When the central bank target rate increases, other interest rates in the economy will increase (and the money supply will decrease, but that is not important here).
• With higher interest rates, it is more expensive to borrow and more advantageous to save. Therefore, consumption and investment will decrease (we say that the central bank "cools off" the economy).
• As consumption and investment fall, GDP is reduced and unemployment will rise. This will cause inflation and the growth rate in wages to fall. The exact details in this mechanism will be discussed in the following chapters.

The real interest rate

Interest rates and inflation

Suppose you have 1 million on 1st January 2008. A basket of goods and services similar to the CPI basket costs 100,000. You can then buy exactly 10 such baskets on 1st January 2008.

Say that you can invest your million at a 10% interest rate. On 1st January 2009, you will then have 1.1 million. 1.1 million may not be enough for 11 baskets as prices may have changed. Say that inflation was 4% in 2008. The price of a basket has then increased to 100,000 * 1.04 = 104,000 and you can buy 1,100 / 104 = 10.58 baskets, which is 5.8% more than last year. Even though your wealth has increased by 10% (in whatever currency you use), your real wealth (in baskets) has only increased by 5.8% and we say that the real interest rate is 5.8%.

Nominal and real interest rates

To distinguish the real interest rate from the "normal" interest rate, the latter is called the nominal interest rate. The nominal interest rate shows the growth of your money while the real rate shows the growth of what your money can buy.

Expected inflation

Note that it is changing in prices during 2008 which matters for the high real interest rate (the time period when your deposit is earning interest). This means that you can never know how high the real rate is actually going to be when you start to save on 1st January 2008, even if you know the nominal interest rate exactly. Crucial to the determination of the real rate is the expected inflation - the inflation expected in the year you save.

The relation between nominal interest rate, real interest rate and inflation

If we denote the nominal interest rate by R, the real rate by r and the expected inflation by πe then the real interest rate is defined by:

r = R – πe or R = r + πe

Many textbooks use actual inflation (as measured during the previous period) instead of expected inflation in the definition of the real interest rate. Such a definition is not entirely incorrect (although the correct definition uses expected inflation), as expected inflation is often close to the current observed inflation.