The Determination of Interest Rates

 

  1. Introduction
  2. We have referred in various places in the course to the 'interest rate' in the economy and we have considered the interest rate as an instrument of monetary policy. However, we have not looked in a systematic way at the factors influencing the level of interest rates in the economy. In fact, two quite different appraoches to the determination of interest rates have been taken by economists. One of these we considered when we were discussing the demand for money - notably, the idea of the speculative demand for money put forward by Keynes. This is known as the liquidity preference theory of interest rates. Influential though this model has been, another theory has dominated the thoughts of most economists. It is known as the loanable funds theory. We shall look at it first here.

     

  3. The Loanable Funds Theory of Interest Rates
  4. The loanable funds theory is a theory of the determination of real interest rates - that is, rates of return expressed in terms of real purchasing power. The theory derives from the notion that savers make a decision between consumption now and consumption in the future. The more people consume now out of present income (and the less they save and hence the smaller are the funds available for investment), the lower will be future income. Thus, a trade off always exists between present consumption and future consumption. It is assumed that people would prefer to consume now, other things being equal. Hence, to persuade them to save and provide funds for investment, they must be paid interest. The real interest rate is therefore the rate needed to persuade people to forgo present consumption. It was sometimes referred to as the reward for waiting - the reward for postponing the pleasure of consumption and waiting to consume later. It follows that savings will be positively related to the rate of interest.



    Real investment, on the other hand, is a negative function of the interest rate since the interest rate reflects the productivity of investment projects. The lower the rate of interest the more investment projects become profitable and the more willing investors will be to borrow in order to invest. Thus, we obtain savings and investment curves as shown in Figure 1.

    Thus, the real interest rate is determined by the intersection of the demand for savings (the willingness to forgo present consumption - sometimes referred to as thrift) and the demand for investment (reflecting the productivity of investment projects). This all assumes that present income and the rates of return on investment projects are known, allowing people to make a rational choice between goods now and goods in the future.

    One problem with this is that the interest rates one sees quoted every day are not expressed in real terms. Rather, they are nominal rates of interest, reflecting the money return on savings and investment. This can be overcome by adding to the real interest rate, the rate of inflation. This is based on the argument that a saver wanting a real rate of return of, say 5 per cent, will take into account the rate of inflation over the period of the loan he is making. If the rate of inflation is 4 per cent, he will demand a return of 9 per cent per annum, so as to obtain the 5 per cent real rate he is seeking. Actually, the nominal rate of interest should equal the real rate of interest plus the expected rate of inflation. Of course, if we assume that savers know what the future rate of inflation will be, there is no problem since the expected rate of inflation will be equal to the actual rate of inflation in the future. If people make incorrect forecasts of the future rate of inflation, the real rate of interest will be different from the rate of interest savers want.

    Assume that a saver makes a loan of 1,000 for one year and charges 8 per cent interest - a real rate of 5 per cent which he wants to persuade him to save and lend the money rather than to spend it himself now on goods and services plus an extra 3 per cent which is his estimate of the rate of inflation over the next year. Suppose now that the rate of inflation turns out to be 10 per cent. The actual real rate of interest will then turn out to be negative (-2%). According to this theory, however, this can only be a temporary phenomenon. As soon as our saver realizes what the true rate of inflation is, he will adjust the nominal rate of interest he charges on his loan - he will ask, in this case, for a rate of interest of 15 per cent. It follows that in equilibrium (or, the long run since peopple are, by definition, in equilibrium in the long run), the nominal rate of interest will be equal to the real rate of interest (which must be positive) plus the actual rate of inflation.

     

  5. Lack of Information and Liquidity Preference

We have noted above, however, that the notion that people make rational decisions about the allocation of real income between the present and future periods requires them to have a great deal of knowledge about real income in the current period and about real rates of return into the future. Potential investors also must know a good deal about the profuctivity of future investment. It is easy to argue that in the real world this level of information and of certainty about the future does not exist. It is also easy to argue that in fact people bargain over and make decisions about nominal values rather than real values and about the present rather than the future.

If one accepts these propositions, it is possible to adopt the view taken in the IS-LM model at the beginning of the course - that the key element in determining the actual amount of saving that takes place in a given time period is the level of income itself. Interest rates might, of course, have an impact on savings levels but the difference between the amount of saving in one period and that in another is much more likely to be because the level of income has changed. In other words, people make saving plans on the basis of their expected level of income and the expected rate of inflation (as in the loanable funds model) but these plans are often not fulfilled because their expectations, especially about the level of income, are frequently wrong. Under these circumstances, the most pressing question does not concern current and future consumption but is about the way in which to hold the existing level of wealth. In an uncertain world, people seek a degree of liquidity and it is this demand for liquidity that is a major element in the determination of interest rates. This gives us the model illustrated by IS-LM, with the rate of interest being determined by the demand for money (liquidity preference) and the supply of money.

 

4. Loanable Funds and Liquidity Preference - an accommodation?

It is theoretically possible to bring the two theories together by suggesting that liquidity preference is a short-run or disequilibrium theory while loanable funds provides a long-run theory. In other words, loanable funds operates in equilibrium when people's expectations are correct. Under these circumstances, we are back in a world of certainty and people are able to make plans about the future and can assume that these plans will be fulfilled.

However, bringing the theories together in this way is artificial since the proponents of liquidity preference theory do not believe that the world is ever in long-run equilibrium. In their view, people make decisions in a constantly changing series of short-run situations in which they are always uncertain about the future and cannot depend on their plans being fulfilled. Equally, the supporters of loanable funds theory argue that the short-run in Keynesian economics is unimportant. The basis of economics, they argue, is the allocation of scarece resources - a real decision. Concentrating on the short run, they would say, is simply confusing real decisions with temporary factors. In the short-run people might act irrationally. They might suffer from money illusion (confusing monetary values with real values) but this does not mean that economic decisions should be based on the short run. To do so is likely to lead to an inefficient use of resources in the economy.

This is a very old battle. Keynes, who first stated the liquidity preference theory of interest rates in a fully developed way, argued that 'in the long run we are all dead'. What he meant was that economic analysis and economic policy should be based on the world as it is rather than on some theoretical model of a world in equilibrium that does not exist. People live in the short run. Thus, to attempt to combine the two interest rate theories is to misunderstand the reason for the distinction between them. In practice, one can of course adopt some sort of half-way position suggesting that people try to take account of the trade-off between present and future consumption and the productivity of investment but that interest rates vary quite a lot from the rates that would equate the rate of time preference with the marginal productivity of investment because of the factors that enter into the liquidity preference model.

The only problem with this is that we do not have a clear answer as to which set of factors (those stressed in loanable funds theory or those that enter into liquidity preference theory) are the most important in practice.

 

5. Relative rates of interest - risk premiums

All of this theory is, as we noted at the beginning, about the determination of a single rate of interest in the economy. But we all know that in any economy there are a large number of different interest rates. It may be true that all of these rates tend to rise and fall together (although not perfectly in unison) but nonetheless the differences can be very large. Compare, for example, the rate of interest a bank will pay on a current account deposit with the rate of interest it will charge on an outstanding credit card bill. We have seen that one small element covers the costs and provides the profits of financial intermediaries (the spread between borrowing and lending rates of interest). This does not take us very far towards explaining different rates of interest.

One important element comes from the different degrees of risk associated with different uses of funds. Consider a saver choosing between two alternative uses of his savings - a current account deposit with a large bank that he believes to be very safe, and the purchase of units in an off-shore fund located in the Channel Islands and operated by people of whom he has never heard. The only information he has about this second investment is from an advertisement in a newspaper and from some material that he has been sent by the company itself. The company does not offer him a definite rate of interest but indicates that the rate of return on this kind of investment in the past has always been much higher than the rate of interest obtainable from a bank or a building society. These days, the advertisement would always include a statement that the value of this investment could go down as well as up. Our saver does not know anyone who has invrested with this company. Despite this lack of knowledge about the company and the risks associated with it, he might still choose to put his savings with them rather than in the current account - but only if the interest rate offered by the company is much higher than that offered by the bank. If he goes ahead and does this we would say that he is trading off risk against return. Alternatively, we could say that the higher interest rate offered by the Channel Islands fund manager includes a significant risk premium.

One of the major things we are interested in in this course is the difference in interest rates among countries. We can now see that rates of interest in the UK might be higher than rates of interest on similar types of investment in Japan because markets judge that it is more risky to hold funds in sterling than in yen. In other words, UK interest rates include a risk premium reflecting the degree of risk associated with holding sterling.

What sort of risk are we talking about here? Clearly, it is the risk that the value of sterling will fall relative to the Japanese yen. In other words, the markets must think that there is a much greater chance that sterling will depreciate against the yen than that the reverse will happen. Why might they feel that this is likely? Well, foreign exchange rates are influenced by many things, but if we were to look for the 'fundamentals' of the exchange rate, we would think principally of factors influencing the international competitiveness of the country's and services and hence of the balance of trade. A major element in this is the rate of inflation relative to inflation rates in the country's trading partners. Thus, assume that the inflation rate in the UK is 3 per cent per year while Japan has an inflation rate of only 1 per cent. Other things being equal, British goods will steadily become less competitive, British exports will fall and imports will rise. The balance of trade will worsen. This means that the demand for sterling on foreign exchange markets declines, the supply of sterling increases and, if the exchange rate was perfectly free to change, the value of sterling in terms of yen would fall. This fall in the value of sterling would temporarily restore the balance in the balance of trade.

This all means that if the markets believe that inflation in the UK will be high they will not want to hold funds in sterling because of the fear that the value of sterling will go down in the near future. As before, to persuade them to hold sterling, interest rates will need to be higher than in Japan. They will need to include a risk premium - in this case, the risk we are talking about is a foreign exchange risk - the risk that the value of the currency will fall. We shall return to this issue later when we talk of the independence of central banks. The central point we are making here is that:

 

Anything that helps to persuade financial markets that the rate of inflation in a country will fall should make people in the markets more willing to hold the country's currency and should allow interest rates in the country to fall relative to those in other countries.

 

6. Relative rates of interest - term premiums

Another source of difference in rates of interest in an economy is the length of time for which a loan is made. The central idea of the loanable funds theory, remember, is that savers need to be rewarded for forgoing present consumption by the payment of interest. The implication of this is that the rate of interest demanded by savers on longer loans should be higher than that on shorter loans. That is, savers need to be paid higher rates of interest to forgo consumption for ten years, say, than for one year. Any difference in interest rates on this basis is known as the term premium - an extra element in the interest rate to reflect the length of time for which the loan is made.

Another way of saying much the same thing is that the longer savers tie up their funds, the less liquid their assets become - that is, the less easy it is for them to convert their funds into goods and services. Thus, the extra interest rate paid on longer loans can be regarded as a premium paid to compensate lenders for the loss of liquidity. It is possible to draw a curve that shows the interest rate payable at the present moment on assets with different terms to maturity. This is known as the time yield curve. If the only consideration was the loss of liquidity to savers, we might expect the time yield curve to rise but to gradually flatten out, as in Figure 2, to indicate that the marginal benefit obtained from future consumption falls as then length of time from the present increases. Of course, the steepness of the time yield curve will depend on the time preference of the population.

 

 


If people generally strongly preferred consumption now to saving in order to consume more in the future, the time yield curve would slope up steeply. Our diagram (Figure 2) on the other hand suggests only a weak preference for consumption in the present period over consumption in the future.

However, this notion of time preference is only one possible factor influencing the shape of the time yield curve. A second important factor is the expectations people have about future interest rates. Assume now that lenders are equally happy to hold short-term or long-term securities (we are ignoring the time preference/liquidity argument here). People will choose between short-term and long-term securities only on the basis of relative interest rates. Thus, a series of five one-year bonds is a perfect substitute for a five-year bond. This means that the returns from buying a one-year bond and then at the end of the year re-investing the proceeds in another one-year bond and so on for five years must equal the proceeds from investing now in a single five-year bond.

We can see that this must be the case by considering what would happen if it were not. Suppose the proceeds from a long-term bond were greater than from a series of short-term bonds. People would buy long-term bonds, pushing up their price and pushing down the rate of return on them. This would continue until there was no advantage to be had from holding the long-term bonds. Then people would be inf=different between the two types of bond. This must mean that the long-term rate would depend entirely on the expected future short-term rate.

The simplest form of this theory assumes that lenders have perfect information and know what is going to happen to short-term interest rates in the future. In this case, long-term interest rates will be an average of the known future short-term rates. This relationship between long-term and short-term rates can be expressed in the formula:

 

(1 + i*)n = (1 + i1)(1 + i2)(1 + i3)(1 + in)

 

where i* is the interest rate payable each year on a long-term bond and n is the number of years to maturity of the bond; i1 is the rate of interest payable now on a one-year bond, i2 is the rate of interest that will be payable on a one-year bond in a year's time; i3 is the one-year rate two years into the future and so on.

It follows that if short-term rates are expected to rise, long-term rates will be higher than the current short-term rate and the yield curve will slope up. Equally, of course, if short-term interest rates are expected to fall, the long-term rate will be lower than the current short-term rate and the yield curve would slope down. For a numerical example of this and an exercise based upon it see pages 186-87 of Howells and Bain (1994), Financial Markets and Institutions.

In the first week of December, 1998 the base rate of interest in the UK was 6.75 per cent. It was generally expected, however, that on the 10th December the Monetary Policy Committee would cut the base rate. It was also expected that interest rates would continue to fall during the first half of 1999. Thus, if the only influence on long-term interest rates was expectations regarding short-term rates we would have expected the yield curve during the first week in December to be sloping down, with the long-term rate being below 6.75 per cent.

The following were the interest rates on interbank sterling deposits in London money markets at the close of trading on the 7th December 1998:

 

Overnight 7.63% - 6.75%

7 days notice 7.06% - 6.93%

one month 6.69% - 6.56%

three months 6.5 % - 6.38%

six months 6.25% - 6.125%

one year 6.03% - 5.91%

 

Even though we are only dealing with up to one year ahead here, these figures provide support for the importance of expectations of future interest rates in the shape of the yield curve.

 

7. Market Segmentation and Preferred Habitat

Consider the relationship we have so far proposed between short-term and long-term interest rates. Assume the current interest rate on a one-year bond is 6 per cent and that on a five year bond is 8 per cent. This might reflect:

 

 

Suppose next that the current one-year rate falls to 5 per cent. Five-year bonds at 8 per cent now seem more attractive than before and people switch towards them, pushing up their price and forcing down the yield on them to below 8 per cent. The position of the yield curve changes but there is no change in shape. It is usually assumed that this will all happen very quickly - that is, that short-term and long-term interest rates are very closely linked. In effect, it is assumed that there is a single market for funds and that changes in one part of the market are quickly communicated to other parts of it.

It is possible, however, to question whether this is the case. Imagine that people holding short-term bonds so strongly wish to keep their funds in liquid form that the greater relative attractiveness of long-term bonds does not influence them. Perhaps they are very strongly capital-risk averse. Alternatively, they may, as with banks and building societies, need to keep a proportion of their assets in very liquid form in order to meet unexpected calls upon them. Further, there may be high transactions costs in switching from short-term to long-term securities. For one reason or another, the market might be segmented. That is, long-term bonds may not be at all a close substitute for short-term bonds. In this case, a change in short-term interest rates might have only a limited impact on long-term rates.

It is easy to think of savers who may be strongly attached to the market for funds - for instance, small savers who habitually save in National Savings or Building Society accounts despite changes in interest rate differentials. Such savers are said to have a preferred habitat. If these attachments to a particular part of the market are strong, they are unlikely to be broken by small changes in relative interest rates. However, larger changes might persuade people to move some (but not all) of their assets from short-term to long-term or vice versa. That is, assets of different maturities may be only imperfect substitutes for each other. This is a half-way position between the idea that changes in one part of the market quickly affect the market as a whole and the idea of market segmentation.