Nouriel Roubini and David Backus

Lectures in Macroeconomics

Chapter 2. Business Cycle and Financial Indicators

Business Cycles and Economic Indicators
Unemployment Rate, Okun's Law, Inflation, the Phillips Curve and the NAIRU
Yield Curve 1: Bond Prices and Yields
Yield Curve 2: The Expectations Hypothesis
Real and Nominal Rates of Interest
Forecasting with the Yield Curve
Further Readings
Further Web Links and Readings

Business Cycles and Economic Indicators

One of the leading uses of economists (one that tends to give us a bad name) is in forecasting the economy. But as John Kenneth Galbraith put it (Wall Street Journal, Jan 22, 1993, C1): "There are two kinds of forecasters: those who don't know, and those who don't know they don't know.'' Still, forecasting is the next subject, so let's see what we can make of it. The national income and product accounts give us, as we've seen, some idea of the current state of the economy as a whole. We'd also like to know, if (say) we're planning to expand capacity, what the economy is likely to be doing in the next few months or years. The answer, if we are honest about it, is we know a little about the future, but not much. In fact we typically don't even know where we are now. Thus on October 27, 1992, the BEA announced its preliminary estimates of third quarter GDP for 1992: in 1987 prices, real GDP was 4924.5. Compared with the previous quarter of 4891.0, the growth rate was 2.6 percent annually (you multiply by 4 to get an annual growth rate). One month later, the estimate was revised upwards to 4933.7, a growth rate of 3.5 percent. This may not sound like a big difference, but it might have had a significant impact on the election, and on Clinton's thinking about whether to focus policy on long term growth or the short term. The fact is, it's difficult to compute GDP until all the data is in, sometimes a year or more down the road. The best advice I can give you is to realize that there is an unavoidable amount of uncertainty in the economy. This is even more true of firms and their financial statements.

So what do we do? My choice is to get out of this game altogether, but not everyone has this option---a firm, for example, has to forge ahead the best it can. The first thing you should know is that there's a lot of uncertainty out there, and no amount of commercial forecasting is going to change that. If you're Al Checchi at Northwest Airlines, it doesn't help to say that your forecasters didn't predict the Gulf War, the 1991 recession, and the related decline in air traffic. Or GM: their forecasters reportedly came up with three scenarios for 1991, and what happened was worse than all of them.

But you still want to get the best forecasts possible. Business economists look at anything and everything to get an idea where the economy is headed. Among the best variables are those related to financial markets. One of these is the stock of "money,'' by which I mean the stock of cash and bank deposits held by firms and households. There are a number of different monetary aggregates, as we'll see later, but we'll focus for now on M2, which includes most of the deposits at commercial banks and other other financial institutions that accept deposits. You see in Figure 1 that the growth rate of the money stock moves up and down, roughly, with the growth rate of GDP. In this sense it is a good indicator of the state of the economy. And since money stock measures are generally made available more quickly than GDP, it tells us something about the current state of the economy as well.

Even better indicators are financial prices and yields, which have the additional advantage of being available immediately. As you might expect if you've ever taken a finance course, asset prices tend to incorporate "the market's'' best guess of future events and, by and large, they are as good predictors of the economy as we have. Maybe the best of these is the stock market. In Figure 2 I've plotted the annual growth rate of real GDP with the annual growth rate of the S&P 500 composite stock index. What you might expect is that the stock market anticipates movements in the economy: in recessions profits and earnings are down so stock prices should fall as soon as a recession is anticipated by the market. That's pretty much what you see. In the figure we see that every postwar downturn in the economy has been at least matched, if not anticipated, by the stock market. The problem is that there have been several downturns in the stock market that didn't turn into recessions---so-called false signals. A classic case is the October 1987 crash, which was followed by several years of continued growth. As we say in the trade, the stock market has predicted twelve of the last eight recessions.

Other useful financial variables are yield spreads, especially the long-short spread (the difference between yields on long- and short-term government bonds) and the junk bond spread (the difference between yields on high- and low-grade bonds). Both of these have been useful in predicting downturns in the economy. Recent work by Stock and Watson for the NBER suggests that stock prices and yield spreads contain almost all the usable statistical information about the future of the economy.

Financial variables and some others are combined in the official index of leading indicators, which is constructed every month by the Conference Board and reported in the Wall Street Journal and other business publications. The current index of leading indicators (it changes from time to time) combines the following series:

Leading Indicators

1. Hours of production workers in manufacturing

5. New claims for unemployment insurance

8. Value of new orders for consumer goods

19. S&P 500 Composite Stock Index

20. New orders for plant and equipment

29. Building permits for private houses

32. Fraction of companies reporting slower deliveries

83. Index of consumer confidence

99. Change in commodity prices

106. Money growth rate (M2)

(The numbers are labels assigned in Business Conditions Digest, a Commerce Department publication on the state of the economy.) We see in Figure 3 that the index is closely related to the cycle, but only leads it by a month or two (which is hard to see in the quarterly data that I've graphed). Nevertheless, this is useful, since we don't know yet what GDP was last month. A related index of coincident indicators (Figure 4) does not lead the cycle, but has a stronger correlation with it. Its components are

Coincident Indicators

41. Nonagricultural employment

47. Index of industrial production

51. Personal income

57. Manufacturing and trade sales

Both of these indexes combine economic indicators to give us a clearer picture of current and, to a limited extent, future economic conditions.

What are the business cycle properties of other macroeconomic variables ? The attached figures of various macro series presented at the end of the chapter can be interpreted as follows. Industrial production is pro-cyclical and coincident; both consumption and investment are pro-cyclical with investment more sensitive than consumption to the business cycle, as durable goods are a larger fraction of investment than of consumption; capacity utilization is procyclical; employment is pro-cyclical and coincident; the unemployment rate is countercyclical; the inflation rate is pro-cyclical and lags the business cycle (it tends to build up during an expansion and fall after the cyclical peak); the short-term nominal interest rate is pro-cyclical and lagging; corporate profits are very pro-cyclical as they tend to increase during booms and strongly fall during recessions.

More information on business cycle is provided in the course homepage on Business Cycle Indicators and the Hyptertext Glossary of Business Cycle Indicators.

If we use these data, how well do we do in forecasting the future? The short answer is that there's a lot of uncertainty in the economy, and no amount of economic or statistical sophistication is going to change that. Let me try to make this specific (at the risk of being a little technical). Using time series statistics (which I'll presume you remember from your Data Analysis course) you might estimate a linear regression of the form,

gtk = a + b xt ,

where gtk is the annualized growth rate between time t ("now'') and time t+k ("later''), with time measured in quarters. The variable x is whatever you use to predict g . If we do all this, we can use the estimated equation to forecast future GDP and get a quantitative measure of the amount of uncertainty in the economy as a whole. That is, we plug in the current value of the leading indicators for x and the latest estimate of GDP, and use the equation to tell us what GDP in k quarters is expected to be, relative to GDP now.

We find, of course, that our predictions are invariably wrong, sometimes by a little, sometimes a lot. A measure of how well we do is the standard deviation of the forecast error, the difference between what we predicted and what actually happened. To make this concrete, I used for x the spread between the ten-year treasury yield and the 6-month tbill yield. The parameters a and b of the regression line were then estimated by least squares. The estimates of b are invariably positive, indicating that upward sloping yield curves (see the next section) indicate high growth, downward sloping yield curves the reverse. The overall performance of this procedure is summarized by the statistics:

Forecast Horizon (k)   Std Deviation of Forecast Error     R2

1 quarter                 0.9%                             0.11

4 quarters                2.1%                             0.30

8 quarters                3.2%                             0.25
The technical aspects were discussed in your Data Analysis course, but to understand what the numbers mean let me run through the predictions for k=4. We find that for predictions of the growth rate of GDP between now and a year from now (k=4) that only 30 percent of the typical yearly variation (the variance) is predictable. The other 70 percent is unpredictable (at least by this method). We also see that the standard deviation of the forecast error is 2.1 percent: that is, we expect our prediction to be within 2.1 percent, in either direction, of what actually occurs about 70 percent of the time, which is a pretty wide band (Think of telling your boss: sales will either grow 3 percent this year or fall 1 percent.) This is a simple procedure, you might be able to do better. But it's unlikely that you'll consistently do a lot better. (If you do, you should go into business.) It gives us a concrete measure of how much uncertainty is out there in the economy as a whole, and indicates that there's a lot going on that's unpredictable. For individual firms it's worse, since lots of things affect individual firms that don't show up in the aggregate.

Perhaps the best lesson you can take from this is that the future is, to a large extent, unpredictable. It's misleading, and probably dangerous, to assume otherwise, no matter what you pay your economists. One of the things you probably want to do in business is learn to deal with uncertainty. You might do this by making contingency plans, so you'll be prepared when something unexpected occurs, by following flexible manufacturing methods so that you can adapt your product quickly if the market changes, by adopting a financial strategy that hedges you against (say) adverse movements in interest rates or currencies, and so on. That's not the topic of this course, but it may help to put some of what you learn in other courses in perspective.

Unemployment Rate, Okun's Law, Inflation, the Phillips Curve and the NAIRU.

We consider now a number of other important business cycle concepts.

The labor force is the sum of employed and unemployed:

Labor Force = Number of Employed + Number of Unemployed

L = N + UN

The Unemployment Rate is defined as the percentage of the labor force that is unemployed:

U = (Unemployment Rate) = 100 (Number of Unemployed) / (Labor Force)

U = 100 (UN / L)

Okun's Law: The relation between the growth rate of GDP and changes in the unemployment rate.

Since employed workers contribute to the production of goods while unemployed workers do not, increases in the unemployment rate should be associated with decreases in the growth rate of GDP. This negative relation between changes in the unemployment rate and GDP growth is called Okun's Law. Based on U.S. data we can write such a law as:

Growth rate of GDP = (Natural Growth Rate of GDP) - 2 (Change in the Unemployment Rate)

(Yt - Yt-1)/Yt-1 = 2.5% - 2 (Ut - Ut-1)

where the subscript t refers to the period under consideration. If the data are on a yearly frequency, the expression above relates the growth rate of the GDP between year t and year t-1 to the change in the unemployment rate between year t and year t-1. The law says that if the unemployment rate stays the same relative to the previous year, real GDP in a year grows by around 2.5% per year; this is the normal long-run growth rate of the economy (or natural rate of growth) due to population growth, capital accumulation and technological progress. In the example above this natural rate of growth is assumed to be 2.5%. For the US economy such a natural rate of growth is currently believed to be in the 2.5% to 3.0% range. More on this issue will be discussed below.

Another relation to consider is the Phillips Curve or the relation between the inflation rate and the unemployment rate: this relation suggests that when the unemployment rate is low inflation tends to increase while when the unemployment rate is high inflation tends to decrease. More specifically, this curve posits that the inflation rate depends on three factors:

1. The expected inflation rate (pte) in year t.

2. The deviation of the unemployment rate (Ut ) in year t from the natural unemployment rate (Utn).

3. A supply shock (x) (for example, an oil price shock).


pt = pte - a (Ut - Utn) + x

where the inflation rate (pt) is the yearly rate of change of the price level (the % rate of change of the CPI or GDP deflator between year t and year t-1):

pt = (Pt - Pt-1 )/ Pt-1

(Utn) is the natural rate of unemployment determined by structural long-term factors that determine how many workers will be unemployed even the the economy is running at full capacity and close to its long-run potential growth rate.

If, as appears to be the case in the United States today, the expected rate of inflation (pte) is well approximated by last year's inflation rate (t-1), the relation becomes:

pt = pt-1 - a (Ut - Utn) + x

This relation links the the difference between the actual rate of unemployment and the natural rate of unemployment to the change in inflation. When the actual unemployment rate exceeds its natural rate, inflation decreases; when the actual unemployment rate is less than the natural rate, inflation increases. So, the natural rate of unemployment can be seen as the rate of unemployment required to keep inflation constant. This is why the natural rate of unemployment is also called the Non-Accelerating Inflation Rate of Unemployment or NAIRU. Note that the natural rate and its changes over time are hard to measure since we observe only the actual unemployment rate. There is currently a debate in the U.S. about what is the natural rate or the NAIRU. Usually, the level and the broad changes in the natural rate can be measured by comparing average unemployment rates in various decades. The average unemployment rate was 4.4% in the 1960s, 6.2% in the 1970s, 7.2% in the 1980s and 6.2% in the 1990s. If we believe that the natural rate is equal to the average unemployment rate in the decade, the current (November 1996) 5.4% unemployment rate is below the natural rate of 6.2%. Most mainstream economists believe that the natural rate is now closer to 5.5% as the actual unemployment rate was high during the 1990-91 recession. Even if the natural rate is 5.5%, we get a puzzle: according to the NAIRU curve, the inflation rate should have been increasing since the late part of 1995 when the unemployment rate fell below the 5.5% level. Instead there is no evidence that the inflation rate is accelerating these days. What can explain this contradiction ? There are very different alternative explanations:

1. According to some, there are structural changes in the economy that have led to a reduction of the NAIRU to a level closer to 5% or even below that.

2. According to others, we are already below the natural rate now and inflation will start to increase soon. According to this interpretation we have not seen the increase in inflation yet only because there were a series of favorable supply shocks (x) that have maintained the inflation rate low so far. But inflation will start to increase soon unless the economy growth rate slows down and the unemployment goes back above the 5.5% level.

For more on this current policy debate see the course homepages on the NAIRU controversy and the New Economy.

Yield Curve 1: Bond Prices and Yields

The yield curve for US treasury securities is published every day in the Wall Street Journal . And lots of other places, too: for example, the Department of Commerce home page gives you daily data for the Treasury yield curve. Nice charts of the yield curve (and expected future interest rates) can be found in the 'Monetary Policy' section and 'Interest Rates' section of the "Economic Trends" by the Research Department at Federal Reserve Bank of Cleveland, a monthly source of analysis of US macroeconomic conditions.

The yield curve tells you at a glance how short- and long-term interest rates differ and also provides, as we've seen, an indicator of economic growth; see Figure 5 for some recent charts of the yield curve. We'll come back to that shortly, but first we need to go through the arithmetic of treasury prices and yields.

The first lesson is that price is fundamental. Once you know the price of a bond, you can easily compute its yield. The yield---or more completely, the yield to maturity---is just a convenient short-hand for expressing the price as a rate of return: the average compounded return on a security if you hold it until it matures. Equivalently, prices are present values, using yields as discount rates. The details reflect a combination of the application of the theory of present values and the conventions of the treasury market (or whatever market you're looking at).

We'll start with a relatively simple problem: yields on bonds with no coupons. These are generally referred to as "strips'' or "zeros'' (for "zero-coupon''), with prices reported under "Treasury Bonds, Notes & Bills'' in Section C of the Journal. By convention the principal or face value of the bond is $100. If we label the price of a one-year bond of this type p1 , then the price plus interest at rate i equals the principal; that is,

100 = p1(1 + i).

Equivalently, we say that the price is the present discounted value of the principal:

p1 = 100/(1 + i).

We refer to i as the short rate since it's the yield on a short-term bond, but it's also the yield-to-maturity on a one-period bond, which we might label y1 ( y for yield). Mathematically what we've shown is that when you know the price, you can solve one of these equations to find the yield. [For some weekly updated charts (going back to 1995) of short-term and long-term US interest rates look at the Interest Rate Charts in the home page of the Minneapolis Fed]. Longer sample series that are updated every month can be charted using the Economic Chart Dispenser .

Longer bonds work pretty much the same way. For a two-year bond (again, with no coupons) we can think of the yield as the compounded return over two periods, 100 = p2(1 + y2)2 , which gives us the present value relation

p2 = 100/(1 + y2)2.

Similarly, for an n-year bond the formula would be

pn = 100/(1 + yn)n ,

where pn and yn are the price and yield of an n-year bond. As with the one-year bond, you can compute the yield from the price. A similar method is used for treasury securities and corporate bonds in the US, but by convention yields in these markets are compounded every six months rather than once a year, a complication we will ignore.

Examples. Let the prices of zero-coupon bonds be

Maturity in Years      Price

1                       94.24
2                       87.70
3                       81.22
4                       75.16
5                       69.66
The yields are, resp, 6.11 percent per year, 6.78, 7.18, 7.40, and 7.50. This gives us five points on a yield curve.

With coupons, bond pricing gets a little more complicated, but the idea is the same: the price is the present value of cash flows, discounted at a rate we call the yield. In this case the cash flows include coupons as well as principal. Given the price, we solve this relation for the yield. Take, for example, a 6% 3-year bond, with a coupon of 6 dollars every twelve months for every 100 dollars of face value. (Again: US treasury and corporate bonds are slightly different, with coupon payments every six months.) Then the yield is the discount rate that equates the price with the sum of the present discounted values of coupons plus principal. Mathematically (this may be one of those cases where the math is simpler than the words),

p = 6/(1+y) + 6/(1+y)2 + 106/(1+y)3 .

That is, we get 3 coupons and one principal payment, discounted accordingly. By way of example, if the price is 97.01 the yield is 7.14 percent (which you'll note is a little smaller than the three-year yield on a zero, 7.18).

This solution for the yield y involves some nasty algebra once we add coupons, but is easily accomplished on a spreadsheet. Probably the most straightforward way to do this is to define a formula relating the price to the yield y, then choose different values for y until one gives you the price quoted in the market. Another way, which runs the risk of confusing you, is to use a built-in function on your calculator or spreadsheet. Warning: these functions differ in subtle ways. I suggest you test yours with this or other example before relying on the answers it gives.

Yield Curve 2: The Expectations Hypothesis

Now that we have some idea what the yield curve is, we can try to interpret its shape. The idea I want to get across is that the yield curve tells us about future short term interest rates. If the yield curve is downward sloping, for example, this generally means that the market anticipates a decline in short term interest rates in the future. The theory to this effect is called the expectations hypothesis, since it's based on the idea that long rates incorporate market expectations of future short rates.

Forward rates. To make this concrete, we need to use (unfortunately) more complicated notation. Let us say, to be specific, that we are interested in the yields on one- and two-period zero-coupon bonds, with periods of one year. Then we know, for example, that the price of a two-year bond satisfies

100 = p2 (1+ y2)2 = p2 (1 + y2)(1 + y2).

One interpretation of this relation is that the owner of the bond gets a rate of return y2 in the first period and y2 again in the second, compounded. The subscript 2 on y means that this is the yield on a two-period bond.

A second interpretation allows the two periods to have different rates of return, since there's no particular reason periods must be alike. In the first period the return is simply the short rate in the first period, which I'll label i1, the yield y1 on a one-period bond. The added subscript 1 in i1 means that we're talking about the first period, something we took for granted earlier. The second period of the bond, considered on its own, is what we call a forward contract: we contract now for an investment made one period from now and lasting until the end of the second period. Thus, a two-period bond is a combination of a one-period bond and a one-period-ahead forward contract. By this interpretation the 100 principal is, again, the purchase price plus two periods of interest:

100 = p2 (1+ i1)(1+ f2),

where f2 is the return on a forward contract in the second period. We can combine the two relations in the equation,

(1 + y2)2 = (1+ i1)(1+ f2),

which shows us how the yield curve defines the forward rate.

Although it's not necessary for our purposes, we can extend this use of forward contracts to as many periods as we like. Eg, a four-period bond is a combination of a one-period bond and three successive forward contracts. Thus we can express the yield in terms of the rates on these contracts:

(1+ y4)4 = (1+ i1)(1 + f2)(1 + f3)(1 + f4).

From the prices or yields of bonds with maturities 1 through 4, we can compute the implicit forward rates. Alternatively, we could compute forward rates directly from bond prices: 1 + fn = pn / pn+1. These forward rates define a forward rate curve, analogous to the yield curve. This curve is not the same as the yield curve, but if the forward rate curve is upward (downward) sloping, then so is the yield curve. They simply report the same information in slightly different ways. The reason for all this is to try to make sense of the maturity structure of bond prices, and this is a little more direct if we use forward rates rather than yields.

Example (continued). Consider the bond prices and yields from the last section. You might verify that the forward rates are

Maturity Price Yield Forward Rate 
1 94.24 6.11 (6.11) 
2 87.70 6.78 7.45 
3 81.22 7.18 7.98 
4 75.16 7.40 8.06 
5 69.66 7.50 7.90 
Expectations hypothesis. Now consider what investors might demand of forward rates. An investor with a two-period time horizon has (at least) two choices. She could buy a two-period bond, thus getting (according to our second interpretation) i1 in the first period and f2 in the second. Alternatively, she could "roll over'' a one-period bond, getting (again) i1 the first period and the short rate i2 in the second. The notation i2 here means the short rate in the second period. These two possibilities can be pictured like this:
                Rollover Strategy

           i1                i2


           i1                 f2

                Long Bond Strategy
If i2 were known with complete certainty, then we would expect the market to drive the forward rate f2 and the future short rate i2 together: if, say, the future short rate were higher, then no one would buy the long bond. In an uncertain world, a similar guess might lead us to guess that the forward rate is the market's best guess of the future short rate, with some adjustment for risk. Mathematically, we could write

f2 = E( i2 ) + risk premium,

where E(.) means the expectation of what's in parentheses and the risk premium is the (presumed constant) adjustment for risk. With more distant forward rates we might say, for similar reasons,

fn = E( in ) + risk premium,

with the understanding that the risk premium can differ across maturities n .

In words: the expectations hypothesis is that forward rates are forecasts of future short-term interest rates --- plus a risk premium. Thus we can read the forward rate curve as a forecast of what short rates will do in the future. For example, if forward rates are below the current short rate, we interpret this as saying that bond buyers expect the short rate to decline in the future. And if forward rates exceed the current short rate by more than the risk premium, then they expect the short rate to increase. The trick is estimating the risk premium. There are as many ways to do this as there are finance professors, but a relatively simple method is to use the average difference between the short rate and the n-period forward rate as an estimate of its risk premium. Thus we see in Table 1 that the average short rate (the 12-month yield in the table) over the more recent 1982-1991 period has been 8.563 percent per year. The average 2-year forward rate f2 has been a little higher: 9.472 (I read this from the 24-month forward rate in Panel B of the same table). The difference of 0.909 I use as an estimate of the risk premium. Similarly, the risk premium for the 3-year forward rate is, similarly, the difference between 9.923 and 8.563, or 1.360 percent. If we continue to fill out the table this way we get

Maturity    Price    Yield   Forward Rate   Risk Premium  Future Short Rate

1           94.24    6.11       (6.11)            0.00        (6.11)
2           87.70    6.78        7.45             0.91         6.54
3           81.22    7.18        7.98             1.36         6.62
4           75.16    7.40        8.06             1.27         6.79
5           69.66    7.50        7.90             1.62         6.28
We see, roughly, that the risk premium increases with maturity. The exception at 4 years is as likely to be noise in the data as anything else.

Given estimates of the risk premiums, we simply subtract to get an estimate of the market's forecast of future short rates. Thus the forward rate of f2 = 7.45 indicates, given an estimated risk premium of 0.91, a forecast of 6.54 for the short rate one year from now, an increase of 43 basis points (0.43 percent) relative to the short rate reported in the table.

In short, the expectations hypothesis tells us we can read the yield curve, and the closely related forward rate curve, as telling us the market's prediction of future short rates. This theory is the starting point for more advanced bond pricing theories, some of which you can learn about in the Debt Instruments course. More advanced theories generally go on to relate the risk premium to the risks involved in buying and selling bonds of different maturities.

Real and Nominal Rates of Interest

Yields, as we have constructed them, have units of dollars: they tell us how many dollars we get in (say) one year in return for a given investment of dollars now. For example, if a 12-month treasury bill has a price of 96 dollars, its yield i is the solution to

96 (1+i) = 100 ,

implying an interest rate of about 4 percent. Thus each dollar invested today gives us about 1.04 dollars in 12 months. Since i is measured in dollars, we refer to it as the nominal or money rate of interest. For many purposes, though, we want to know not only the dollar yield, but how much the 1.04 will buy when we get it. Given an inflation rate now of about 3 percent per year, we can expect that about 3 percent of the 4 percent rate of interest will be eaten up by inflation. The investment only gains us about 1 percent per year in terms of what it will buy.

This inflation adjustment defines a real rate of interest r : the difference between the nominal rate of interest i and the expected rate of inflation, which I label pe . As an equation, we might express this

r = i - pe .

A more complex version of this follows, but can easily be skipped if you think this makes sense as it stands.

The idea behind this expression is that interest rates have units, and in principle we can measure them in any units we want. We will see, for example, that interest rates measured in different currencies are not the same (dollar, say, and yen interest rates). Suppose we are interested not in money but in what the money will buy. If by "what the money will buy'' we mean a price index P (think of the CPI, the price of a basket of goods) we can define a real rate of interest r (with "real'' determined by the basket of goods in the index) by

(93/Pt) (1 + rt ) = (100/Pt+1),

where rt is the real rate of interest from t (now) to t+1 (one year from now) and Pt and Pt+1 are the values of the price index now and one year from now. What we are doing is expressing the current bond price, measured in terms of what it will buy, as the present discounted value of the face value, also measured in units of what it will buy in one year. Thus 93/Pt tells us what 93 dollars buys now, and 100/Pt+1 tells us what 100 dollars buys one year from now. Since both quantities are "real''---that is, measured in units of the basket of goods that P applies to, rather than units of money---the discount rate r is called the real rate of interest. Of course, for different baskets we get different real rates r . Comparison of the real and nominal tbill price equations tells us that the real and nominal interest rates are related by

1 + it = (1 + rt ) (Pt+1 /Pt) = (1 + rt) [ 1+ (Pt+1 - Pt)/Pt] ,

where (Pt+1 - Pt)/Pt is the rate of inflation between dates t and t+1 . This gives us, approximately,

it = rt + (Pt+1 - Pt)/Pt.

Generally we replace the inflation rate (Pt+1 - Pt)/Pt with the expected inflation rate pte, since we don't know the inflation rate when we invest. That gives us the relation between real and nominal interest rates we saw earlier or what is known as the Fisher Condition:

it = rt + pte

So, the nominal interest rate is the sum of the real interest rate and expected inflation.

Forecasting with the Yield Curve

We return, at long last, to the use of the yield curve to predict movements in the economy, as measured by GDP. The rule of thumb, you'll recall, is that a downward sloping yield curve indicates a coming recession. (There's a long history to this, but for recent examples see Harvey's paper in the September/October 1989 Financial Analysts Journal or Estrella and Hardouvelis in the June 1991 Journal of Finance and a recent article Predicting Real Growth Using the Yield Curve by two economists at the Cleveland Fed). Does this make sense?

We have seen that when the yield curve and forward rate curve are downward sloping, the market is predicting a decline in the short rate of interest. Generally we see that low levels of the short rate are associated with recessions, as in the 1991 recession, with 3-month treasury bill rates below 3 percent. Conversely, interest rates tend to be high in booms. So a downward-sloping yield curve is also a prediction, by the market, that a recession is coming. The classic example was 1981-2, when short-term interest rates were in the neighborhood of 18 percent, with long-term rates substantially lower. Sure enough, this was followed by one of the sharpest recessions of the postwar period. Similarly, in late 1989 the yield curve was again "inverted,'' as we say, and the economy fell into recession in late 1990. This is shown in Figure 6: the yield curve was inverted when the difference between long-term and short-term interest rates was negative as in 1981-82 and in 1989. [More charts on the yield curve can be found at Dr. Ed Yardeni's Economics Network home page].

Another use of the yield curve is to predict inflation. In the last section we saw that yields could be decomposed into a real yield and an expected rate of inflation. A downward sloping yield curve, then, might be a forecast that real yields will fall, or that the inflation rate will decline. Conversely, a sharply increasing yield curve could tell us either that real rates are expected to rise or that inflation is expected to increase.


  1. Among the best indicators of movements in the economy are financial variables, like the S&P 500 stock price index or the slope of the yield curve.
  2. Since our ability to predict the future is limited, businesses must have strategies for dealing with uncertainty.
  3. Bond prices and yields contain information about the future paths of interest rates and real output.
  4. The global business environment is reflected in trade in goods and assets, in prices of these goods, and in interest rates.

Further Readings

The discussion of bond yields is a standard part of investments textbooks. See, for example, Zvi Bodie, Alex Kane, and Alan Marcus, Investments, Second Edition (Homewood IL, 1993), chapters 13 and 14.

Further Web Links and Readings

You can find more Web readings on the topics covered in this chapter in the course home pages  Business Cycle Indicators, the Hyptertext Glossary of Business Cycle IndicatorsMacro Analysis and  Macro Data. The home page "Economic Trends" by the Research Department at Federal Reserve Bank of Cleveland is an excellent monthly source of data, analysis and charts of US business cycle conditions. Latest economic statistics are charted and the current state of the economy is discussed in detail. Topics analyzed include: The Economy in Perspective, Monetary Policy, Inflation and Prices, Economic Activity, Labor Markets, Regional Conditions, Agricultural Policy, Banking Conditions, International Trade, Global Savings and Investment.

The course homepages on the debate about the NAIRU , the New Economy and the Business cycle perspectives for 1998 are a good source of WEB readings on current business cycle conditions and the current controversy on the NAIRU.

Table 1
Bond Yields and Forward Rates
The data are monthly estimates of annualized continuously-compounded zero-coupon US government bond yields and instantaneous forward rates computed by McCulloch and Kwon. Mean is the sample mean, St Dev the standard deviation, and Auto the first autocorrelation. 
                                                                1952:1 to 1992:2                           1982:1 to 1992:2 
Maturity Mean St Dev Auto Mean St Dev Auto 
A. Yields 
1 months 5.314 3.064 0.976 7.483 1.828 0.906 
3 months 5.640 3.143 0.981 7.915 1.797 0.920 
6 months 5.884 3.178 0.982 8.190 1.894 0.926 
9 months 6.003 3.182 0.982 8.372 1.918 0.928 
12 months 6.079 3.168 0.983 8.563 1.958 0.932 
24 months 6.272 3.124 0.986 9.012 1.986 0.940 
36 months 6.386 3.087 0.988 9.253 1.990 0.943 
48 months 6.467 3.069 0.989 9.405 1.983 0.946 
60 months 6.531 3.056 0.990 9.524 1.979 0.948 
84 months 6.624 3.043 0.991 9.716 1.956 0.952 
120 months 6.683 3.013 0.992 9.802 1.864 0.950
B. Forward Rates
1 month 5.552 3.140 0.979 7.781 1.753 0.915 
3 months 5.963 3.200 0.981 8.334 1.961 0.921 
6 months 6.225 3.256 0.976 8.579 1.990 0.923 
9 months 6.263 3.169 0.981 8.925 2.050 0.933 
12 months 6.358 3.169 0.984 9.320 2.149 0.942 
24 months 6.516 3.037 0.986 9.472 2.093 0.943 
36 months 6.696 3.071 0.989 9.923 1.966 0.943 
48 months 6.729 3.026 0.990 9.833 2.050 0.949 
60 months 6.839 3.062 0.991 10.182 1.972 0.953 
84 months 6.838 2.997 0.992 10.068 1.900 0.952 
120 months 6.822 2.984 0.991 10.058 1.522 0.908 

Figure 5

Figure 6

Copyright: Nouriel Roubini and David Backus, Stern School of Business, New York University, 1998.