**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,

g_{t}^{k} = a + b x_{t} ,

where g_{t}^{k} 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 RThe 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.^{2 }1 quarter 0.9% 0.11 4 quarters 2.1% 0.30 8 quarters 3.2% 0.25

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)

(Y_{t} - Y_{t-1})/Y_{t-1} = 2.5% - 2 (U_{t}
- U_{t-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 (p_{t}^{e}) in year t.

2. The deviation of the unemployment rate (U_{t} ) in year t
from the natural unemployment rate (U_{t}^{n}).

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

So:

**p _{t} = p_{t}^{e} - a (U_{t}
- U_{t}^{n}) + x**

where the inflation rate (p_{t}) 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):

**p _{t} = (P_{t} - P_{t-1} )/
P_{t-1}**

(U_{t}^{n}) 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 (p_{t}^{e}) is well approximated by last
year's inflation rate (t-1), the relation becomes:

**p _{t} = p_{t-1} - a (U_{t}
- U_{t}^{n}) + 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.

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 p_{1} , then the price plus interest at rate
i equals the principal; that is,

**100 = p _{1}(1 + i).**

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

**p _{1} = 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 y_{1} ( 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 = p_{2}(1 + y_{2})^{2} , which
gives us the present value relation

**p _{2} = 100/(1 + y_{2})^{2}.**

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

**p _{n} = 100/(1 + y_{n})^{n}
,**

where p_{n} and y_{n} 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 69.66The 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.

* 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 = p _{2} (1+ y_{2})^{2}
= p_{2} (1 + y_{2})(1 + y_{2}).**

One interpretation of this relation is that the owner of the bond gets
a rate of return y_{2} in the first period and y_{2} 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 i_{1}, the yield y_{1} on a one-period
bond. The added subscript 1 in i_{1} 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 = p _{2} (1+ i_{1})(1+ f_{2}),**

where f_{2} is the return on a forward contract in the second
period. We can combine the two relations in the equation,

**(1 + y _{2})^{2} = (1+ i_{1})(1+
f_{2}),**

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+ y _{4})^{4} = (1+ i_{1})(1
+ f_{2})(1 + f_{3})(1 + f_{4}).**

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 + f_{n} = p_{n} / p_{n+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 |

.

.

.

Rollover Strategy iIf i_{1}i_{2 }X--------------X------------X i_{1}f_{2 }Long Bond Strategy

**f _{2} = E( i_{2} ) + 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,

**f _{n} = E( i_{n} ) + 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 f_{2} 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 6.28We 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
f_{2} = 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.

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 p

**r = i - p ^{e} .**

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/P_{t}) (1 + r_{t} ) = (100/P_{t+1}),

where r_{t} is the real rate of interest from t (now) to t+1
(one year from now) and P_{t} and P_{t+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/P_{t} tells us what 93 dollars buys now,
and 100/P_{t+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 + i _{t} = (1 + r_{t} ) (P_{t+1}
/P_{t}) = (1 + r_{t}) [ 1+ (P_{t+1 }- P_{t})/P_{t}]
,**

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

**i _{t} = r_{t} + (P_{t+1 }-
P_{t})/P_{t}.**

Generally we replace the inflation rate (P_{t+1 }- P_{t})/P_{t
}with the expected inflation rate p_{t}^{e}, 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**:

**i _{t} = r_{t} + p_{t}^{e}**

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

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.

- 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.
- Since our ability to predict the future is limited, businesses must have strategies for dealing with uncertainty.
- Bond prices and yields contain information about the future paths of interest rates and real output.
- The global business environment is reflected in trade in goods and assets, in prices of these goods, and in interest rates.

**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 Indicators, Macro 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.

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 |