Chapter 2. Business Cycle and Financial Indicators

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.

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,

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: 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)

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:

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):

(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:

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

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

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 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

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:

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

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:

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