Table 1 shows some descriptive statistics about the spread and its two components when the short
term rate is m = 3 months4.
|
sample jan64-sep97 |
long term maturity ( n ) | ||||||
|
obs 405 |
6 |
12 |
24 |
36 |
60 |
120* | |
|
spread |
mean |
0.2306 |
0.4216 |
0.6446 |
0.8116 |
1.0064 |
1.3204 |
|
st.dev. |
0.2348 |
0.4656 |
0.7447 |
0.9395 |
1.1693 |
1.3977 | |
|
thspr |
mean |
0.0058 |
0.0174 |
0.0339 |
0.0538 |
0.0820 |
-0.0690 |
|
st.dev. |
0.5492 |
0.9302 |
1.4742 |
1.8200 |
2.1443 |
2.4942 | |
|
"tp |
mean |
0.2463 |
0.4221 |
0.6185 |
0.7545 |
0.9159 |
1.3697 |
|
st.dev. |
0.6017 |
0.9926 |
1.5284 |
1.8281 |
2.0629 |
2.4257 | |
|
— | |||||||
Table 1
The mean of both the spread and the term premium is increasing with maturity (n); whereas the
mean of the theoretical spread is almost constant5. The standard deviation of all variables is
increasing with maturity. According to Campbell (1995), the empirical failure of the expectations
theory can be rationalized by noting that the standard deviations of the expected changes in the
interest rates (theoretical spread) are smaller relative to the standard deviations of the term premia.
In our data set this occurs for medium-short horizons (n ≤ 36). Term premia reflect the unexpected
future changes in interest rates, i.e. the unpredictable evolution of the yield curve, which is regarded
to be a measure of investors’ risk aversion; in addition, when agents are well informed about future
movements in interest rates the variability of term premia should be lower than the variability of the
perfect foresight spread. Consistently with this idea, Mankiw and Miron (1986), among others,
suggest that the empirical failure of the expectations hypothesis can be attributed to the increased
unpredictability of interest rates after the creation of the Federal Reserve System.
In Figure 2 we plot the yield spreads (left diagram) and the term premia (right diagram). Shaded
areas indicate periods of NBER recession6. The spreads tend to be negative immediately before
recessions. This fact is consistent with the prevalent view that an inverted, or flat, yield curve
anticipates a decline in economic activity; since a flat yield curve is supposed to reflect agents’
expectations of a severe tightening in the monetary policy conduct. On the contrary, term premia
tend to rise before recessions, denoting an accentuated risk-averse attitude of investors in bad states
of the world.
4
The sample ends in September 1997 which is the most recent available observation for the theoretical spread obtained
by rolling over the 10-year bond.
5 Similar results are obtained by Campbell (1995).
6 NBER recessions: 1969q4 - 1970q4; 1973q4 - 1975q1; 1980q1 - 1980q3; 1981q3 - 1982q4; 1990q3 - 1991q1; and
2001q1 - 2002q1.