1 Public Affairs 974-001 Menzie D. Chinn Fall 2010 Social Sciences 7418 University of Wisconsin-Madison Expectations Hypothesis of the Term Structure, the Liquidity Premium and Economic Activity Background The linkage between the long-term and short-term interest rates can be decomposed thus: ntentettntlniiii ++++=−+=)...(11 (1) Where nti is the interest rate on a bond of maturity n at time t ,is the expected interest rate on a one period bond for period jt + , based on information available at time t, and ntl is the liquidity (or term) premium for the n-period bond at time t . This specification nests the expectations hypothesis of the term structure (EHTS) (corresponding to the first term on the right hand side of equation 1), and the liquidity premium theory (corresponding to the second term). The EHTS merely posits that the yield on a long-term bond is the average of the one period interest rates expected over the lifetime of the long bond. The liquidity premium theory allows that there will be supply and demand conditions that pertain specifically to bonds of that maturity (this is the segmented markets hypothesis). The presence of idiosyncratic effects associated with a certain maturity of bond is sometimes linked to the “preferred habitat theory”, the idea that certain investors have a preference for purchasing assets of specific maturities. Since 0>ntl and is expected to rise as n becomes large, the yield curve will slope upward when short rates are expected to be constant over time. The liquidity or term premium is assumed to rise with maturity n because holders of longer term bonds face greater interest rate risk. Now, for the sake of simplicity, consider the case where 0=ntl (i.e., the EHTS explains all variation in long rates). Suppose further expected short rates are lower than the short rate today. Then the long rate will be lower than the short rate (i.e., the yield curve inverts). Since low interest rates are typically associated with decreased economic activity, an inverted yield curve should imply an expected downturn, especially given that 0>ntl, then an inversion should imply a downturn a fortiori. Application to the United States One of the implications of the EHTS is that expectations of a sequence of low short term rates in the near future will result in the long rate being lower than usual. Short term interest rates are typically low when the economy has encountered a slowdown, or has entered in a recession. At the same time, many recessions have been triggered by increases in the short term policy rate2 (the Fed funds rate). Hence, it is often thought that an inversion of the yield curve presages a recession. In Figure 1, I plot two spreads: (i) the 10 year-3 month spread, and (ii) the 10 year-2 year spread. Figure 1: Ten year-three month spread (blue), and ten year-two year spread (red). NBER defined recession dates shaded gray. Source: St. Louis Fed FRED, and NBER. Notice that inversions of the yield curves (when the lines dip below zero, or come close is) often precede recession. There is a large literature which tries to assess whether the relationship between the yield curve and subsequent economic activity (either growth or recession) is robust. A separate, but related, question whether the term premium provides additional information above and beyond that provided by lagged income and other indicators. The studies assessing the US evidence include Harvey (1988, 1989), Stock and Watson (1989), Nai-Fu Chen (1991), and Estrella and Hardouvelis (1991). A general reading of the literature is the yield curve did have some predictive power, but was declining over time. Wright (2006) argued that the level (namely, the level of the short term interest rate) as well as the slope of the yield curve needed to be included. -3-2-10123451970 1975 1980 1985 1990 1995 2000 200510 yr - 3 mo spread10 yr - 2 yr spread3 Cross-country Analysis The evidence for predictive power across other countries is less developed. Harvey (1991), Davis and Henry (1994), Plosser and Rouwenhorst (1994), Bonser-Neal and Morley (1997), Kozicki (1997), Estrella and Mishkin (1997) and Estrella, Rodrigues and Schich (2003) examined non-US OECD countries using post-1970 data, and generally conclude that the yield spread can be used to some extent in predicting future economic growth. However studies conducted by Davis and Fagan (1997) and Smets and Tsatsaronis (1997) provided less promising evidence in terms of forecasting. The graphs analogous to Figure 1, for European countries and Japan are presented in Figure 2. Figure 2. Ten year-three month spread. ECRI-defined recession dates shaded gray. Source: St. Louis Fed FRED, and ECRI. The graphs are suggestive, but do not confirm the posited relationships.4 Table 1: Yield Curve/Growth Recessions, Full Sample (1970-2009) 1 Year 2 Year Constant Slope Constant Slope Canada 0.208 1.854 0.954 1.212 0.532 0.209 0.420 0.180 France 0.271 1.383 0.998 0.527 0.554 0.338 0.372 0.200 Germany 0.075 1.416 0.623 1.006 0.634 0.259 0.372 0.137 Italy 1.273 0.871 1.567 ‐0.025 0.629 0.300 0.402 0.178 Japan 1.333 1.299 1.983 0.297 0.762 0.391 0.553 0.286 Netherlands 0.173 0.946 0.655 0.482 0.526 0.246 0.244 0.117 Sweden 1.021 0.746 2.178 ‐0.061 0.710 0.263 0.545 0.212 U.K. 0.620 0.882 0.781 0.604 0.403 0.207 0.285 0.113 United States ‐0.037 1.630 0.362 1.456 0.628 0.289 0.442 0.190 Notes: OLS regression coefficients. HAC robust standard errors below OLS estimates. Bold entries indicate significance at 5% msl.5 Table 3: Yield Curve/Growth Recessions, Late Sample (1998-2009) 1 Year 2 Year Constant Slope Constant Slope Canada ‐1.138 1.066 ‐0.812 0.933 1.696 0.705 1.556 0.708 France ‐4.091 2.923 2.693 2.016 2.148 1.237 1.334 0.739 Germany ‐4.147 5.055 ‐1.855 3.123 1.742 1.743 1.708 1.055 Italy 4.955 3.451 ‐1.930 1.259 2.429 1.462 1.750 0.926 Japan ‐8.507 7.063 0.925 ‐0.447 6.627 4.730 2.367 1.575 Netherlands ‐0.846 1.386