Another look at yield spreads: the role of liquidity

Southern Economic Journal, April, 2008 by Dong Heon Kim

[e.sub.t] = [r.sup.L.sub.n,t] - [E.sub.t-1][r.sup.L.sub.n,t], (19)

[[xi].sub.t] = [L.sub.t] - [E.sub.t-1][L.sub.t]. (20)

I also assume that [e.sub.t], [[xi].sub.t] and [v.sub.t j] for all j's are serially uncorrelated and mutually independent. Substituting Equations 18 20 into Equation 17 and rearranging it, I get

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (21)

Equation 21 provides plausible parameter values for the risk premium and liquidity premium under the above assumptions. The second term on the right-hand side of Equation 21, [[delta].sub.0] [[delta].sub.1][L.sub.t], and the third term, 1/n (r.sup.F.sub.t-1] - [r.sup.F.sub.t n-1]), capture the risk premium and the liquidity premium, respectively. Subtracting [r.sup.F.sub.t] from both sides of Equation 21 and rearranging results in

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (22)

The model 22 implies that the simple EH does not hold because of the liquidity premium and the risk premium. I can estimate this model and examine if the EH might be a more realistic model when the liquidity premium and the risk premium play a role.

3. Estimation of the Term Structure Model

The Data

The weekly data set we use runs from February 1, 1984, to December 27, 2000, giving 882 observations, (15) Interest rates are taken from Federal Reserve Statistical Release H. 15 provided by the Federal Reserve Board of Governors. I also take quantities of loans from item H.8 (assets and liabilities of all commercial banks in the United States) of the Federal Reserve Statistical Release. (16) Since this series refers to outstanding loans at each period, I use the change in this series as a proxy for the volume of new loans extended. We consider federal funds rates as a short-term rate and one-month and three-month CP rates as long-term rates. All interest rates are averages of seven calendar days ending on Wednesday and annualized using a 360-day year. (17) Here, the CP rate is viewed as a substitute for the rate on banks' loans to financial and industrial companies.

Figure 1 shows movements of the federal funds rate and the one-month and three-month CP rates during this sample. One interesting feature is that the federal funds rate fluctuated around the CP rates before the 1990 U.S. recession, but after the recession the CP rates were higher than the federal funds rate. Sample period averages of the federal funds rate, one-month, and three-month CP rates are 6.23%, 6.28%, and 6.29%, respectively, and thus the one-month and three-month CP rates are higher on average by five and six basis points, respectively, than the federal funds rate. However, the standard deviation of the federal funds rate is 1.93, higher than those of the one-month and three-month CP rates, 1.84 and 1.82, respectively, which implies that the volatility of the federal funds rate is somewhat higher than those of the CP rates.

[FIGURE 1 OMITTED]

A Test of the Expectations Hypothesis

I start from a test of the simple EH, which implies that the long-term rate is a weighted average of the current short-term rate and expected future short-term rates and that the current spread between the long-term rate and short-term rate predicts the change in future short-term rates. That is,