Another look at yield spreads: the role of liquidity

Southern Economic Journal, April, 2008 by Dong Heon Kim

[r.sup.L.sub.n,t] = 1/n [E.sub.t][n-1.summation over (i=0)][r.sup.F.sub.t i], (23)

where [r.sup.F.sub.n,t] and [r.sup.F.sub.t] are the n-period CP rate (our substitute for the n-period loan rate) and one-period federal funds rate, respectively. Assuming rational expectations, one can rearrange Equation 23 to yield the following relationship as the term structure regression for empirical investigation:

Model I: [[delta].sub.0] = [[delta].sub.1] = 0, [[eta].sub.t] = [E.sub.t][[eta].sub.t n] 1/n [n-1.summation over (i=0)][r.sup.F.sub.t i] - [r.sup.F.sub.t] = [alpha] [phi] ([r.sup.L.sub.n,t] - [r.sup.F.sub.t]) [[epsilon].sub.t], (24)

where [[epsilon].sub.t] = 1/n [n-1.summation over (i=0)][r.sup.F.sub.t i] - 1/n [E.sub.t][n-1.summation over (i=0)] [r.sup.F.sub.t i] and should be uncorrelated with any variable known at time t. Here, n corresponds to 4 or 12 weeks for one- and three-month commercial paper, respectively. Equation 24 can be estimated by OLS with autocorrelation-heteroskedasticity consistent errors. According to the simple expectations hypothesis, [alpha] = 0, and [phi] = 1. This test can be nested within our term structure model (Equation 22) by imposing the restrictions [[delta].sub.0] = [[delta].sub.1] = 0, and [[eta].sub.t] = [E.sub.t][[eta].sub.t n].

Table 1 shows the results for estimation of Equation 24. The coefficient on the spread is significantly less than unity and different from zero at conventional significance levels. In addition, the estimated coefficients on the constant are significantly less than zero. These results are very similar to those of previous empirical studies. (18)

Test of the Expectations Hypothesis with Liquidity Premium and Risk Premium

Our model developed in section 2 implies that the simple EH does not hold because of the liquidity premium and the risk premium. Since banks' optimal behavior is subject to a CIA constraint, banks' liquidity causes the shadow price of the CIA constraint to play an important role in yield spreads and the term structure of interest rates. Thus, the model suggests that I need to incorporate a liquidity premium and a risk premium into the simple EH. The model (Equation 22) forms the basis of the tests of the term structure on which to focus. Subtracting 1/n [r.sup.F.sub.t n-1] from both sides of Equation 22 to avoid including the ex-post future interest rate in the equation as a regressor, I get:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (25)

Then, Equation 25 involves running the regression:

Model II: [[delta].sub.0][not equal to]0, [[delta].sub.1][not equal to]0, [E.sub.t-1][[eta].sub.t] = [r.sup.F.sub.t-1], [E.sub.t-1][[eta].sub.t n] = [E.sub.t-1][r.sup.F.sub.1 n-1]

1/n [n-2.summation over (i=0)][r.sup.F.sub.t i] - [r.sup.F.sub.t] = [alpha] [phi]([r.sup.L.sub.n,t] - [r.sup.F.sub.t] [[gamma].sub.1][r.sup.F.sub.t-1] [[gamma].sub.2][L.sub.t] [[epsilon].sub.t], (26)

where [L.sub.t] is the quantity of new loans at time t, and [[epsilon].sub.t] = 1/n [[summation].sup.n-2.sub.i=0][v.sub.t] i [[delta].sub.1][[xi].sub.t] - [e.sub.t]. Regression 26 differs from all tests of EH in the existing literature, where the regressand is not 1/n [[summation].sup.n-2.sub.i=0][r.sup.F.sub.t], but 1/n [[summation].sup.n-1.sub.i=0] [r.sup.F.sub.t i] - [r.sup.F.sub.t]. Equation 26 cannot be estimated by OLS because [[epsilon].sub.t] is correlated with the regressors [r.sup.L.sub.n,t] and [r.sup.F] Rational expectations require [[epsilon].sub.t] to be uncorrelated