Three- and six-month Treasury bill rates (constant maturity).
On the basis of the pure random walk model (i.e., no intercept, no trend), both the rates were stationary. Including intercept, trend, and one lagged difference, the results suggested that the two rates might be trend stationary; the trend coefficient in both cases was negative and significant at about the 7 percent level. So, depending on which results we accept, the two rates are either stationary or trend stationary.
Regressing the 6-month T bill rate (TB6) on the 3 month T-bill rate, we obtained the following regression.
TB6t = -0.0456 + 1.0466TB3t t = (-1.1207) (171.6239) R2 = 0.9921 d = 0.4055 (21.12.3)
Applying the unit root test to the residuals from the preceding regression, we found that the residuals were stationary, suggesting that the 3- and 6-month T bill rates were cointegrated. Using this knowledge, we obtained the following error correction model (ECM):
where Ut-1 is the lagged value of the error correction term from the preceding period. As these results show, 0.20 of the discrepancy in the two rates in the previous month is eliminated this month.49 Besides, short-run changes in the 3-month T bill rate are quickly reflected in the 6-month T bill rate, as the slope coefficient between the two is 0.9360. This should not be a surprising finding in view of the efficiency of the U.S. money markets.
49Since both T bill rates are in percent form, this would suggest that if the 6-month TB rate was higher than the 3-month TB rate more than expected a priori in the last month, this month it will be reduced by 0.20 percentage points to restore the long-run relationship between the two interest rates. For the underlying theory about the relationship between short- and longrun interest rates, see any money and banking textbook and read up on the term structure of interest rates.
Econometrics: Some Basic Concepts
830 PART FOUR: SIMULTANEOUS-EQUATION MODELS
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