RDP 9504: The Link Between the Cash Rate and Market Interest Rates Appendix 1: Unit Root Tests

Philip Lowe

May 1995

The null hypothesis of a unit root is tested using the Augmented Dickey-Fuller test. This involves estimating the following equation and testing the null hypothesis H0:ρ=0.

The null hypothesis of no co-integration between the cash rates and each of the interest rates is tested using the unrestricted error-correction model. This involves estimating the following equation and testing the null hypothesis H0:φ=0.

The table below reports the t-statistics for the unit roots and co-integration tests.

Table A1: Unit Root and Co-integration Tests
Unit root tests Co-integration tests
m=4 m=6 m=1 m=2 m=4 m=6
Cash rate −0.72 −1.08 n.a. n.a. n.a. n.a.
Money-market rates
3–6-month CD −0.79 −1.08 −3.28 −2.53 −2.37 −1.70
90-day bank bill −0.84 −1.20 −3.77 −2.10 −0.77 −0.61
180-day bank bill −0.94 −1.40 −2.30 −1.35 −0.74 −0.45
13-week treasury note −0.86 −1.89 −2.59 −2.69 −2.96 −4.42
Long-term bonds
2-year treasury bonds −1.06 −1.59 −1.68 −1.68 −1.82 −0.77
5-year treasury bonds −1.08 −1.54 −1.85 −2.09 −1.97 −1.28
10-year treasury bonds −1.11 −1.67 −1.96 −2.33 −2.50 −2.25
Deposit rates
Cash management trust −0.69 −2.58 1.62 1.66 0.64 1.99
Low-balance accounts −0.89 −1.28 −2.35 −2.55 −2.17 −1.59
High-balance accounts −0.95 −1.44 −3.59 −2.73 −1.20 −0.45
1-month fixed deposit −1.58 −1.60 −2.29 −2.03 −1.69 −1.25
1-year fixed deposit −1.35 −1.64 −2.72 −2.60 −1.36 −1.03
Lending rates
Business indicator rate −1.02 −1.30 −2.50 −2.29 −1.46 −1.47
Housing rate −1.26 −1.68 −2.79 −4.03 −4.11 −3.84
Personal instalment rate −0.48 −0.70 −2.36 −2.73 −2.73 −2.61
Credit card rate 0.40 −0.06 −1.44 −2.32 −1.57 −1.53

1. The t-statistics have been calculated using the White procedure.
2. The critical values for the augmented Dickey-Fuller tests are 2.89 (5 per cent) and 2.59 (10 per cent). The critical values for the test of co-integration using the Unrestricted Error-Correction Model have not been tabulated, however they lie between the Dickey-Fuller critical values and the standard critical values.