RDP 1977-06: Interest Rates and Exchange Rate Expectations in the RBA76 Model 4. The Influence of the Debenture Rate
October 1977
The influence of the debenture rate on private sector decision making is tested by including the debenture rate, in addition to the bond rate, in the functions for money demand, non-bank demand for government securities, and net foreign demand for Australian assets. In the latter case, the marginal product of capital is also entered; in the case of bonds and money demand the coefficients on the rate of return on real capital are assumed to be zero.[10] In the case of demand functions for bonds and net Australian assets the interest rate parameters are constrained to sum to zero, so that an equal change in all interest rates will not change the desired holdings of these assets. This constraint is not imposed in the money demand function as the unobserved own rate on money (whose parameter is assumed to be zero in the other asset demand functions) is likely to be important in this case. (The own rate of return on money is assumed to be a constant and/or proxied by the bond rate.) The relevant parameters are otherwise freely estimated, except that the parameters on the debenture rate and the marginal product of capital in the net foreign demand for Australian assets function are constrained to be equal and opposite; this constraint seems reasonable, as the marginal product of capital can be regarded as a proxy for the return on equities, and debentures[11] and equities could be considered competing assets in this context.
The estimated interest rate parameters of the several asset demand functions with respect to the several rates of return in the model are reported in Table 3.
An interesting feature of these results is that while the estimated bond rate elasticity of the money demand function is negative in Model A, it is positive in Model B, the model most comparable with Model A in terms of the treatment of exchange rate expectations. This suggests that in Model B the presence of the alternative domestic financial asset, company debentures, in the portfolio choice available allows the bond rate to act as a proxy for own rate effects in the determination of money demand; the small negative, insignificant estimates of the corresponding parameters in Models C and D appear to support this view.
| Model A | Model B | Model C | Model D | |
|---|---|---|---|---|
| Demand for money | ||||
| bond rate | −2.88(1.58) | 3.26(1.91) | −0.58(.30) | −0.32(.23) |
| debenture rate | 0.0 | −5.83(6.42) | −5.19(5.47) | −3.05(3.36) |
| marginal product | 0.0 | 0.0 | 0.0 | 0.0 |
| world rate | −7.23(3.07) | −4.81(5.86) | −2.53(3.09) | −1.28(1.74) |
| Demand for bonds | ||||
| bond rate | 17.80(3.96) | 24.64(7.66) | 30.37(6.66) | 31.44(6.04) |
| debenture rate | 0.0 | −10.43(5.58) | −10.78(4.57) | −10.57(3.92) |
| marginal product of capital | 0.0 | 0.0 | 0.0 | 0.0 |
| world rate | −17.80(3.96) | −14.21 | −19.59 | −20.87 |
| Net foreign demand for Australian assets | ||||
| bond rate | 18.48(3.92) | 11.97(4.53) | 22.76(5.81) | 29.75(5.11) |
| debenture rate | 0.0 | −3.19(3.96) | −5.18(5.99) | −4.36(4.11) |
| marginal product of capital | 0.0 | +3.19 | 5.18 | 4.36 |
| world rate | −18.48 | −11.97 | −22.76 | −29.75 |
With respect to other interest rate effects, the results are reasonably consistent in each model. When the debenture rate is added to the vector of interest rates, the bond rate response is increased in the demand function for bonds. In the bond rate equation of Model C for example, the mean bond rate elasticity is approximately 1.5, considerably higher than estimates in earlier studies and in earlier versions of the RBA76 model.
In the function for net foreign demand for Australian assets, the interest rate responses are also significant, with an elasticity of response to bond rates slightly in excess of unity in Models C and D. It is also interesting that there is a small and apparently significant response of capital flows to the gap between the marginal product of business capital and the debenture rate, although this result needs to be qualified in view of the constraint which is imposed in obtaining it.
It should be noted that there is no term representing the effect of flow disequilibrium in the money market in the equation for net capital inflow, as there is in the version of the RBA76 model presented in Jonson and Taylor (1977). This effect was not significant when tested in the models in this paper, and it appears that the negative influence of the debenture rate on capital inflows in the current models may be representing the same effect as monetary disequilibrium in models which do not include the debenture rate.[13]
Other results of relevance are the adjustment coefficients of investment, bonds, net capital inflow and the bond rate in the four models. These are shown in Table 4, and Table 5 presents fit statistics for certain key equations in each model.
| Equation | Model A | Model B | Model C | Model D |
|---|---|---|---|---|
| Business fixed investment | .83 (4.73) |
.89 (5.30) |
1.00 (5.92) |
.92 (5.08) |
| Bonds | .09 (5.61) |
.13 (9.64) |
.13 (10.52) |
.11 (9.34) |
| Net capital inflow | .07 (5.19) |
.11 (7.28) |
.11 (7.78) |
.11 (6.94) |
| Bond rate | .04 (5.02) |
.04 (8.91) |
.04 (8.86) |
.15 (6.94) |
Of these adjustment speeds, that for business fixed investment is the fastest, with an average lag of around one quarter in each model. In the case of financial assets, the adjustment speeds are similar in each model and each equation, with a mean time lag of close to ten quarters. This result is similar to that in earlier versions of the RBA76 model, and in comparison to the earlier results, it is obtained without imposing the restriction that α13 = α14. As in earlier results, the adjustment of the bond rate to the target level determined by the monetary growth rate is around six years in Models A, B and C, and the main short run influences on the bond rate are the assignment effects represented by the usual stabilization policy variables. In Model D, in which the bond rate adjusts to the debenture rate, the average lag is rather faster at just under two years, although the stabilization policy variables are also important influences on the bond rate in the short run.
| Equation | Model A | Model B | Model C | Model D | |
|---|---|---|---|---|---|
| y | r2 | .2547 | .2512 | .2612 | .2707 |
| RMSPE1 | 2.1071 | 2.1119 | 2.1095 | 2.1000 | |
| RMSPE2 | 2.1008 | 1.9758 | 1.9328 | 2.4059 | |
| p | r2 | .4127 | .4916 | .5036 | .5183 |
| RMSPE1 | 1.0392 | .9899 | 1.0798 | .9540 | |
| RMSPE2 | 3.8956 | 4.2931 | 5.9553 | 5.3470 | |
| R | r2 | .3480 | .3496 | .1678 | .0584 |
| RMSPE1 | 5.2230 | 5.1633 | 6.0902 | 7.0228 | |
| RMSPE2 | 17.1103 | 18.5429 | 16.1463 | 21.0982 | |
| F | r2 | .3261 | .3288 | .1003 | .0568 |
| RMSPE1 | 1.9900 | 1.9774 | 2.3409 | 2.5987 | |
| RMSPE2 | 6.8599 | 8.2705 | 10.3510 | 13.7824 | |
| B | r2 | .3276 | .4240 | .4323 | .3212 |
| RMSPE1 | 1.3675 | 1.2649 | 1.2530 | 1.3892 | |
| RMSPE2 | 3.3370 | 4.8349 | 3.4334 | 4.8784 | |
| M | r2 | .6817 | .6811 | .6799 | .6809 |
| RMSPE1 | .6856 | .7141 | .7211 | .7000 | |
| RMSPE2 | 6.9561 | 5.1943 | 6.0105 | 6.9035 | |
| rb | r2 | .4698 | .6513 | .5707 | .5080 |
| *RMSE1 | .0017 | .0014 | .0014 | .0014 | |
| *RMSE2 | .0093 | .0042 | .0046 | .00 | |
| rd | r2 | .4021 | .4514 | .3983 | .2149 |
| *RMSE1 | .0022 | .0022 | .0022 | . 0028 | |
| *RMSE2 | .0083 | .0062 | .0056 | .0062 | |
|
* These figures are root mean square errors, and not root mean square percentage errors. |
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Turning to the fit statistics for key variables in each model, it can be seen that it is hard to discriminate among them on the criteria in Table 5. Model C, which is a constrained version of model B, has a considerably lower r2 for capital flows and for changes in international reserves, although the dynamic simulation performance of model C with respect to the level of international reserves is better. Model D is less satisfactory than model C for several equations, notably for capital flows, international reserves, and for the debenture rate. This seems to be important evidence in favour of the proposition that, on average over the past sixteen years, the bond rate has determined the debenture rate in the short run rather than the other way round.
Footnotes
This assumption was necessitated by program limitations, but seems reasonable. [10]
In the absence of this constraint the estimated debenture rate elasticity of the desired net Australian assets function is very large and negative while the coefficient on the marginal product of capital is small and negative. This result is rejected as implausible, but it is clearly worthy of further investigation. [11]
Note that an approximate mean elasticity of response can be calculated for each parameter by dividing the estimates in Table 3 by 20 (corresponding to a mean interest rate of .05). [12]
As noted above (p.9), when monetary disequilibrium is significan in the debenture rate equation it takes a negative sign; with a negative effect of the debenture rate upon net capital inflows, this implies a net positive effect of excess demand for money on capital inflow, consistent with the results obtained by Jonson and Taylor (1977). This point may be relevant in interpreting the tendency for the parameter on debenture rate to take on a very large negative value in some model runs, as noted in footnote 2, page 11. [13]