4.2 Tests of the Substitution Effect (continued)
| Value of Workplace Super scheme | Value of Personal Super scheme | |
|---|---|---|
Slope coefficient  |
0.09 | 0.11 |
| t-value | 2.70*** | 3.43*** |
| Sample size | 422 | 552 |
| Adjusted R-squared | 0.42 | 0.32 |
Note: The coefficients are from regressions of net worth on a constant and a set of 19 explanatory variables, based on a sample of those couples with at least one partner enrolled in a superannuation scheme. Adjusted net worth and value of the superannuation scheme (total held by both partners combined) enter the equation in logarithms rather than in levels. The t-statistics are based on the test of the hypothesis that the coefficient is different from zero. ***Significant at the 1% level. These coefficients are also significantly different from -1 at the 1% level. For full regression results, see Appendix Table 10.
The estimates of the slope coefficients (βi) from the log-linear regressions in Tables 3 and 4 can be read directly as elasticities. In each case they show the percentage change in net worth (excluding superannuation) of a given percentage change in the holdings of superannuation. An alternative way to interpret these estimates is to convert them to absolute changes. This involves a simple adjustment described below.
In general an elasticity is defined as 
where in this case:
Y = the value of total net worth excluding the value of holdings in workplace or personal superannuation; and
X = the value of holdings in workplace or personal superannuation.
The marginal impact on total net worth of a dollar invested in superannuation schemes is then found as 
where the effect has been evaluated at the median ratio of (X/Y), and the term +1 is included so as to capture the effect on total net worth rather than on just net worth in vehicles other than superannuation schemes. The results are reported in Table 5.
The striking feature is that in all but one case the effect is greater than unity. In other words, these results lead to the conclusion that an additional dollar invested in superannuation schemes is associated with a more than proportionate and significant increase in total net worth. There is no substantial evidence that those contributing to such schemes do so by reducing their holdings in other vehicles. The effect is strongest for unpartnered males in personal schemes.
| Workplace | Personal | |||
|---|---|---|---|---|
| Elasticity | Marginal dollar effect | Elasticity | Marginal dollar effect | |
| Individuals | ||||
| -Unpartnered females | 0.25 | $ 1.74 | 0.32 | $ 3.00 |
| -Unpartnered males | 0.11 | $ 2.10 | 0.26 | $ 5.33 |
| -Partnered females | 0.13 | $ 1.81 | 0.16 | $ 2.14 |
| -Partnered males | -0.01 | $ 0.98 | 0.10 | $ 1.50 |
| Couples | 0.09 | $ 1.47 | 0.11 | $ 2.00 |
Notes: In the case of couples the combined holdings of the partners in either workplace or personal superannuation has been used. The estimates of the impact are derived by taking the regression coefficients from the log-linear model and dividing by the median ratio of the holdings of superannuation funds (either workplace or personal) to the total net worth excluding superannuation holdings. Note that to the resulting effect one dollar has been added to get to the total effect.
