4.2 Tests of the Substitution Effect
In this section we construct a formal test of whether those who are enrolled in a super scheme (either employer based or personal) substitute saving in these schemes for other forms of saving. In other words if a person contributes say $100 per month to a workplace scheme, is it the case that they reduce the savings they hold in other forms of retirement accumulation by a comparable amount? If the costs of subscribing to all schemes were approximately equal, and if the expected returns, rules of the plan and degree of risk were similar across schemes, then there would be no reason to suppose that people would not substitute, reducing commensurately their holdings in other vehicles. This proposition follows from the life cycle hypothesis of consumption and saving, which would suggest that individual savings depend, among other things, on the income that people expect to receive in retirement from both public and private pension schemes.
We exploit the cross sectional variation in the data to estimate the relation between the net worth and the value of holdings in a super scheme. To account for the possibilities that this relationship varies from males to females and from unpartnered to partnered individuals, we include dummies for gender and partnering status, as well as interacting these dummies with the value of the pension scheme in question. In the regression analysis, attention centres on the estimated coefficient on the variable representing the value of holdings in the super scheme (VS) and the differential slope coefficients in the following regression model:
where:
ANWi = Total net worth adjusted by subtracting the value of holdings in the super scheme for the i-th individual;
D1 = 1 for males, 0 otherwise;
D2 = 1 for partnered individuals, 0 otherwise;[6]
VSi = the value of holdings in the super scheme (either workplace or personal);
Zij = a set of independent variable for personal characteristics of the individual (eg age, ethnicity, education, region, income, main source of income etc);[7]
ε i = a random error term.
If the slope (β1) is equal to -1.0, then any additional holdings in a super scheme would be fully offset by lower holdings in other savings vehicles. This is the case of complete substitution. If in contrast, the slope were negative but between zero and minus one, then there would be partial substitution. Finally there is the possibility that the slope might be positive, indicating complementarity. In this third case additional amounts in a super scheme are accompanied by additional amounts saved in other forms as well.
It is important to control for the effect of variables that could result in a spurious relation between adjusted net worth and the value of holdings in a personal or workplace scheme. As Venti and Wise (1996) note:
“…both pension wealth and personal financial asset saving will increase with income, thus without controlling for income persons with greater personal financial wealth will almost certainly have greater pension wealth as well.” (p.24)
In the previous section, the finding that in some cases people who hold a super scheme have higher net worth, all else equal, provides evidence that they have not completely substituted scheme holdings for other forms of saving. We now formally test for the effect of a super scheme on the holdings in other forms, by estimating the above regression model. The value of both workplace and personal schemes was tested separately. In the earlier results which tested for the effect of membership we included all observations in the sample; ie both those who had and those who did not have a superannuation scheme. To test the extent of substitution, only those people holding a scheme were included in the sample for estimating the regressions.
To assess the robustness of the results, we have tried several estimators (OLS, OLS excluding outliers, median regressions, robust regressions, and log-linear form[8]). It appears that the results vary considerably across specifications. However, we have chosen to focus the discussion on the log-linear regressions, since from diagnostic tests and visual inspection of the residual plots this functional form appeared superior to others.[9] Besides, the estimate of β1 from the log-linear regression measures the elasticity of the superannuation scheme value with respect to wealth holdings in other forms. In theory, these elasticity estimates convey more economically meaningful interpretations than absolute dollar estimates, since the marginal effect of an additional dollar spent on a superannuation scheme for someone who has a net worth of, say, $10,000 is not the same as that for someone who holds ten times as much wealth.
The results are summarised in Tables 3 and 4. In each panel, the estimate of Β1 is reported, along with the estimates of the differential slope coefficients Β2 and Β3 for regressions on individuals. If the slope is negative, there is some substitution between the scheme and other forms of saving. If the slope is positive then there is complementarity, and greater investment in a workplace or personal scheme is associated with greater total net worth in some or all other forms of wealth accumulation (housing, shares, bank deposits, rental property, farms or businesses, etc). The remaining rows show the number of observations that were included and an adjusted R-squared statistic which measures the goodness of fit of the regression.
Table 3 presents the results for individuals. The Household Saving Survey provides information on assets and liabilities for unpartnered individuals and for couples. However, it was necessary to estimate the net worth of those individuals who identified as being partnered (ie part of a couple). To do this, we identified the persons in a couple and assigned to them 50% of all the net worth of the couple, with the exception that we allowed for separate information for each partner on their individual student loans and the value of their individual holdings in super schemes. The results shown for individuals were obtained by pooling the data for unpartnered individuals and individuals in couples.
For individuals, are super schemes a substitute for other forms of saving? The answer appears to be no. In the case of workplace superannuation, the estimated coefficient of the scheme value on the net worth in other forms is 0.25 for unpartnered females, indicating that higher savings in the form of workplace superannuation for these people are associated with a 25% increase in other wealth. The corresponding effect is higher (0.32) for personal schemes. For both types of schemes, the effect is halved for partnered individuals and is further reduced for males, so that the impact on other type of net worth of holding a workplace pension scheme is almost zero for partnered males. In every case for both workplace and personal schemes, the estimates are significantly greater than -1, thereby rejecting the hypothesis of complete substitution.
| Value of Workplace Super scheme | Value of Personal Super scheme | |
|---|---|---|
Slope coefficient  (reference group: unpartnered females) | 0.25 | 0.32 |
| t-value | 4.74*** | 6.51*** |
Differential slope coefficient (males) | -0.14 | -0.06 |
| t-value | 2.48** | 1.23 |
Differential slope coefficient  (partnered) | -0.12 | -0.16 |
| t-value | 2.19** | 3.08*** |
| Sample size | 553 | 835 |
| Adjusted R-squared | 0.52 | 0.40 |
Note: The coefficients are from regressions of net worth on a constant and a set of 21 explanatory variables, based on a sample of those people who are enrolled in a superannuation scheme. Adjusted net worth and value of the superannuation scheme 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 5% level. ***Significant at the 1% level. The b1 coefficients are also significantly different from -1 at the 1% level. For full regression results, see Appendix Tables 9.
The final set of results is for couples (Table 4), where the models were estimated using the combined value of the holdings in workplace or personal schemes. The results show that there is a positive relation between the amount held in either workplace or personal super schemes and the value of other net worth; ie, the more a couple has in a super scheme of either type, the more they tend to have in other forms of wealth. This result corresponds to the case of complementarity rather than substitution. The effect is strikingly similar between the two types of schemes. More specifically, a 10% increase in holdings of either workplace or personal super is associated with a 1% increase in other net worth. These estimates also significantly differ from -1, which allows us to conclude that the hypothesis of complete substitution can be rejected.
Notes
- [6]D1 and D2 are only applicable to regressions on individuals. A possible refinement to this model would be to interact each of the dummy variables ( D1 and D2) with each of the explanatory variables in the vector Z. In principle this would have allowed for the effect on net worth of say, migrant status, to differ between partnered and unpartnered individuals and males and females. In fact we did do this and run the extended model with all interactions, amounting to a total of 53 variables. It was found that almost all the interaction effects were highly insignificant and the overall explanatory power of the model as measured by the R2 was hardly increased. For this reason we pursued the simpler model without interaction terms.
- [7]Age of both the respondent and partner (if a couple) is allowed for as a linear, squared and cubic term; income as a linear and squared term; education is measured by years of schooling plus post schooling training for both the respondent and the partner and ethnicity classified into two groups (Pakeha and non-Pakeha which includes Maori, Pacific Islander, Asian, and “Other”).
- [8]Where the adjusted net worth and the value of the superannuation scheme enter the equation in logarithms rather than in levels.
- [9]The log-linear regressions give considerably higher R-squared values, more individually statistically significant t-ratios, as well as the most “well-behaved” residuals. These merits are, however, somewhat compromised by the fact that observations with negative or zero net worth drop out, as a result of the logarithmic transformation. Results from alternative specifications are available from the authors upon request.
