RDP 9511: Superannuation and Saving 5. Empirical Results

Our procedure for testing the effect of superannuation on other saving follows Pitelis (1985). We estimate a model of saving in which non-superannuation saving is expressed as a function of superannuation saving and other factors that may help explain saving behaviour. The specification of the model (equation 9b) is repeated below:

A coefficient of −1 on the superannuation saving term implies perfect substitution between superannuation and non-superannuation saving; a coefficient of 0 implies independence between the two forms of saving.

To allow for the possibility that the different components of superannuation saving may have different effects on non-superannuation saving we also estimate (9b) with net superannuation contributions and superannuation earnings entered separately. In addition, we estimate a version in which a broader measure of earnings (including capital gains) is used, rather than the narrow and less meaningful national accounts measure.

The data used in estimating equation (9b) are described fully in Appendix B. Briefly, non-superannuation saving is calculated as net household saving as measured in the national accounts less the national accounts' measure of saving through life offices and superannuation funds, expressed as a ratio to household disposable income.^[24]

The superannuation saving term is the national accounts measure of saving through life offices and superannuation funds, also expressed as a ratio to household disposable income. The term is the sum of net contributions to superannuation (employer and employee contributions less claims and administrative expenses) and interest on life offices' and superannuation funds as measured in the national accounts.

The saving measures are not inflation adjusted, but inflation is included directly in the estimating equations to capture uncertainty effects as well as to control for any possible measurement bias due to the effects of inflation.

5.1 Unit Root Tests

A preliminary to time series analysis is to establish the order of integration of the data. The Augmented Dickey-Fuller (ADF) test and the Phillips-Perron Zt tests are employed over the study period 1959/60 to 1993/94, and the results are reported in Appendix C. Briefly, both test procedures show that all the variables are I(1), except the income volatility term which is I(0).^[25] This is expected since income volatility is measured as a three-year moving standard deviation of real per capita household disposable income. Further tests confirm that in all cases we can reject the null hypothesis that any of the series are I(2).

While over a long time span the saving rate is likely to be stationary, we accept that large behavioural shifts have occurred over the past few decades and that the variables are I(1) over the estimation period. As a result, we use an error correction formulation which encompasses both long-run equilibrium relationships and short-run dynamics.

5.2 Estimation

The model is estimated over the period 1959/60 to 1993/94 as an unrestricted error correction model (ECM). This approach enables the long-run equilibrium relationship and the short-run dynamics to be estimated simultaneously. It is recommended over the two-step Engle-Granger procedure, particularly for finite samples, where ignoring dynamics when estimating the long-run parameters can lead to substantial bias.^[26]

The unrestricted ECM is outlined in equation (10) below, where the α's are the long-run parameters, and γ is the error correction coefficient indicating how quickly the system returns to equilibrium after a random shock. The significance of the error correction coefficient, γ, is a test for cointegration. Kremers, Ericsson and Dolado (1992) have shown this test to be more powerful than the Dickey-Fuller test applied to the residuals of a static long-run relationship. The general model is:

The long-run parameters (the α's)^[27] are unbiased, but their t-values do not follow a t-distribution and are therefore not interpretable. The Bewley (1979) transformation is applied to provide approximately normally distributed t-statistics on those parameters.

To obtain our preferred equation, we commenced with a general unrestricted ECM using the important determinants of saving behaviour outlined in Sections 3 and 5. Insignificant regressors were sequentially deleted to arrive at a preferred specification. As a final check, F-tests were conducted on the omitted variables to ensure that they were collectively insignificant. The final equations using different measures of superannuation saving are shown in Table 4. The equations appear to be well specified, passing a host of diagnostic tests which are reported in Appendix D.

A note of caution is in order, however, particularly with respect to the quality of the data and the low power of the tests. The national accounts measures of saving (calculated as a residual) and superannuation flows are generally regarded as poor quality estimates. Data are only available on an annual basis and this restricts our degrees of freedom and reduces the efficiency of our estimates. On the positive side, however, the data cover a period of over 35 years and so potentially contain a lot of information. It is likely that any data deficiencies will have a more serious impact on the short-term dynamics than on the broad long-term relationships which the cointegration methodology seeks to identify.

5.2.1 Short-run results

The first point to note from Table 4 is that the parsimonious equation explains non-superannuation saving quite well. The dynamic model is specified in difference form, but still explains 90 per cent of the changes in non-superannuation saving. The error correction coefficient is significant at the 1 per cent level, supporting the hypothesis that the variables identified as significant in the long run are cointegrated. The speed of adjustment back towards long run equilibrium after a shock appears to be reasonable. The coefficient on the error correction term of −0.57 in column 1 suggests that about half of the disequilibrium is eliminated in the subsequent year, and after three years, about 90 per cent of the shock has dissipated.

The pattern of the short-term dynamics accords reasonably well with our priors. As expected, the human wealth term is very significant in the short term, reflecting the importance of the business cycle in explaining short-run shifts in the saving rate. This is consistent with a number of Australian studies including Edey and Britten-Jones (1990) which find that consumption smoothing is quite important over relatively short periods.

There was no evidence that non-human wealth or demographic factors were important in the short run. The real bond rate was not significant, consistent with theory that points to offsetting income and substitution effects, and the results of many other studies which have tried to identify interest rate effects.

The change in the unemployment rate was significant, suggesting that precautionary motives may have some influence on saving behaviour, at least in the short term.

The moving standard deviation of real per capita income was not significant, but this measure may not be a good proxy for uncertainty.

The results suggest that there are quite large, though incomplete, offsets between superannuation and other forms of saving in the short run. The coefficient on the superannuation saving term suggests that, in the short run, a one percentage point increase in superannuation is offset by a 0.75 percentage point fall in other forms of saving.

This result is conditional, however, on the restriction that the coefficients on the two components of superannuation saving are the same. Tests show that this is clearly not the case. Column 2 in Table 4 reports the results where the two components of superannuation (net contributions and earnings) are entered separately. The coefficient on the contributions term is significant and quite large, but the coefficient on the earnings term is small and insignificant. Similar results are obtained when the superannuation term is split into contributions and a broader measure of earnings that includes capital gains (column 3). The coefficient on the contributions terms is significant and close to −1, and the coefficient on the earnings term is small and insignificant. This suggests that the large short-run offsets between aggregate superannuation and other savings are largely the result of substantial offsets against contributions.

5.2.2 Long-run results

The estimated long-run relationships are reported in the bottom panel of Table 4.^[28] There is evidence of cointegration between non-superannuation saving and the other variables (human and non-human wealth, the demographic term and the superannuation saving term). The long-run equilibrium equation explains most of the structural decline in the non-superannuation saving rate over the past few decades (Figure 6), even though there are likely to be additional factors explaining changes in saving rates – financial deregulation, changing attitudes towards debt and so on.

Both wealth terms, i.e. non-human wealth and our measure of expected future labour income, have the expected signs and are significant at the 1 per cent level in the long run. The coefficient on the non-human wealth term indicates that the rise in non-human wealth is capable of explaining up to about 3 percentage points of the 13 percentage point fall in the non-superannuation saving rate between the peak in the mid 1970s and the trough in the early 1990s.

The human wealth term is more important, explaining about 6 percentage points of the fall in the non-superannuation saving rate over this period.^[29] It appears that the large long-run shifts in household saving rates in Australia – the rise in the mid 1970s, and the subsequent decline – are closely related to shifts in current disposable income relative to longer-run movements in labour income. Saving rates rose sharply in the mid 1970s when current disposable income was high compared with longer-run trends in labour income and then declined as current disposable incomes fell relative to longer-run trends in labour income. This is consistent with the consumption smoothing behaviour of consumers in life-cycle/permanent income models as well as other models which are characterised by slow adjustment of consumption to income or in which consumers accumulate assets in good times as insurance against the possibility of less favourable conditions in the future.

The demographic term was also significant at the 1 per cent level with the expected sign, explaining about 2 percentage points of the fall in saving rates since the mid 1970s. Inflation was not significant at the 5 per cent level, but was retained in the final equation because of its important role in controlling for any measurement bias induced by inflation.

The results provide strong support for the inclusion of the superannuation term in the cointegrating vector (Figure 6).^[30] The importance of including the superannuation term in the long and short run is highlighted by the deterioration in the equation's goodness of fit from 91 per cent to 80 per cent, if the superannuation term is excluded. The superannuation saving term was significant at the 1 per cent level and the coefficient of −0.74, implies a large (though incomplete) degree of substitution in the long run between the two saving measures for the historical period covered by the regression. However, in evaluating this result, the low quality of superannuation and saving data and the low power of statistical tests should be kept in mind.

Once again, however, this result is conditional on the restriction that the coefficients on the two components of superannuation saving are the same in the long term.^[31] The results in columns 2 and 3 show that when superannuation saving is split into its two components, the coefficients on the net contributions term are not significantly different from −1 and the coefficients on the earnings terms are not significantly different from zero. However, the standard errors suggest that our estimates are not very precise, particularly in the case of superannuation earnings where the large standard errors make it difficult to draw any firm conclusions. The standard errors are much smaller for the broader measure of earnings (including capital gains) and we can be more confident that in this case the coefficient is reasonably well estimated. Overall, these estimates suggest that, as best we can tell, there have been large offsets against net contributions, but only small, if any, offsets against superannuation earnings.

Footnotes

The measure of household disposable income is net of employer contributions to superannuation and imputed interest on superannuation funds. More detail on how the Australian Bureau of Statistics measures superannuation saving is provided in Appendix A. [24]

Although the tests report the real bond rate to be I(1), Mishkin and Simon (1994) have shown that these tests are biased towards finding a unit root and that Monte Carlo studies suggest the real interest rate is more likely to be I(0). We share this view and therefore include the real bond rate in the dynamics of the unrestricted ECM model but not in the long run. [25]

Banerjee et al. (1993) and Inder (1994) show that substantial biases in static OLS estimates of the cointegration parameters can exist, particularly in finite samples, and that unrestricted error correction models can produce superior estimates of the cointegrating vector. [26]

Apart from the interest rate and income volatility term (which were found to be stationary and therefore not included in the long run), the coefficients on the long-run variables are the same as in equation (9b). [27]

Our analysis has generally ignored possible effects of corporate saving or government saving on household saving behaviour. If these sectors are ultimately the agents of the household sector and savers can ‘pierce the veil’, household saving may also respond inversely to changes in saving by these other sectors. There was no evidence, however, to support the inclusion of either of these terms in the cointegrating vector. The coefficients on corporate saving and public sector saving were small and insignificant. [28]

The results were quite sensitive to the specification of this term, but alternative specifications (for example, using current rather than trend labour income as an indicator of expected future labour income) produced inferior results, both in terms of the explanatory power of the equations and the performance of individual explanators. [29]

Even when the superannuation term is excluded, there is evidence of cointegration. Of course, when the term is excluded, the equation is misspecified and the estimates are biased. [30]

Standard tests reject this restriction in the case of contributions and the broader measure of earnings (including capital gains), but because of the large standard errors we are unable to reject the restriction in the case of contributions and the narrow measure of earnings. [31]