RDP 9511: Superannuation and Saving 3. Superannuation and Saving – Some Theory

3.1 Models of Saving Behaviour

Saving is a decision about how much of current income should be retained to finance some future contingency. Models of saving behaviour differ in how they attempt to formalise these decisions, but they are linked by the common theme of intertemporal choice.

Life-cycle/permanent income models have provided the theoretical underpinnings for much of the research on aggregate wealth accumulation over the past few decades and they are a useful starting point for looking at the effects of superannuation on saving behaviour. There are other models, however, also consistent with the basic theory of intertemporal allocation, that give additional insights into saving behaviour and asset choice. More complex formulations, for example, relax some of the strict assumptions underlying the basic life-cycle model and extend the basic model of intertemporal choice to allow other factors such as uncertainty and liquidity constraints to influence consumption and saving behaviour. These models do, however, retain many of the useful features of the basic life-cycle model and are largely extensions on a common theme.

Models of consumption and saving behaviour often have strong microeconomic foundations. The standard mechanism for modelling consumer behaviour is the maximisation of utility subject to a linear budget constraint. In the life-cycle model consumers' intertemporal preferences are widely represented by a utility function of the form of equation (1) in which preferences are intertemporally additive, and where the single period subutility functions are increasing and concave:^[12]

The form of the utility function is quite important, because it governs consumers' attitudes towards uncertainty. In simple formulations, increases in uncertainty do not affect saving. Lifetime consumption profiles are introduced by writing:

where z captures variables that influence the desirability of consumption at different points in the life cycle (such as demographic factors) and δ is the rate of time preference.

Utility is maximised subject to a lifetime budget constraint. Lifetime income is comprised of initial assets A₁ and a stream of future labour income, y. Funds held over from period to period earn a real return, r.

Solving the optimisation problem gives the familiar formulation in which current consumption is a function of current real non-human wealth, A, and the present value of future labour income, H.

where γ depends on the parameters and variables of the utility function, the rate of time preference and the interest rate. In this simple framework, households accumulate wealth during the pre-retirement period by consuming less than current income; after retirement, wealth is gradually run down to finance consumption. Saving is positive during the pre-retirement phase of the life-cycle and negative during the retirement phase. Assuming there are no initial endowments and no bequests, saving will average zero over the life-cycle.

Permanent income theory yields similar results. Consumption is determined by permanent income, which itself is close to the annuity value of lifetime resources shown in equation (4). However, compared with the life-cycle model, permanent income theory places more emphasis on the way in which individuals form their expectations of future income and about how consumption and saving respond to changes in income, particularly in the short term. Individuals will consume out of permanent income, but transitory shifts in income will not affect consumption. Like the life-cycle model, permanent income theory predicts that people save when current income is high relative to some measure of average lifetime incomes and dissave when current income is below lifetime income.

The formation of expectations of future income emphasised by the permanent income theory can be combined with the variables suggested by the life-cycle approach. It is unclear how consumer expectations of lifetime incomes are formed in practice, but the statistical properties of the data provide some information about how labour income actually evolves and how consumers may value expected future labour income (Deaton 1992). If, for example, labour income is an I(1) series (that is, stationary in differences), shifts in current income are permanent and could be thought of as shifts in permanent income. If, on the other hand, income is stationary around a deterministic trend, trend growth in income might provide a better measure of permanent income.

Assuming that labour income follows the latter process, and that future labour income is related to trend labour income, y_L, by θ, equation (4) becomes:

Replacing c with (y-s) and dividing by disposable income, y, gives an expression for the saving rate, (s/y):

Aggregation of (6) yields a loosely specified aggregate saving function in which saving depends on human and non-human wealth, the real interest rate, and demographic characteristics of the population, D.

One of the most important insights provided by this simple specification of the life-cycle model is that human and non-human wealth play a central role in saving decisions. The theory predicts that, given expected income, an increase in real wealth will allow a rise in lifetime consumption and reduce the share of current disposable income that is saved. Higher wealth allows households to enjoy a higher level of lifetime consumption, even though current labour income is unchanged. Both non-human and human wealth are negatively related to saving in this framework.

Interest rate effects, however, are ambiguous. Higher real interest rates make saving more attractive by making future consumption cheaper relative to current consumption.^[13] On the other hand, higher real interest rates increase future income and reduces the need to save to achieve any given level of consumption.

Demographic factors affect consumption and saving by changing the proportions of individuals within the different life-cycle groups. Higher proportions of individuals in the pre-retiree age group (roughly 45 to 64) would be expected to increase saving. Higher proportions in the retiree age groups (65+) would be expected to lower saving. As a result demographic factors such as life expectancy, average retirement age and labour market participation may influence consumption and saving. Other factors bearing on the need to save for retirement, such as social security provisions, may also affect consumption and saving.

The life-cycle model can be extended to include other variables to the list of possible influences on saving behaviour. The addition of precautionary motives is particularly important. Precautionary motives, although consistent with the basic theory of intertemporal allocation, are ruled out by the assumption of certainty or certainty equivalence that supports the life-cycle model (Deaton 1992). The quadratic subutility functions that underlie the permanent income hypothesis do not support a precautionary motive for saving. However, other, more analytically complex formulations of the utility function do allow for precautionary saving.

Potentially, this is very important, because in practice we know that households face uncertainty about their lifespan, health, future earnings and lifetime expenses. Cabellero (1990) has shown that uncertainty as to the permanence of a shock to income can have large effects on saving behaviour. Even shifts in permanent income may have only a sluggish effect on consumption spending (and therefore change saving) if households are uncertain.^[14]

In models that include precautionary motives, households will save more (borrow less) earlier in life than in the certainty equivalence case because of the possibility that they may experience an unfavourable event. In extreme cases, households may choose not to borrow at all. The utility that households gain by having a stock of assets to draw against, if required, more than offsets the loss from forgoing some immediate consumption opportunities. Older households will dissave less than in the certainty equivalent case because of uncertainty about lifespan, medical costs and asset returns. Because older households will maintain a buffer against uncertainty, (accidental) bequests are also likely to occur.

In terms of our aggregate saving function, precautionary motives are likely to increase the level of saving while reducing the sensitivity of the saving rate to life-cycle influences. Theory suggests that a measure of volatility of income, , may be an appropriate measure of uncertainty, but in practice uncertainty is difficult to measure directly and indicators are often used to model states likely to be associated with higher uncertainty. Two possible indicators are the rate of inflation, Π, and the change in the rate of unemployment, ΔU, both of which would be expected to be positively related to uncertainty (Carroll 1992). These measures of uncertainty are added to equation (7) to give:

Liquidity constraints are also ruled out by assumption in the standard life-cycle models but are often linked with saving behaviour. Life-cycle models assume that capital markets are perfect and that households are able to borrow against lifetime incomes. However, studies find that, in practice, up to half the population is liquidity constrained (or act as if they are) and borrowing constraints are likely to prevent many households from optimising according to the predictions of the life-cycle model.^[15] One implication of this is that consumption is more likely to follow current household income than in the standard life-cycle model.

The effects of liquidity constraints on saving, however, are unclear. In an extreme case, continuously binding liquidity constraints imply that individuals bound by this constraint do not save. If liquidity constraints are not continuously binding, however, expectations of possible future constraints may induce people to hold more assets as a buffer stock against future needs than would otherwise be the case (Deaton 1992). The inability to borrow may increase consumption uncertainty and strengthen the precautionary motive for saving. If constraints are more (less) binding when income is low (high), liquidity constraints may increase the sensitivity of aggregate saving to shifts in aggregate income. Households will save when income is relatively high and run down saving during periods when lower incomes and liquidity constraints would otherwise cause a sharp decline in consumption spending.

3.2 Introducing Superannuation into Saving Models

The basic life-cycle model focuses on the intertemporal allocation of resources, but does not give much attention to the types of assets that facilitate the process. Assets are assumed to be riskless and superannuation assets and other forms of savings are effectively assumed to be perfect substitutes.

The effects of changing the level and conditions of superannuation saving in this framework are quite clear. An increase in superannuation saving, for example, resulting from an increase in the returns available on superannuation relative to returns available on other assets (and assuming aggregate returns remained unchanged) would result in a shift in saving, at the margin, into superannuation saving and a reduction in one of the other forms of saving. An increase in superannuation saving resulting from a compulsory levy would have a similar effect. The levy would raise total saving above preferred levels and households would adjust other saving downward to compensate for the increase. In both cases, a rise in superannuation would result in a one-for-one reduction in other forms of saving with no increase in aggregate saving, under the extreme assumptions of perfect certainty and perfect substitutability.

Once uncertainty and capital market imperfections are introduced, however, the likely effects of superannuation on other types of saving are more complex. If income flows are uncertain and households have to rely on a portfolio of risky assets to provide for future consumption, and to provide insurance in different states of the world, consumption decisions and portfolio choice are not independent. In this framework, assets are no longer perfect substitutes and we would not expect to see one-for-one offsets between superannuation and other types of saving.

Households will allocate the sum of non-human wealth and labour income between consumption and a selection of assets that may differ in terms of riskiness, return and liquidity, and across a number of other dimensions. Households will choose a portfolio of assets so that, having regard to the different characteristics of available assets, the marginal utility obtained from holding each asset is the same. Increments to the stock of assets (saving) will be apportioned accordingly.

As with other forms of saving, the proportion of new saving held in the form of superannuation will depend on the characteristics of that asset compared with the characteristics of other assets that could potentially be added to the portfolio. Saving may be encouraged to flow into superannuation assets by concessional tax treatment which raises the yield on superannuation assets above that of most other assets, or as a result of institutional arrangements such as compulsory levies and long-term contractual arrangements. The extent to which households will offset these increases (decreases) in superannuation saving with decreases (increases) in non-superannuation saving will depend on the degree of substitutability, at the margin, between the different forms of saving. If superannuation saving can provide households with an equivalent, or better, level of future consumption (for example, in terms of yield) and/or the same insurance against future contingencies (for example, in terms of liquidity and risk), then it is likely that higher superannuation saving would be wholly or partly offset by lower non-superannuation saving. In practice, however, it is likely that informational problems and capital market imperfections will reduce the perceived substitutability of the different forms of saving and reduce the extent to which households will be prepared to substitute superannuation for other forms of saving.

Savers who are myopic or likely to be liquidity constrained may place a high discount rate on superannuation saving because benefits are generally not available until retirement. As a result, they may not reduce other forms of saving to compensate for (forced) higher superannuation saving. Even if they do value superannuation saving as highly as other retirement saving, they may not reduce other saving if credit market frictions may prevent them from borrowing against lifetime income to return to a desired consumption path.

Savers who are concerned about uncertainty prior to retirement are also likely to regard superannuation assets as an imperfect substitute for other forms of savings. Increased superannuation saving may be a good substitute for retirement saving for some households, but a poor substitute for other forms of saving aimed at meeting contingencies prior to retirement.

A similar lack of substitutability may apply in the case of savers who are concerned about insuring against post-retirement uncertainty. These savers may have limited knowledge of employer contribution rates and may be unaware of the rate at which superannuation assets are likely to accumulate over time.^[16] They may also be unaware of taxation arrangements and uncertain of the fee structures (such as entry, exit and management fees) related to the administration of their superannuation savings. In this case, households may maintain other retirement saving even if superannuation saving increases.

Even savers who are fully informed and who optimise according to standard life-cycle theory may place a low value on superannuation assets if holdings of superannuation assets have unfavourable tax consequences or reduce entitlements to public pensions and benefits.

In summary, there are a number of factors, including information problems, credit market frictions and institutional arrangements, which suggest that aggregate household saving may not be independent of the form in which saving is held and that changes in superannuation saving may therefore change total saving. A crude, but simple, way of allowing for this possibility is to augment equation (8) by directly including superannuation saving, S^s:

Noting that total saving is the sum of superannuation saving, S^s, and non-superannuation saving, Sⁿ, we can rewrite equation (9a) as:

which is the basic form of the estimating equation used later in the paper. If increases in superannuation saving are offset one-for-one by reductions in other forms of saving, the coefficient on superannuation saving (α₈−1) would equal −1 and the equation would collapse to the extended life-cycle model represented by equation (8). If there were no offsets, (α₈−1) would equal 0. In this case, an increase in superannuation saving would increase aggregate saving by a similar amount.

Empirical evidence on the likely size of the coefficient on the superannuation saving term in equation (9b) is limited. Overseas private pension schemes are quite different to Australia's superannuation scheme, and they are not very useful in assessing the effects on saving of the Australian scheme. A recent OECD paper, however, suggests there is an increasing body of evidence pointing to at least partial substitutability between saving in retirement saving schemes and other forms of saving (OECD 1994). A recent IMF study on saving in Asia also reports substantial offsets (Faruqee and Husain 1995). It finds little evidence that compulsory provident fund saving has increased the trend rate of saving in Malaysia and finds that, in Singapore, about three-quarters of the rise in compulsory saving has been offset by a reduction in other saving. Recent US studies also find evidence of substantial offsets.^[17]

Australian empirical evidence is limited, although Goode (1994) finds evidence of partial substitution. The FitzGerald (1993) report uses a ratio of 50 per cent substitution, although the measure is an assumption rather than an estimate.^[18]

Footnotes

The overview of consumption theory and the simple exposition of the basic life-cycle and permanent income models in Section 3.1 is closely based on Deaton (1992). [12]

The general rate of return concept used here is a proxy for the rate of return available on a mix of financial and real assets. In Australia, where leveraged housing wealth is a large component of total household wealth, the returns available from foregoing consumption should also reflect the returns available from investing in housing (such as imputed dwelling rent and capital gains). In the empirical work, we use a more conventional measure of real interest rates under the assumption that returns available on different assets, after adjusting for risk and other factors, will generally move together over time. [13]

For example, see Skinner (1988) and Engen et al. (1994). [14]

See McKibbin and Richards (1988), Lattimore (1994) and Blundell-Wignall, Browne and Tarditi (1995). [15]

Even where savers can predict future entitlements accurately, changes in superannuation saving through either contributions or earnings may have little effect on behaviour. In the case of defined benefit schemes, for example, employees are entitled to clearly defined benefits on retirement and these payments are at least partly independent of measured contributions. [16]

See Gale and Scholz (1994), Joines and Manegold (1991) and Engen et al. (1994). For contrary evidence see Venti and Wise (1987, 1990, 1991, 1992). [17]

See FitzGerald and Harper (1993). [18]