6 A Model of Prescribed Saving Rates for Retirement
The system of retirement income provision in New Zealand means that for many wives, retirement, and the receipt of NZ Superannuation, may mark an improvement in their economic status relative to their husband. Hence, in this setting, working age women with more bargaining power than their husbands will not necessarily have wealth accumulation as their goal. Instead, it may be rational for these women to finance greater current consumption, by reducing household wealth. This hypothesis is certainly consistent with the finding from Section IV that various measures of women’s relative bargaining power are associated with lower net worth for couples.
To explore this hypothesis we construct a consumption smoothing model of saving for retirement, following Moore and Mitchell (1997). Our purpose is to see whether, given an objective of smoothing their consumption through retirement, women in New Zealand have lower saving requirements than men. While our interest is mainly in couples, because of the tension that may exist between husbands and wives when making savings plans, we have no way to determine the individual wealth and prescribed saving rate for each person in a couple. While the Household Saving Survey has individual data for some components of net worth (inheritances, work-related pension schemes, and student loans) the major components of wealth (real estate, businesses, farms, and financial assets) are reported on a joint basis. We therefore apply the model to the uncoupled individuals from the 45-55 year old cohort. This group is still relevant because many women in couples will eventually become uncoupled due either to the death of their spouse or divorce (which might be precipitated by conflict over wealth bargaining). If women in couples observe that uncoupled women have lower saving requirements than do uncoupled men, it presumably will affect their own decision on optimal wealth accumulation.
Our simple model of saving for retirement is built on the life cycle approach to consumption and saving. We estimate the saving rates and the replacement rates that are implied if individuals attempt to sustain an equal level of consumption before and after retirement; i.e., we invoke consumption smoothing as the aim of retirement saving. In this simple model the person chooses a constant level of consumption that can be financed from income over the working life, and then from savings during retirement. This ignores the fact that when life expectancy is uncertain consumption will tend to rise until retirement and fall subsequently, rather than remaining uniform throughout. According to Mitchell and Moore (1997), “The effect of this uncertainty is to make the consumption line become humped, rising during the working years and declining during the retirement years. (In any event it still changes less drastically with age than does earned income.) This new shape is the result of the household weighing needed saving to finance future consumption by the probability of living, and comparing that to the value of wasted consumption due to saving if the household does not survive” (p.11) . Other forms of uncertainty that give rise to precautionary saving are also ignored.
A graphical illustration of the model we apply is given in Figure 2. An individual has a net worth (depicted as Wa) as measured in the Household Saving Survey. This is projected to grow to an amount denoted Wp by the time they reach a predetermined retirement age (here we assume 65). In order to have a given level of income in retirement they would need to have accumulated retirement wealth depicted in Figure 2 as the stock, Wr. Part of their retirement income is provided by NZ Superannuation so the stock of wealth at retirement equivalent to this flow of income is incorporated in Wr and Wp. The difference between the required wealth (Wr) and the projected wealth Wp is labelled as the shortfall and is the amount which would need to be accumulated between now and retirement in order to add to the projected stock and hence support an income in retirement of level (denoted Yr). This additional amount, in the absence of inheritances or unanticipated windfall gains or losses in asset values, would need to be accumulated through savings
- Figure 2 – A Stylised View of Stocks and Flows of Income, Savings and Retirement Wealth in a Model of the Joint Determination of Saving and Replacement Rates
The flows of income, consumption, savings and taxes that are derived from the projected and required wealth stocks, and the shortfall, are depicted in Figure 2(b). It is assumed that some fixed share of pre-retirement income will be saved (s=S/Yp) and the replacement rate (R) is given by the ratio of gross income in retirement to gross income pre-retirement (i.e., R= Yr/Yp). Under the New Zealand taxation system, post retirement taxes (denoted as Tr) can be assumed to be zero, so real after tax consumption is equal to total post-retirement income. Clearly some values of retirement income could imply a substantial shortfall in retirement wealth, which might in turn require unrealistic or unfeasible levels of saving pre-retirement. It is for this reason that the prescribed saving rate and predicted replacement rates are jointly determined. While some people will already have sufficient existing wealth to retire with full replacement of their pre-retirement income, for others the stock of wealth will not be enough. Therefore, there is no expectation that replacement rates will be equal to unity and nor are they expected to be the same for men and women.
A number of additional factors arise which are not depicted in Figure 2. Uncertainty is ignored by assuming that individuals correctly predict their life expectancy. Instead of a constant pre-retirement income we assume that income grows from its actual level (as observed in the survey) by a fixed annual growth rate of one percent (chosen to approximate the average annual rate of labour productivity and real wage growth in the economy). Similarly, NZ Superannuation payments grow at one percent annually in real terms, matching the growth in average real wages. Housing wealth, which is the current equity in the principal residence, is excluded from the calculation of retirement wealth, Wr. A somewhat typical pattern is for those owning a primary residence to retain this, partly as a precautionary investment and partly as a potential bequest. In such cases it would not be appropriate to include the net value of housing assets as part of retirement wealth and thereby available to be converted into an annuity along with other accumulated assets.
- In divorce-threat bargaining models the threat point is the maximal level of utility attainable outside the marriage (Lundberg, 1999).
- Studies such as Bernheim (1992) and Scholz, Seshadri and Khitatrakun (2004) use a formal optimisation approach based on maximising consumer utility subject to an intertemporal budget constraint. We follow Moore and Mitchell (1997) who note in relation to their choice of a simpler framework: “From a theoretical perspective, this is less appealing than a true life cycle-dynamic programming approach as it ignores utility theory and behavioural responses to uncertainty. However it is a popular model among retirement planning practitioners and can be seen as a relatively tractable approximation or rule of thumb to the life cycle model”. For a comparison of a utility maximising approach and the model used here see Scobie and Gibson (2003) who find that the results from both models are remarkably similar.
- A complete derivation of the model is given in Scobie and Gibson (2003).
- In the context of the New Zealand system of taxation, private retirement saving is made from after-tax pre-retirement income and the earnings on the investments are taxed. However, once those accumulated funds are withdrawn (in this case to purchase an annuity) then there is no further taxation payable by the recipient; taxes on earnings are paid by the seller. Furthermore, New Zealand Superannuation payments are received net of tax. Hence under this system, it is appropriate to assume for the purpose of the modelling that there is no post retirement taxation (i.e. tr = 0).