4  Saving for retirement - the model

To model adequacy of retirement saving, we adopt a framework of joint determination of saving and replacement rates. This framework seeks to smooth consumption throughout the life cycle.

4.1  General assumptions

For simplicity, we ignore uncertainty. Specifically, this assumption means that an individual will retire at a certain age as planned; does not engage in the work force after retirement; knows exactly what their income until retirement will be; can accurately project the rate of return on investments; has a known life expectancy at the age of retirement; knows the amount of NZS that they will receive; plans and executes whatever bequests they wish to make; has no unexpected changes in health status that would affect income or expenditures; and assumes tax rates and other policies remain unchanged.[7]

In the absence of uncertainty, the life cycle saving and consumption patterns can be illustrated as in Figure 4. The household chooses a level of consumption that can be financed from income over the working life, and then from savings during retirement. This implies (ignoring interest for the moment) that savings are equal to consumption needs in retirement.

Figure 4 – A life cycle model of income, savings and consumption

Source: Adapted from Moore and Mitchell (1997).

This simple life cycle pattern can be modified to allow for uncertainty. As shown by Moore and Mitchell (1997), when life expectancy is uncertain, consumption will tend to rise until retirement and fall subsequently, rather than remaining uniform throughout (see Figure 4b). However, the basic pattern of earnings and savings before retirement and wealth decumulation throughout retirement to finance consumption is left unaltered. In the face of uncertainty, some precautionary savings may be accumulated, which, if not needed, may lead to bequests. Conversely, if accumulated savings prove inadequate due to unforeseen events, some source of assistance income in retirement would be required.

Abstracting from uncertainty has the advantage of significantly simplifying the analysis. Clearly, the results can not be interpreted as applying to a particular individual whose incomes, expenditures, returns on assets and life expectancy are all subject to shocks. However, when these shocks are both unanticipated and distributed equally among both positive and negative changes, the outcomes illustrated here can be interpreted as expected values for any given population group.

4.2  A model of joint determination of saving and replacement rates

This approach[8] calculates jointly the saving and income replacement rates for each person or couple. A complete derivation of the model is given in Scobie et al (2005, Appendix C) and reprinted in Appendix B, while a graphical illustration is presented in Figure 5. At the current time a person/couple has a net worth as measured by SOFIE. This wealth is projected to grow to by the time they reach a pre-determined retirement age. In order to have a given level of consumption in retirement they would need to have accumulated a stock of wealth equivalent to . Part of their retirement income is provided by NZS and the stock of wealth equivalent to the NZS income is incorporated in and .

The difference between the required wealth and the projected wealth is the shortfall that would need to be accumulated between now and retirement. This additional amount, in the absence of inheritances or unanticipated revaluation in asset values, would need to be built up through savings. These flows are depicted in Figure 5b.

The approach assumes that some fixed share of pre-retirement income will be saved () and the replacement rate is given by the ratio of gross income in retirement to gross income pre-retirement (). Under the New Zealand income tax system of TTE,[9] retirement taxes are zero, so consumption is equal to income in retirement. Clearly, some values of retirement income could imply a substantial shortfall in retirement wealth, which might in turn require unrealistic or infeasible levels of savings before retirement. It is for this reason that the saving and replacement rates are jointly determined.

Figure 5 – A model of joint determination of saving and replacement rates

4.3  Specific assumptions

The retirement age is set at 65. We apply an after-tax, real rate of return of 2% per year for all compounding and discounting. We project pre-retirement income from its current level using an annual growth rate of 1%, chosen to approximate the average rate of labour productivity and real wage growth in the economy. Pre-retirement tax rates are based on this pre-retirement income . NZS payments are assumed to grow at 1% annually in real terms, matching the growth in average real wages.[10] Bequests involve only the current equity in the principal residence.

The model for couples is complicated by the fact that the two partners of each couple may neither retire nor die at the same time. The retirement phase for couples is assumed to start when the older partner reaches 65 (the younger partner will continue earning an income, which may affect the value of NZS received by the retired partner). We further postulate that after one partner dies, the surviving partner will have a consumption level equivalent to 60% of the couple's level. We compute life expectancies from mortality rates projected by Statistics New Zealand. These projections take into account predicted changes in health status based on `medium' assumptions around fertility, mortality and migration. We assume that Pacific Islanders have the same mortality rates as Maori and that mortality rates are the same for all other ethnic groups. As such, we are able to calculate life expectancies at retirement for each gender, broad ethnic group and year of retirement.