2.3  The Relationship between Material Well-being and Current Income

We now turn our consideration to the specification and interpretation of the relationship between the living standards of older New Zealanders and observable factors that may help “explain” individuals’ living standards. In particular, we focus here on two factors: first, the relationship between living standards and current income; and, second, the relationship between living standards and accommodation costs. We discuss issues associated with each of these in turn.

Despite the fairly low correlation revealed by Figure 2, the estimated relationship between income and material well-being was statistically significant. The main focus of our attention in this paper is the interpretation and robustness of this relationship. In particular, although current income is correlated with material well-being, this does not necessarily imply a causal link. That is, higher income in older age may act as a proxy for some other factor that independently determines a person’s material well-being. For example, if a person has extra income because of paid employment, his or her material well-being score may, in part, reflect a positive human capital or “health” factor that has facilitated an extended career. Alternatively, if extra income is primarily in the form of investment returns, this might indicate a wealth effect on material well-being. Similarly, if additional income is received in the form of benefit allowances, this might indicate that the person faces unusually high costs and might not have a high level of material well-being in relation to that income level.

One implication of the simple model specification adopted in the 2001 Report is that the marginal dollar of income has the same effect on material well-being irrespective of the source of that dollar (NZS, earnings, investment returns or benefit allowances). Testing this hypothesis helps to shed some light on the question of causation since, if different income sources have different sized effects on material well-being, this would suggest that income is acting as a proxy for one or more other factors.

In order to develop this idea further, we start with the original report’s generic regression specification for modelling the relationship between material well-being and income, controlling for demographic and other characteristics, which we express here as

(1)     

where Y_i is the material well-being score of observation-i (pertaining to either an individual or a couple), log(Inc_i) is the (natural) logarithm of their total net (annual) income,[11] X_i is a vector of other observable control variables,[12] u_i is a residual term to capture unobserved effects, and β₁ and γ are regression model coefficients. In this specification, a 1% increase in net income is associated with a β₁ increase in material well-being. (If this association is treated as causal, then a 1% increase in income “causes” a β₁ point increase in material well-being.)

As discussed above, the specification in equation (1) restricts the relationship between material well-being and net income to be the same across different sources of income, in the sense that a marginal increase in income has the same (associative) effect on material well-being irrespective of the source of that income. There are various ways in which this restrictive aspect of the specification could be relaxed and tested. The approach we adopt in the analysis reported below is to extend specification (1) to include the fractions of income from alternative sources:

(2)     

where IncSrc_ji is the fraction of CEU-i's income that is derived from source j, and λ_j is the regression coefficient on this fraction. In the analysis below, we consider two alternative source groupings. First, a fine grouping of income from seven sources: New Zealand Superannuation, wages and salaries, self employment, investment income, overseas income, private pensions, and benefit allowances. Second, we adopt a broader grouping into four sources, by aggregating wages and salaries and self employment income into “earned income”; and aggregating investment income, overseas income and private pensions into “capital income”.

The specification in equation (2) nests the original specification (1). In particular, if the hypothesis that only total income (and not the source of income) matters, then λ_j=0 for all sources. That is, the original specification is correct and equation (2) reduces to equation (1). On the other hand, if the source of income (as well as the level of income) has an associative effect on material well-being, then we would expect λ_j≠0 for at least one income source j. Thus, testing whether λ_j=0 for all sources of income provides a test of the simple specification in the original report via the hypothesis that only total income, and not the source of the income, affects material well-being. As discussed above, if this hypothesis is rejected, possible reasons may include that, conditional on total income (and other factors), higher fractions of earned income may proxy for better health, and/or that higher fractions of capital income (or lower fractions of benefit allowances) may proxy for higher wealth levels, both of which may be associated with higher material well-being.

We summarise the incidence of alternative income sources in Table 1: columns (1) and (2) describe the fractions of the sample with income from the various sources, while columns (3) and (4) describe the fractions of income from these sources. NZ Superannuation is the dominant income source with (almost) all the sample receiving NZS, and accounts for 74% of gross income of older people. In contrast, 16% have earned income (11% have wage and salary employment, and 7% have self employment), accounting for 5% of gross income; 77% received capital income (74% investments, 15% private superannuation, and 2% overseas income) accounting for 19% of gross income; and 19% of older people receive additional benefit allowances, which accounts for 2% of gross income.

As the sum of the income fractions across either set of sources is necessarily 1, we need to omit one source fraction from the regressions and choose to omit the fraction of income derived from NZ Superannuation. Given this specification, holding (the log of) total income (ie log(Inc_i)) constant, a 1% higher fraction of income from source j (matched by a 1% lower fraction of income from NZ Superannuation) is associated with a λ_j/100 unit higher level of material well-being.

Notes: The number of observations used is 2,986. All table entries are based on weighted calculations.