3 Empirical Analysis and Results

We now turn to our empirical analysis. Before reporting the results for the extensions to the specifications for the relationships between material well-being and current income and accommodation costs discussed above, we first briefly discuss our replication of the base specification from the original report. All the analysis presented here is weighted so as to be representative of the over-65 population of older New Zealanders. The weights used are a revised set of weights provided by the original researchers that, except for a scale adjustment, are the same as the original (Statistics New Zealand provided) weights for single CEUs, and for couple CEUs whose respondents’ partners are also over-65, but equal to one-half of the original weights for couple CEUs with partners aged under-65.

3.1 Replicating the Original Results

We first present our replication of the base specification we adopt from the original report (Table 7.11) because we understand that some data editing by Statistics New Zealand has resulted in different versions of the base data being available. As a result of this issue and possibly different identification of outliers and/or treatment of missing data values, our analytical sample does not match exactly that used in the original report. For example, our sample has about 100 more observations than originally reported for the model that we adopt as our base specification.In particular, we compare the original results reported in Table 7.11 of the original report with our estimated version of this model. These results are reported, respectively, in columns (1) and (2) of Table 3 and appendix Table A1. Table 3 contains the estimates of the income variable coefficients, while the remaining coefficient estimates are reported in the appendix Table A1. Overall, the replicated results are close to the original results. Each of the estimated coefficients is not statistically significantly different from the original estimates at conventional levels of significance,[16] and only two coefficient estimates (on the interaction between the Couple CEU dummy variable and the Number of Adverse Events, and the NZSEI Score variable) differ by more than 1 standard error. Also, that the R-squared from our regression model (0.39) is a little lower than the original specification (0.40), suggests that the more inclusive sample used here contains more outliers than in the original analysis.

Although we have been unable to achieve a complete replication, we believe the results of the analysis presented here are sufficiently close to provide confidence that our analysis closely replicates the earlier analysis. Subsequently, we treat the specification in column (2) of Table 3 as our base specification for extending the analysis of the relationship between material well-being and incomes and accommodation costs outlined above. We now turn to our main analyses.

Notes: Estimated standard errors are in parentheses. All table entries are based on weighted calculations.

3.2 Relaxing the Income Specification

We first focus on the relationship between material well-being and current income. Columns (3) and (4) of Table 3 contain estimates from two alternative specifications considered for relaxing the income specification in the model presented in column (2).

The first specification, in column (3), includes the fraction of total income from each of the six (excluding NZ Superannuation) income sources wages and salaries, self employment, investment income, overseas income, private pensions and benefit allowances. The results of this exercise imply, first, that the estimated associative effect of log(income) on material well-being is about one-half that presented in column (2), suggesting that current income per se is less important than the original report found. That is, a 10% increase in income is associated with about a 0.24 increase in material well-being score compared to an estimate of about a 0.46 in column (2).

Second, controlling for the level of total income (and other factors), the fraction of income from each of these sources, other than from overseas, is individually significantly correlated with material well-being. A 10 percentage point increase in wage and salary, self-employment, investment, or private pension income, at the expense of a 10 percentage point decrease in NZ Superannuation, is associated with an increase in material well-being score of 0.4—0.6, while a 10 percentage point increase in benefit allowances is associated with a 0.7 point fall in material well-being score.

It is also worth noting that the standard error on the coefficient of log(income) in this specification is roughly double that in column (2). This is due to the income source fractions being quite strongly correlated with log(income), and implies potential difficulty in identifying effects associated with (the log of) income versus the source of income. Nonetheless, there remains sufficient precision in the estimates to reject, at conventional levels of statistical significance, the hypotheses that the coefficients on the income source fractions are zero, and that the coefficient on log(income) is the same as estimated in column (2).

The comparative similarity between the estimated coefficients on the fractions of income from wages and salary and self-employment income, and on the fractions of income from private pensions, overseas and other income, lead us to consider aggregating these two sets of income sources, giving four income sources: NZ Superannuation, “earned” income, “capital” income, and other benefit allowances. The regression results based on this more parsimonious specification are reported in column (4) of Table 3. The results are similar to those reported in column (3), and the two sets of restrictions are individually and collectively accepted statistically.[17]

The results presented here imply that the originally specified relationship between material well-being and current income is incomplete and, at least, too simplistic to be interpreted as representing direct causal effect from current income to material well-being. Although, we are not necessarily proposing the extended specifications here as being “correct”, we believe the results from these specifications provide a better appreciation of the observed relationship(s) between material well-being, current income and its sources for older New Zealanders. For example, the results are consistent with the hypotheses that current income, at least partially, proxies for other factors that affect material well-being, and that these factors may be related to the health and wealth holdings of older New Zealanders.