3  Data and Estimation Issues

In this paper we use the Household Saving Survey (HSS), a survey of the assets and liabilities, household characteristics, and income of New Zealand residents conducted in 2001 by Statistics NZ for the Office of the Retirement Commissioner (Statistics New Zealand 2002). This survey is most comparable in coverage and methodology to the Canadian Survey of Financial Security (Statistics Canada, 2001) and the U.S. Survey of Consumer Finances. The survey covered those over 18 years old living in private dwellings and usually resident in New Zealand. It is important to stress that the term household refers to the unit of selection. One person from those qualifying in a selected household was chosen at random, and information was collected from and about that individual. In the case where they had a partner, information was collected for the couple, i.e., where the respondent and his/her partner were living in the same household the couple was interviewed as a single unit. Thus, we have data on couples, and on uncoupled individuals. This is a useful feature because couples who are engaged in bargaining are likely to look at the wealth status of uncoupled individuals when forming their views about utility outside of the marriage.

We focus on those aged between 45 and 55 (inclusive) because this an age group that is near retirement but which is still actively saving.[4] The effects of bargaining, due to gender differences in preferences for wealth accumulation, should be more apparent in this group than for other ages. All of our analyses are based on weighted results, to reflect the sample design, so that we can make inferences about the population. The weights reflect the probability of selection of an individual within the household, of the household within the Primary Sampling Unit (PSU), and of the PSU within its stratum. In addition there are adjustments for non-response and to ensure the population counts for age, sex and ethnicity correspond to national benchmark estimates.

We study total net worth, which is defined as the difference between total assets and liabilities. The assets covered by the survey include residential and investment property, farms, businesses, life insurance, bank deposits, positive credit card balances, shares and managed funds, money owed, motor vehicles, cash, collectibles, and holdings in personal superannuation and defined contribution schemes. The liabilities include property mortgages, student loans and other bank debt, and negative credit card balances

Notes: Net worth estimates are in NZ$. At the time of the survey, NZ$2.38 = US$1.00.

^a For couples, membership of this cohort occurs if either the respondent or their partner is 45-55 years old.

^b A respondent with a partner, the net worth estimate is for the couple.

^c A respondent who was not living with a partner.

The mean net worth of the couples in the cohort we study is NZ$412,330 (Table 1). The mean is more than 50 percent above the median, and for uncoupled individuals it is more than 80 percent above the median. The difference between means and medians is even greater when we consider all age groups. The large discrepancy between the mean and the median is indicative of a highly skewed distribution of net worth with a long “right hand tail” to the distribution created by a few very wealthy individuals and couples.

This skewness indicates a major problem in fitting wealth regressions to these data. When net worth is used in linear form as the dependent variable, the results will tend to be dominated by those with very high wealth. Alternatively if one takes the logarithm of wealth then a significant number of households with zero or negative wealth would have to be deleted from the sample, reducing the applicability of any findings to a subset of the population. Our solution is to rely mainly on regressions through the median of the net worth distribution, using the least absolute deviations (LAD) estimator (Koenker and Bassett, 1978). These median regressions are more robust to the presence of outliers, and in the case of wealth it is arguable that the median is a better summary measure than is the mean.

The second estimation issue is how to define empirical measures of bargaining power. In the literature, at least six different measures of power have been used. Three of these – relative education, relative age, and female share of income – were used by Lundberg and Ward-Batts (2000b). The others include family status (Beegle et al., 2001), female share of assets in the marriage (Doss, 1996), and female share of assets brought to the marriage (Quisumbing, 1994). In the HSS data we use there are no family status indicators because questions were not asked about the parents of the respondents. There are also no reliable measures of female control of assets because most of the assets of couples are reported jointly. However, that still leaves four measures: age, education, income and assets brought to the marriage (as proxied by individual inheritances).

The differences between women and men in the sample, in terms of each of these four indicators, is reported in Table 2. On average, wives are 2.6 years younger than their husbands, have 0.6 years less post-secondary education, inherit NZ$700 less, and have annual incomes that are NZ$20,000 lower. While these differences are easily understandable, it is not clear that any one of them by itself adequately captures the theoretical notion of bargaining power. Thus, one approach would be to use all four indicators at once. However, to the extent that they may be highly related (for example, the daughters of wealthy families receive more education and inherit more) multicollinearity may cloud the effects.

Note: Means and standard deviations are based on weighted data.

Power Index #1 is the first principal component of ΔAGE, ΔSCHOOL, ΔUNIV, and ΔINHERIT. Power Index #2 is the first principal component of those four variables and ΔINCOME.

Another approach, recently used by Varadharajan (2003), is to use factor analysis to form an index for the underlying latent concept of power. The weights are estimated from the data, and the created index, which is a Principal Component, captures the common elements in each of several measures. Varadharajan (2003) found many inconsistencies when six individual proxies for bargaining power were used to explain outcomes such as children’s school enrolment, children’s health and households’ food budget shares. But when one or two factors were extracted from the common elements in all of the proxies, using Principal Components analysis, there was much greater success at explaining outcomes in a way that was consistent with prior notions of bargaining power.

We follow this approach and construct two Principal Components as indexes of women’s bargaining power. The first captures the common elements from the difference in age, years of secondary school and post-secondary school, and inheritances. The second power index uses these four proxies and also the difference in income between women and men. If there is endogeneity in this income difference term (because of the link to savings through relative wages and time use), it will only affect interpretations of results for the second power index. Because the mean for each power index is zero and the standard deviation is close to one, an easy interpretation of the results using these variables are that unit changes represent an approximate standard deviation increase in the latent variable, women’s bargaining power.

The third estimation issue is how to specify the other covariates in the model of net worth (that is, the columns of X in equation (4)). The characteristics we use are age, education, ethnicity, marital and migration status, inheritances, location, and income levels and sources. Work status is not used because labour force participation and retirement are affected by wealth, so are endogenous. Neither health status nor the age of children is included as neither was not collected by the survey.[5] Another issue concerns whose characteristics to use. Many studies simply use a husband’s characteristics as explanatory variables, but Lundberg and Ward-Batts show that this ignores relevant information. We agree, and our explanatory variables always reflect the characteristics of both the respondent and their partner. However, in the presentation of the results, a specification where the characteristics of both people are combined is often used because this is more efficient (fewer explanatory variables) and in no way affects the results of interest.[6]