2 Previous Evidence on Marital Bargaining and Household Savings
Most theoretical models of wealth accumulation for retirement focus on the optimal behavior for a single individual. When these models are applied to data, a unitary model of the household is typically assumed and there is no treatment of bargaining issues. An alternative theoretical approach is offered by the model of Browning (2000) but it does not lend itself to straightforward empirical investigation of the relationship between bargaining power (as measured in the model by the wife’s share of income) and the level of wealth. Another approach is offered by Lundberg and Ward-Batts (2000b), and this approach has proved influential in the development of the empirical model used in this paper and so is summarized below.
Lundberg and Ward-Batts (2000b) start with a simple multi-period unitary model in which the lifetime utility of the couple is:
where U(•) is the couple’s utility from consumption, ρ is their subjective discount rate and at is the probability at time t that both partners are alive. The second and third terms are for when one spouse dies, with M(•) the widower’s utility of wealth, pmt the probability that the husband becomes a widower at time t (i.e. that the wife dies and the husband is still alive), F(•) is the widow’s utility of wealth, and pft is the probability that the wife becomes a widow at time t. The final term, B(•) gives the couple’s expected discounted utility from bequests of wealth, wt given at the time of death of the last surviving partner. In the unitary model the couple would maximize this common objective function subject to a pooled resource constraint.
In the collective model that Lundberg and Ward-Batts use to guide their reduced form econometric specification, the couple bargain over the consumption path because the male and female partners have separate utility functions:
In these separate utility functions, each person may place a different weight on joint consumption, on the value of bequests, and on the value of wealth that they or their spouse receives upon death of the other partner. Both cooperative bargaining models (e.g., McElroy and Horney 1981) and more general collective models, such as Chiappori (1992), impose a Pareto efficient solution to this bargaining problem, in the sense that decisions are made such that no-one can be made better off without making their spouse worse off. In the current context, this requires the couple to maximize a weighted sum of their individual utilities:
where the “sharing rule” μ(Z)depends upon variables that affect the relative bargaining power of husband and wife, such as each spouse’s control over household resources and the value of the best alternative to agreement, which may be outside the marriage.
The sharing rule is not identified by Lundberg and Ward-Batts. Instead, factors that may belong in Z are inserted into an econometric model of household net worth
where X is a matrix with a ‘standard’ set of covariates, such as the age, education and income of each partner and Z is a matrix of factors that affect bargaining power. The hypothesis that they test with this model is that, in periods near retirement, the net worth of households in which the wife has greater bargaining power will be greater than the net worth of households that possess the same total lifetime resources but in which the wife has less power. Thus, as long as the Z’s are defined appropriately (higher when the women has greater power), the 
coefficients should be positive. It is important to note that this hypothesis does not necessarily apply across all ages. For example, a wife’s optimal saving rate may be lower than her husband’s in some periods if she prefers greater expenditure on some children’s goods than he does.
When estimating equation (4), Lundberg and Ward-Batts include three variables in Z as measures of the wife’s relative bargaining power:
- The difference in age between the husband and wife
- The difference in education between the husband and wife, and
- The wife’s share of current income.
They raise doubts about the interpretation of the income share variable because relative earnings will reflect relative wage rates, which affect time use and savings through the relative prices of husband’s and wife’s time. Thus, this measure is likely to be endogenous with respect to savings behavior. There are also doubts about older wives having more power if their re-marriage probabilities deteriorate with age. Therefore, their preferred measure of power is based on differences in education. According to this measure, when the husband has eight or more years of education more than his wife, the net worth of the couple is about 37 percent lower, even after controlling for levels of education.
In the current paper, we use a similar empirical framework to equation (4) to see whether evidence from New Zealand is as striking as the evidence reported by Lundberg and Ward-Batts. The data and empirical specification issues for that model are discussed in the next section.
