riage occurs if the joint benefit of marriage exceeds the joint benefit of remaining single. The proposition is premised on the notion that welfare is transferable between
spouses. If the welfare of each partner increases independently upon marriage, then both partners agree to marry without the need for transfers. If the welfare of one
partner declines, then one partner can transfer welfare to the other such that both partners agree to marry. This framework lends to the prevailing model of marital
instability: Divorce occurs when the combined benefit of separating exceeds the combined benefit of remaining married.
From these models, Becker, Landes, and Michael 1977 raise an important ques- tion: What factors determine the gains from marriage to explain the observed patterns
of divorce? The authors discuss two factors. The first factor is initial match quality. Intuitively, a union between any two individuals yields a level of match quality, and
only couples whose quality surpasses a specific threshold will result in marriage. However, this threshold declines as search costs to finding a mate increase or traits
for a successful match become harder to find. Lower-quality marriages, in turn, are more susceptible to divorce. The second factor is that the value of marriage is
dynamic and uncertain, so individuals must rely on expectations of value when deciding to marry. Over time, however, the expected value of marriage may deviate
from the realized value. These deviations, referred to as “shocks” in the literature, affect the value of marriage and the value of outside alternatives such that any
shock—for better or for worse—increases the likelihood of divorce.
B. Disability and Divorce
The theory of marital instability provides a framework for a dynamic model of disability and divorce. The model presented here is similar to the models of Weiss
and Willis 1997 and Charles and Stephens 2004. In the model, the dynamic value of marriage between individuals
and is defined by the function
, where i
j ϕ
g ,g
i j
is a disability status indicator that equals one if disabled and zero otherwise. g
Disability onset decreases marital wealth by affecting the ability to earn income and to produce in the home. Other factors that affect the value of marriage, such as
education and religiosity, are suppressed for brevity. The dynamic value of the al- ternatives to marriage is given by the terms
and , which also de-
A g ,g
A g ,g
i i
j j
i j
crease with disability onset. According to Becker 1974, marriage occurs if and only if
. ϕ
g ,g ≥ A g ,g + A g ,g
i j
i i
j j
i j
To characterize the effect of disability on divorce, the value of marriage is sepa- rated into its contemporaneous and future value:
∗ ∗
∗
ϕ g ,g = Vg ,g + ΩE
{
max
[
ϕ g ,g ,A g ,g + A g ,g
] }
.
i j
i j
t i
j i
i j
j i
j
The first term is the contemporaneous value of marriage and is known with certainty; the second term is the future value of marriage—discounted by the factor
—and Ω
is known with uncertainty. As shown, the future value of marriage reflects the option to divorce next period. According to the framework of marital instability, divorce is
expected if
∗ ∗
∗
E
{
A g ,g + A g ,g
}
exceeds E
{
ϕ g ,g
}
.
t i
i j
j i
j t
i j
The realized divorce decision may deviate from the expected decision due to the onset of a work-limiting disability. Without additional constraints, the effect of dis-
ability on divorce is ambiguous because a disability decreases both the value of the current marriage and the value of outside alternatives. However, the framework of
Becker, Landes, and Michael 1977 suggests that the effect of disability on divorce is nonnegative, as the decline in the value of marriage would exceed the decline in
the value of outside alternatives.
2
The magnitude of the effect depends in part on the deviation between the expected and realized values of marriage. To characterize this deviation due to a disability,
three assumptions are made: No one is initially disabled, the likelihood that person becomes disabled is zero, and the incidence of disability for person
is . In this
j i
d
i
case, expected marital value is
∗ ∗
d ϕ 1,0 + 1−d ϕ 0,0;
i i
and if person becomes disabled, realized marital value is
. Thus, the dif-
∗
i ϕ
1,0 ference between the expected and realized value is given by,
∗ ∗
1−d
[
ϕ 0,0−ϕ 1,0
]
.
i
This term is positive because and
. According to Becker,
∗ ∗
0 ≤ d ≤ 1 ϕ
0,0 ϕ 1,0
i
Landes, and Michael 1977, as this term increases, so too does the effect of dis- ability on divorce.
This term has two implications for the effect’s magnitude. First, the expected value of marriage reflects the likelihood of disability onset, so unanticipated disabilities,
measured by the incidence of disability , have a greater effect on marital value than
d
i
anticipated disabilities. Second, the effect of disability on divorce increases with dis- ability severity, measured by the change in marital value
. Ac-
∗ ∗
[
ϕ 0,0−ϕ 1,0
]
cording to the equation above, disability incidence and disability severity interact, so disability’s greatest effect on divorce occurs when disability has a large effect on
marital value and is unanticipated. While the effect of disability on divorce depends on the decline in marital value,
the divorce decision ultimately depends on whether the decline leaves the value of marriage lower than the value of outside alternatives. Thus, given the same incidence
and severity of disability, lower-quality marriages are more likely to dissolve than higher-quality marriages.
III. Data
