Divorce laws and divorce rate in the US

A. Numerical solution and algorithm

The household model is solved numerically by backward induction from the terminal node, under the condition that At each state, I solve for the value function and the optimal policy rules, given the current state variables and the solution to the value function in the next period t<T. Consider any arbitrary period. Each couple enters the period with a stock of assets, and a certain match quality. They draw a new match quality, and choose allocations for the case they remain married, and the case they get divorced.

More specifically, consider the terminal node at time T, when agents are not employed and have not children. The value of being a divorcee i is computed by solving the following problem:

To determine the value of marriage and the decision to divorce, it is necessary distinguish between two divorce law regimes: consensual and unilateral.

Consensual divorce. The intertemporal behavior of a couple in period T is characterized by a Pareto problem, as discussed in Section 5. First, optimal allocations are computed solving the following problem:

Let and for i=f, m, be the solutions of the couple’s problem. Agent i’s value of being married at the current bargaining power μ_T is

Two possible cases may arise. First, for both spouses it is true that then they divorce. Second, if at least one spouse prefers marriage to divorce, they remain married with a value equal to Given spouse i’s value in period T, the decision process in any arbitrary period t<T can be outlined as in Section 5.

Unilateral divorce. The intertemporal behavior of a couple in period T is characterized by a Pareto problem with participation constraints. As explained in Section 8.1, the problem is solved in two steps. In the first step, optimal allocations are computed, disregarding the participation constraints and using the bargaining power μ_T. The problem is

Let and for i=f, m, be the solutions of the couple’s problem. Agent i’s value of being married at the current bargaining power μ_T is

In the second step, it is verified whether the individual participation constraints are satisfied, i.e.,

Three possible cases may arise. First, the participation constraints are satisfied for both agents, hence they remain married with a value equal to Second, the participation constraints are binding for both agents. In this case, both agents are better off as single, and they divorce. Third, only one agent is constrained. Assume that agent f’s participation constraint is binding. The optimal allocation is such that the wife is indifferent between being single and married. This allocation is determined by choosing individual consumption, leisure, and the new bargaining power that solve the following problem:

Let be the solution to this problem. If the participation constraint of agent m is also satisfied, then the spouses remain married with

Otherwise they divorce. Given spouse i’s value in period T, the decision process in any arbitrary period t<T can be outlined as in Section 8.1.

The presence of a discrete choice (decision to divorce) and several continuous decision variables like labor supply, time spent with children and saving implies that the value function of the married agents is not necessarily concave or differentiable. To solve the problem, I use a finite dynamic programming method and approximate the solution to the households’ problems by solving them on a grid. The algorithm used to solve the problem is the following. First, I guess the values of the parameters to be estimated. Given the guesses, I use finite dynamic programming to solve for optimal decision rules for marital status, savings, and time in the market and with children. Next, I simulate the shock histories of 100,000 households. Using the simulated histories and the optimal decision rules, I compute the targeted moments to pin down the values for estimated parameters which produce moments summarized in Table 3. Since the differentiability of the objective function in the estimated parameters is not guaranteed, I use a minimization procedure that does not rely on the existence of the gradient (simplex). Once the estimated parameters are identified, I solve the household problem one more time and save the optimal decision rules. Next, I use the resulting distribution of the match quality shock to run the experiments.

B. Data

Aggregate and age-specific divorce rate. From the end of the 1960s to the beginning of the 1980s, the divorce rate increased from about 13 to 23 divorces per thousands of married females of 15 years and older.³³

The left panel of Figure 2 shows the increase in the divorce rate. This aggregate measure does not reveal age differences in the divorce rate, and it assumes a standardized age structure of women at risk. A more precise measure is given by the age-specific divorce rate, and data are shown in the right panel of Figure 2. The data show that rates increased from 1970 to 1980 with the most dramatic increase occurring in the 20–44 age groups. The 50 years old and over groups show no relevant change in this decade.

Figure 2

Aggregate and age-specific divorce rates per 1000 of married females.

Source: National Center for Health Statistics and Kunz and England (1988).

Kunz and England (1988) and Table 10 report the age-specific divorce rates for the states for which the data were available in both 1970 and 1980. Note that these data include the entire US population without distinction between race or country of origin.

Years of divorce law changes. Table 11 reports the dates in which the unilateral divorce, the equitable distribution of property, and the joint-child custody have been introduced in each state.

Division of property. Table 12 reports the share of property assigned to spouses from a random sample of court dockets of California.

Americans’ use of time, 1965–1966. This dataset includes adults between 19 and 65 years of age living in cities in the United States with a population between 30,000 and 280,000, and in households that had at least one adult employed in a non-farming occupation. Questions related to caring or helping household children are asked in the survey. I use data on “primary child care activity.” This activities include minutes spent providing physical care to children under 5 years and older (including meals, dressing, general supervision, getting up); helping with or supervising schoolwork; reading stories to or talking with children under 19 years old; indoor games or manual instruction; outdoor games or walk; medical care and other child care; trips related to child care. I only include married women with own children in the household.

NLS-72. The fifth follow-up survey of the National Longitudinal Study of the High School Class of 1972 (NLS-72) took place during spring and summer of 1986. The sample members averaged 32 years of age and had been out of high school for 14 years. I consider mothers who have been married and divorced at least once. All of them are in the age group 30–40 by construction of the data set itself. In questions 67 and 68 of the survey (variable FI167 and FI168), respondents are asked to provide information about child custody and visitation agreements. Moreover, I analyze the answers given in question 62A (var. FI62A) and question 62B (var. FI162B) to compute the percentage of property inherited at the time of divorce. For each respondent, those variables provide the (intervalled) amount of properties received by themselves and by the spouse.

IPUMS-CPS. IPUMS-CPS is an integrated set of data from 48 years (1962–2009) of the March Current Population Survey (CPS), and is publicly available for download at the IPUMS-CPS website (King et al. 2004). I concentrate on divorced (and separated) men and women of age 20–75. Alimony and child support payments are deflated using the Consumer Price Index (1982–1984=100). The variable used for the alimony and child support transfer is incaloth.

IPUMS-USA. IPUMS-USA is an Integrated Public Use Microdata Series (IPUMS-USA) consists of more than 50 high-precision samples of the American population drawn from 15 federal censuses and from the American Community Surveys of 2000–2010, and it is publicly available for download at the IPUMS-USA website (Ruggles et al. 2010). I concentrate on married couples and divorced (and separated) men and women of age 20–75. I only consider men and women who worked a positive number of hours in the year preceding the interview. Labor income is deflated using the Consumer Price Index (1982–1984=100). I compute hourly wage by dividing the total yearly earnings by the total hours worked. Figure 3 shows fitted wages in 1970 and 1980.

Figure 3

Fitted wage age-profile, 1970 and 1980.

Source: IPUMS-USA.