The Rise and Fall of Divorce: A Sociological Extension of Becker's Model of the Marriage Market

Abstract

Despite its popularity, Gary Becker's model of the marriage market does not fully predict empirical correlations between married women's labor market participation and aggregate divorce rates. In this article, we show how a simple extension of Becker's model inspired by sociological theory improves the model's predictive power. We extend Becker's model to account for matching agents' preferences for partner specialization, and as a novelty, we introduce a sociologically inspired coordination mechanism for this trait. We show that these extensions of Becker's model improve its predictive power in terms of explaining empirical trends in divorce rates.

Keywords:

• family
• simulation
• theory

Acknowledgments

We thank Michael Svarer, Christian Groth, Richard Breen, Mads Meier Jæger, Dorte Caswell, and Leif Olsen for many helpful comments to preliminary versions of this article. All remaining errors are the sole responsibility of the authors. We also thank the Danish Social Science Research Council, Velfærdsforskningsprogrammet, and AKF, the Danish Institute of Governmental Research for funding the research leading to this article.

Notes

¹Note that the distance between the data points at the x-axis changes in 1998.

² H(·) is characterized by falling marginal productivity of time input. Note that H(·) may reflect complementarity in production of, for example, children (where allowing H((T − t _w )α _w , (T − t _m )α _m ) > H((T − t _w )α _w , 0) + H(0, (T − t _m )α _m )) for small investments of time while still implying substantial substitution possibilities between partners' time investment in connection with household work (and, e.g., ) for higher levels of time investment.

³Consider two men with trait values 1 and 10, respectively, and two women also with trait values 1 and 10. If a couple's resulting utility is found by multiplying trait values then clearly matching the high valued partners will maximize total utility (10*10 + 1*1 as opposed to 10*1 + 10*1 with mixed matching). Now if mixed marriages occur and the two partners with high trait values meet, the man can make the woman a better utility offer than she is getting in her current marriage that only generates 10 utility points to be shared with her current partner (while still leaving him with a gain) since the new marriage will generate 100 utility points.

^a If there is a difference, uncertainty about the u _w trait is larger.

^b Married women's average labor market participation as a fraction of men's.

^c Fraction of men and women who are single.

^d Fraction of married couples who divorce.

⁴Note that 0 < π < 1 and that this weight is not a structural parameter but dependent on the resulting marriage market equilibrium essentially reflecting the relative value of the partner's alternative possibilities on the market.

⁵Formally, irrespective of the family wage distribution π and agreed participation adjustment σ we have that

where maximizes . To see this, note that the definition (6) implies that with equality applying only for the t _w that maximizes . Thus only when σ _m  = σ _w will this t _w also maximize whereby (i) is satisfied with equality. Otherwise (i.e., for σ _m  ≠ σ _w ) only one of the two right-hand side elements can be maximized and so (i) will be satisfied with strict inequality.

⁶Formally letting denote optimal participation in the Becker model and inserting for the optimal participation level in (6) and differentiating , we have:

for traits ϵ and η, and so for any given σ an optimal sorting applying to U(·) also applies to .

Note. We assume some correlation between women's α _w and u _w traits and that there is some difference in uncertainty about the traits (i.e., uncertainty about the u _w trait is somewhat larger).

^a Married women's average labor market participation as a fraction of men's.

^b Fraction of men and women who are single.

^c Fraction of married couples who divorce.

⁷Partners do not consciously look for a potential partner σ trait. Rather, it is an integrated part of subconsciously evaluating general preference compatibility. However, partners do realize that there is a risk of mismatch and divorce due to traits other than those consciously evaluated and take this unspecified risk into account.

Note. We assume some correlation between women's α _w and u _w traits and that there is some difference in uncertainty about the traits (i.e., uncertainty about the u _w trait is somewhat larger).

^a Married women's average labor market participation as a fraction of men's.

^b Fraction of men and women who are single.

^c Fraction of married couples who divorce.