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Rainer, Helmut; Anderberg, Dan; Roeder, Kerstin (July 2016): Family-Specific Investments and Divorce. A Theory of Dynamically Inconsistent Household Behavior. CESifo Working Paper No. 5996
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This paper bridges two distinct areas of inquiry: the economic theory of the family and behavioral research on time-inconsistent preferences. In our model, hyperbolic discounting couples engage in household production activities, thereby accumulating family-specific capital over time. At any given point in time, the gains to continued marriage depend on the accumulated stock of this capital and a temporary random shock to match quality. Couples whose match quality deteriorates may choose to divorce, and this is more likely to happen if past investments in family-specific capital have been low. We obtain three main sets of results. First, present-biased preferences induce couples to underinvest in family-specific capital and to “overdivorce”. Second, sophisticated couples – but not naive ones – may choose to enter marriage on terms which make divorce more costly to obtain. Third, the inefficiencies in the behavior of time-inconsistent couples can be completely undone by means of earnings and divorce taxes that vary over the marital life-cycle. In calibrating the model to the US economy, we demonstrate that the efficiency-restoring earnings tax is genderneutral and fairly flat with respect to marriage duration. The optimal divorce tax is an inverted-U function of marriage duration, reaches its maximum when children are in their teens, and declines thereafter. We use our results to interpret several stylized facts about marriage and divorce that cannot be straightforwardly reconciled with standard models of household behavior. Examples include: marriage contracts that serve as barriers to hasty divorces (e.g., “covenant” marriages, the Islamic “mehr” or the Jewish “ketubah”); couples’ overoptimism regarding the survival chances of their own marriage, despite knowing the statistics on divorce; and frequent regrets among divorced couples about their separation.