The optimal Chapter 7 exemption level in a life-cycle model with asset portfolios

I develop a heterogenous agent life-cycle model that examines the effects of the US personal bankruptcy law on bankruptcy filings and welfare. In addition to facing uncertainty over their labor income, agents also face wealth shocks that stem from unexpected changes in family composition or from unexpected medical expenses. I allow agents to borrow and save simultaneously. Some households borrow at high interest rates while simultaneously saving at low interest rate because of the option value of defaulting. This is consistent data on household assets. Under chapter 7 of the US bankruptcy law, consumers can keep all wealth up to an exemption level. I show that introducing exemption levels is of particular importance in the presence of wealth shocks. My quantitative evaluations show that changes in the exemption level have an impact only for very low exemption levels. Thus, ignoring them biases welfare results. But this impact fades out rather quickly. The reason is that almost no household is affected by medium to high exemption levels because those households who might default do not have much wealth. The welfare results of changes in the exemption level are rather small, less than 0.1% of annual consumption. In contrast to the earlier literature, but consistent with the data, I do not find a strong positive relationship between the exemption level and default rates.