The Insurance Value of Public Insurance Against Idiosyncratic Income Risk

The tax and transfer system partially insures households against individual income risk. We build a framework to assess the size and (welfare) value of this partial insurance, which is based on exploiting distributional differences between household gross income and disposable income. Our approach flexibly accounts for these differences and does not require the specification of a tax function. The key feature of the model around which our framework is built is that the degree of partial insurance is directly parameterized, which allows us to solve for the degree of insurance provided by the tax and transfer system as a fixed point. Our approach works with standard homothetic preferences, and is flexible regarding the distributions of income shocks. Only in the nested special case of homoskedastic log-Normal distributions, the ratio of the dispersion of permanent shocks to gross and disposable incomes provides a sufficient statistic for the degree of government-provided consumption insurance. In an application to data from Swedish tax registers, we find that the degree of partial insurance against permanent shocks by the tax and transfer system amounts to about 49%. Resorting to the Panel Study of Income Dynamics, we also document that the model-based measure aligns well with empirical estimates based on survey data on consumption, implying a degree of insurance of about 25% in the United States.