Quantitative models of sovereign default predict that governments reduce borrowing during recessions to avoid debt crises. A prominent implication of this behavior is that the resulting interest rate spread volatility is counterfactually low. We propose that governments borrow into debt crises because of frictions in the adjustment of their expenditures. We develop a model of government good production, which uses public employment and intermediate consumption as inputs. The inputs have varying degrees of downward rigidity, which means that it is costly to reduce them. Facing an adverse income shock, the government borrows to smooth out the reduction in public employment, which results in increasing debt and higher spread. We quantify this rigidity using the OECD Government Accounts data and show that it explains about 70% of the missing bond spread volatility.

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We study optimal tax policies with human capital investment and retirement savings for present-biased agents. Agents are heterogeneous in their innate ability and make risky education investments which determines their labor productivity and affects their consumption path. We characterize the optimal wedges and show that they are different across education groups. More specifically, we demonstrate how the optimal policy encourages human capital investment with savings incentives. We show that the optimum can be implemented with income-contingent student loans, and existing retirement policies augmented by a new tax instrument that subsidizes retirement savings for college graduates. The proposed instrument takes the form of employer's 401(k) matching contribution proportional to the repayment of student loans, and mimics the latest policy proposals that aim to incentivize college education. We show that the optimal tax system yields significant welfare gains relative to the optimal policies designed for time-consistent agents.

Life insurance premiums display significant rigidity in the data, on average adjusting once every 3 years by more than 10%. This contrasts with the underlying marginal cost which exhibits considerable volatility due to the movements in interest and mortality rates. We build and calibrate a model where policyholders are held-up by long-term insurance contracts, resulting in a time inconsistency problem for the firms. The optimal contract takes the form of a simple cutoff rule: premiums are rigid for cost realizations smaller than the threshold, while adjustments must be large and are only possible when cost realizations exceed it.

We study optimal tax policies with human capital investment and retirement savings for present-biased agents. Agents are heterogeneous in their innate ability and make risky education investments, which determines their labor productivity. We demonstrate that the optimal distortions vary with education status. In particular, the optimal policy encourages human capital investment with savings incentives. Our implementation uses income-contingent student loans and existing retirement policies, augmented by a new tax instrument that subsidizes retirement savings for college graduates. The instrument mimics the latest policy proposals by allowing employers to offer 401(k) matching contributions proportional to student loans repayment. (JEL G51, H21, H24, I26, J24, J26)