Nicola Pavoni

OPTIMAL UNEMPLOYMENT INSURANCE, WITH HUMAN CAPITAL DEPRECIATION, AND DURATION DEPENDENCE

This article introduces the possibility of a deterioration in job opportunities during unemployment into the standard optimal unemployment insurance (UI) design framework and characterizes the efficient UI scheme. The optimal program may display two novel features, which cannot be present in stationary models. First, UI transfers are bounded below by a minimal assistance level that arises endogenously in the efficient contract. Second, the optimal scheme implies a wage subsidy for long-term unemployed workers. Numerical simulations based on the Spanish and U.S. economies suggest that both assistance transfers and wage subsidies should be part of the UI scheme in these countries.

Efficient Allocations with Moral Hazard and Hidden Borrowing and Lending

We analyze a dynamic moral hazard setting, in which agents can borrow and lend and their decisions about effort, consumption and savings are private information. In contrast with previous findings, we show that as long as agents do not have perfect control over publicly observable outcomes, the efficient allocation is welfare improving with respect to the case where the agents can self insure only through borrowing and lending. We identify the main sources of welfare improvement, and we compute substantial efficiency gains. We provide a tractable recursive framework to study the optimal allocation in this setting. The dynamic programming formulation is based on a generalized first order approach, whose validity is verified ex post, using a parsimonious numerical procedure based on the recursive formulation itself.

On the first-order approach in principal agent models with hidden borrowing and lending

is monotone in output. We also investigate a few possibilities of relaxing these requirements.

The Dual Approach to Recursive Optimization: Theory and Examples

We bring together the theories of duality and dynamic programming. We show that the dual of an additively separable dynamic optimization problem can be recursively decomposed using summaries of past Lagrange multipliers as state variables. Analogous to the Bellman decomposition of the primal problem, we prove equality of values and solution sets for recursive and sequential dual problems. In non-additively separable settings, the equivalence of the recursive and sequential dual is not guaranteed. We relate recursive dual and recursive primal problems. If the Lagrangian associated with a constrained optimization problem admits a saddle then, even in non-additively separable settings, the values of the recursive dual and recursive primal problems are equal. Additionally, the recursive dual method delivers necessary conditions for a primal optimum. If the problem is strictly concave, the recursive dual method delivers necessary and sufficient conditions for a primal optimum. When a saddle exists, states on the optimal dual path are subdifferentials of the primal value function evaluated at states on the optimal primal path and vice versa.We bring together the theories of duality and dynamic programming. We show that the dual of a separable dynamic optimization problem can be recursively decomposed. We provide a dual version of the principle of optimality and give conditions under which the dual Bellman operator is a contraction with the optimal dual value function its unique fixed point. We relate primal and dual problems, address computational issues and give examples.

Optimal Life-cycle Capital Taxation under Self-Control Problems

We study optimal taxation of savings in an economy where agents face self-control problems and are allowed to be partially naive. We assume that the severity of self-control problems changes over the life-cycle. We focus on quasihyperbolic discounting with constant elasticity of intertemporal substitution utility functions and linear Markov equilibria. We derive explicit formulas for optimal taxes that implement the efficient allocation. We show that if agents’ ability to self-control increases concavely with age, then savings should be subsidized and the subsidy should decrease with age. We also show that allowing for age-dependent self-control problems creates large effects on the level of optimal subsidies, while optimal taxes are not very sensitive to the level of sophistication. JEL classification: E21, E62, D03. Keywords: Self-control problems, Linear Markov equilibrium, Life cycle taxation of savings.

The Precautionary Saving Effect of Government Consumption

Abstract We study a largely neglected channel through which government expenditures can boost private consumption. We set up a dynamic model in which households are subject to health shocks. We take the model to the data and estimate a negative impact of public health care on household consumption dispersion, wealth and saving. According to our model, this result is explained by a change in the level of precautionary saving, with public health care acting as a form of consumption insurance. We compute the implied consumption multipliers by simulating the typical government consumption shock within a calibrated general equilibrium version of our model, with flexible prices. The impact consumption multiplier generated by the decrease in the level of precautionary saving is positive and sizable. When we include the effect of taxation, the sign of the impact multiplier depends on a few features of the model, such as the persistence of the health shocks. The long-run cumulative multiplier is negative across all calibrations.

Optimal taxation in occupational choice models: an application to the work decisions of couples

We study a general model of occupational choice and optimal income taxation where agents have private cost of work that di ffer across occupations and have both deterministic and random components. We apply our framework to study the work decisions of couples in an extensive set up and give necessary and sufficient conditions under which joint-working households should be subsidized compared to single-worker households.