This paper studies the effect of human capital depreciation and duration dependence on the design of an optimal unemployment insurance (UI) scheme. Our results partially confirm those obtained in most previous studies: benefits should decrease with unemployment duration. The optimal program also generates two main novel features, which are not present in stationary models. First, if human capital depreciates rapidly enough during unemployment, UI transfers are bounded below by a minimal “assistance” level that arises endogenously in the efficient program. Second, we study the optimality of imposing a history contingent wage tax after reemployment. Our numerical simulations based on the Spanish and US economies show that the wage tax should decrease with the length of worker’s previous unemployment spell, and become a wage subsidy for long-term unemployed workers. As a by-product of our study, we develop a systematic approach suitable for studying recursively a wide range of dynamic moral-hazard problems, and other models with similar characteristics.

The household’s labor margin has a substantial effect on risk aversion, and hence asset prices, in dynamic equilibrium models even when utility is additively separable between consumption and labor. This paper derives simple, closed-form expressions for risk aversion that take into account the household’s labor margin. Ignoring this margin can wildly overstate the household’s true aversion to risk. Risk premia on assets priced with the stochastic discount factor increase essentially linearly with risk aversion, so measuring risk aversion correctly is crucial for asset pricing in the model. Closed-form expressions for risk aversion in models with generalized recursive preferences and internal and external habits are also derived.

This paper estimates costs of external finance, applying indirect inference to a dynamic structural model where the corporation endogenously chooses investment, distributions, leverage and default. The cor-poration faces double taxation, costly state verification in debt markets, and linear-quadratic costs of external equity. Consistent with direct evidence on underwriter fee schedules, behavior is best explained by rising marginal costs of external equity, starting at 5.2%. Contrary to the notion that corporations are debt conservative, leverage is consistent with small (11.6%) bankruptcy costs. Investment-cash flow sensitivities are not a sufficient statistic for financing costs. The cash flow coefficient decreases in external equity costs and increases in bankruptcy costs. When the model is simulated using our parameter esti-mates, the cash flow coefficient across Fazzari, Hubbard, and Petersen’s dividend classes is U-shaped. The difference between cash flow coefficients across dividend classes actually decreases as costs are increased.

This paper presents the partial analytical solution to a model of periodic consumption that incorporates imperfect capital markets and uncertainty. Our model assumes that consumption decisions occur more frequently than income receipts. We show that the week-specific consumption functions can be ordered. At low levels of wealth these functions exhibit a "u-shaped" pattern between income receipts. We show analytically that changes in the level of the borrowing constraint affect only the level of consumption function and not the MPC, whilst mean-preserving changes in uncertainty affect both.

By integrating dynamic programming with the theory of order preserving dynamical systems (Hirsch (1982), Smith (1995)) this paper develops a new approach to stability analysis in continuous-time dynamic optimization models. The main results provide simple conditions on the primitives of a model which imply that steady states exist and are globally stable for initial conditions in an open dense set. If the steady state is unique or lattice methods are employed in their study; this completely resolves all stability questions. The methods' applicability is demonstrated through examples from investment theory, growth theory, and renewable resource economics.

By integrating dynamic programming with the theory of order preserving dynamical systems (Hirsch (1982), Smith (1995)) this paper develops a new approach to stability analysis in dynamic economic models. The main results provide simple conditions on the primitives of a model which imply that steady states are globally stable for almost all initial conditions. If the steady state is unique or lattice methods are employed in their study; this completely resolves all stability questions. The methods ’ applicability is demonstrated through examples from investment theory, growth theory, and renewable resource economics.

This paper establishes a theoretical framework to characterise the optimal behaviour of individuals who receive income periodically but make consumption decisions on a more frequent basis. The model incorporates price uncertainty and imperfect credit markets. The simulated numerical solution to this model shows that weekly consumption functions are ordered such that the functions within the payment period are highest in the first and the last week of the payment cycle for all wealth levels. Using weekly expenditure data from the FES, we estimate the coefficient of relative risk aversion (point estimates are between 1.2 and 7) and the extent of measurement error in the data (which accounts for approximately 60% of the variance in the data)

The paper develops a simple economic model of a biological invasion. The natural growth of the invasion is non-convex and the immediate cost of controlling the invasion depends on the level of current control as well as the current size of the invasion. Greater control raises control costs today while reducing damages- now and in the future. In addition, by decreasing the size of the invasion, increased control today raises the marginal cost of control in the future. As a consequence, the optimal path of an invasion is not necessarily monotonic. When the marginal control cost declines sharply with the size of invasion, it may be optimal to allow an invasion to grow naturally before it is controlled. We characterize conditions under which it is optimal to eradicate an invasive species (immediately and eventually) and conditions under which it is optimal to manage an invasion without complete eradication.

This paper extends the existing literature on optimal unemployment insurance by allowing for self-insurance; individuals may save using a one-period riskless asset, but their access to the credit market is restricted. I show that under this market arrangement, an asset based unemployment insurance scheme implements the optimal allocations. The optimal benefit payments policy shows no duration dependence, and relies exclusively upon an individual’s current asset position. Benefit payments are decreasing in wealth and, as a consequence, peaks at a constant level when the liquidity constraint is binding. Over the course of unemployment, individuals decumulate assets and the sequence of benefit payments is thus observationally non-decreasing; a result that stands in sharp contrast with the previous literature. In a quantitative exercise it is shown that the US unemployment insurance programme is surprisingly close to optimal for the asset poor, but too generous for wealthier individuals. The potential cost-savings of switching to the optimal program ranges from roughly 33 % of the present value insurance budget for the affluent, to 7 % for the less fortunate.

Private information and limited enforcement are two frictions that impede the provision of first best insurance against income risk. To mitigate these frictions, societies make costly investments into technologies such as auditing and enforcement systems. The implicit assumption throughout most of the literature is that either or both of these technologies is either costless or infinitely costly. I consider a model of efficient insurance in which at each point in time the principal can choose a level of enforceability that inhibits an agent’s ability to renege on the contract and a level of auditing that inhibits his ability to conceal income. The dynamics of the optimal contract imply an endogenous lower bound on the lifetime utility of an agent, strictly positive auditing at all points in the contract and positive enforcement only when the agent’s utility is sufficiently low. Furthermore, the two technologies operate as complements and substitutes at alternative points in the state space, uncovering dynamics that differ dramatically from the case in which the technologies are studied separately.