Published papers

 

We obtain a recursive formulation for a general class of optimization problems with forward-looking constraints which often arise in economic dynamic models, for example, in contracting problems with incentive constraints or in models of optimal policy. In this case, the solution does not satisfy the Bellman equation. Our approach consists of studying a recursive Lagrangian. Under standard general conditions there is a recursive saddle-point functional equation (analogous to a Bellman equation) that characterizes a recursive solution to the planner’s problem. The recursive formulation is obtained after adding a co-state variable µt summarizing previous commitments reflected in past Lagrange multipliers. The continuation problem is obtained with µt playing the role of weights in the objective function. Our approach is applicable to characterizing and computing solutions to a large class of dynamic contracting problems. Read more

We extend the envelope theorem, the Euler equation, and the Bellman equation to dynamic constrained optimization problems where binding constraints can give rise to nondifferentiable value functions and multiplicity of Lagrange multipliers. The envelope theorem – an extension of Milgrom and Segal’s (2002) theorem – establishes a relation between the Euler and the Bellman equation. We show that solutions and multipliers of the Bellman equation may fail to satisfy the respective Euler equations, in contrast with solutions and multipliers of the infinite-horizon problem. In standard dynamic optimisation problems the failure of Euler equations results in inconsistent multipliers, but not in non-optimal outcomes. However, in problems with forward-looking constraints this failure can result in inconsistent promises and non-optimal outcomes. We also show how the inconsistency problem can be resolved by an envelope selection condition and a minimal extension of the co-state. We extend the theory of recursive contracts of Marcet and Marimon (1998, 2017) to the case where the value function is non-differentiable, resolving a problem pointed out in Messner and Pavoni (2004).Read more

We develop a dynamic, general equilibrium model with two-sided limited commitment to study how barriers to competition, such as restrictions to business start-up, affect the incentive to accumulate human capital. We show that a lack of contract enforceability amplifies the effect of barriers to competition on human capital accumulation. High barriers reduce the incentive to accumulate human capital by lowering the outside value of  ‘skilled workers’, while low barriers can result in over-accumulation of human capital. This over-accumulation can be socially optimal if there are positive knowledge spillovers. A calibration exercise shows that this mechanism can account for significant cross-country income inequality.Read more

We analyze a monetary model with flexible labor supply, cash-inadvance constraints and seigniorage-financed government deficits. If the intertemporal elasticity of substitution of labor is greater than one, there are two steady states, one determinate and the other indeterminate. If the elasticity is less than one, there is a unique steady state, which can be indeterminate. Only in the latter case do there exist sunspot equilibria that are stable under adaptive learning. A sufficient reduction in government purchases can in many cases eliminate the sunspot equilibria while raising consumption/labor taxes even enough to balance the budget may fail to achieve determinacy. Read more

We characterize the optimal sequential choice of monetary policy in economies with either nominal or indexed debt. In a model where nominal debt is the only source of time inconsistency, the Markov-perfect equilibrium policy implies the progressive depletion of the outstanding stock of debt, until the time inconsistency disappears. There is a resulting welfare loss if debt is nominal rather than indexed. We also analyze the case where monetary policy is time inconsistent even when debt is indexed. In this case, with nominal debt, the sequential optimal policy converges to a time-consistent steady state with positive – or negative – debt, depending on the value of the intertemporal elasticity of substitution. Welfare can be higher if debt is nominal rather than indexed and the level of debt is not too high.Read more

In monetary unions, monetary policy is typically made by delegates of the member countries. This procedure raises the possibility of strategic delegation that countries may choose the types of delegates to influence outcomes in their favor. We show that without commitment in monetary policy, strategic delegation arises if and only if three conditions are met: shocks affecting individual countries are not perfectly correlated, risk-sharing across countries is imperfect, and the Phillips Curve is nonlinear. Moreover, inflation rates are inefficiently high. We argue that ways of solving the commitment problem, including the emphasis on price stability in the agreements constituting the European Union are especially valuable when strategic delegation is a problem.Read more

We study a general equilibrium model in which entrepreneurs finance investment with optimal financial contracts. Because of enforceability problems, contracts are constrained efficient. We show that limited enforceability amplifies the impact of technological innovations on aggregate output. More generally, we show that lower enforceability of contracts will be associated with greater aggregate volatility. A key assumption for this result is that defaulting entrepreneurs are not excluded from the market. Read more

We study how competition from privately supplied currency substitutes affects monetary equilibria. Whenever currency is inefficiently provided, inside money competition plays a disciplinary role by providing an upper bound on equilibrium inflation rates. Furthermore, if ‘‘inside monies’’ can be produced at a sufficiently low cost, outside money is driven out of circulation. Whenever a ‘benevolent’ government can commit to its fiscal policy, sequential monetary policy is efficient and inside money competition plays no role.Read more