Selected published papers (2000 – )

We extend the standard Bellman’s theory of dynamic programming and the theory of recursive contracts  with forward-looking constraints of Marcet and Marimon (2019) to encompass non-differentiability of the value function resulting from the presence of binding constraints or non-unique solutions. The envelope theorem provides the link between the Bellman equation and the Euler equations, but it may fail to do so if the value function is non-differentiable. We introduce an envelope selection condition which guarantees that solutions generated from the Bellman equation satisfy the Euler equations with or without forward-looking constraints.  In standard dynamic programming, ignoring the envelope selection condition may result in inconsistent multipliers, but not in non-optimal outcomes. In recursive contracts and dynamic planner’s problems with recursive utilities, it can result in inconsistent promises and non-optimal outcomes. A recursive  method of solving dynamic optimization problems with non-differentiable value function involves expanding the co-state and imposing the envelope selection condition. Read more

The main legacy of the post-Covid-19-crisis euro area fiscal framework should be the development of a unique integrated fiscal policy and of a permanent and independent Fiscal Fund to implement it. To arrive at this conclusion, we analyse the challenges and build on current research on the optimal design of a fiscal fund. We characterise the fiscal policy, and the development of the Fund, together with the role and form that the Stability and Growth Pact can take in the new fiscal framework.

We develop a theory of self-confirming crises in which lenders charge high interest rates because they wrongly believe that lower rates would further increase their losses. In a directed search economy, this misperception can persist because at the equilibrium there is no evidence that can confute it, preventing the constrained-efficient outcome. A policy maker with the same beliefs as lenders will find it optimal to offer a subsidy contingent on losses to induce low interest rates. As a by-product, this policy generates new information for the market that may disprove misperceptions and make superfluous the implementation of any subsidy. We provide new micro-evidence suggesting that the 2009 TALF intervention in the market of newly generated ABS was an example of the optimal policy in our model. Read more


We show that a change in organizational structure from partnerships to public companies—which weakens contractual commitment—can lead to higher investment in high return-and-risk activities, higher productivity (value added per employee) and greater income dispersion (inequality). These predictions are consistent with the observed evolution of the financial sector where the switch from partnerships to public companies has been especially important in the decades that preceded the 21st Century financial crisis.

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