Selected publications (2000 – )

We explore the complementarity between a central bank and a financial stability Fund in stabilizing sovereign debt markets. The central bank pursuing its mandate can intervene with public sector purchasing programs, buying sovereign debt in the secondary market, provided that the debt is safe. The sovereign sells its debt to private lenders, through market auctions. Furthermore, it has access to a long-term state-contingent contract with a Fund: a country-specific debt-and-insurance contract that accounts for no-default and no-over-lending constraints. The Fund needs to guarantee gross-financial-needs and no-over-lending. We show that these constraints endogenously determine the ‘optimal debt maturity’, structure that minimizes the Required Fund Capacity (RFC) to make all sovereign debt safe. However, the Fund may have limited absorption capacity and fall short of its RFC. The central bank may be able to cover the difference, in which case there is perfect complementarity and the joint institutions act as an effective ‘lender of last resort’. We calibrate our model to the Italian economy and find that with a Fund contract its ‘optimal debt maturity’, is 2.9 years with an RFC of 90% of GDP, which is above what the European Stability Mechanism (ESM) could reasonably absorb, but may be feasible with an ECB Transmission Protection Instrument (TPI) intervention. In contrast, the average maturity of Italian sovereign debt has been circa 6.2 years, with a needed absorption capacity of around 105% of GDP, which may call for a maturity restructuring to ease the activation of TPI.

Facing an ageing population and historical trends of low employment rates, pay-as-you-go (PAYG) pension systems, currently in place in several European countries, imply very large economic and welfare costs in the coming decades. In an overlapping generations economy with incomplete insurance markets and frictional labour markets, an employment fund, which can be used while unemployed or retired, can enhance production efficiency and social welfare. With an appropriate design, the sustainable Backpack employment fund (BP) can greatly outperform — measured by average social welfare in the economy — existing pay-as-you go systems and also Pareto dominate a full privatization of the pension system, as well as a standard fully funded defined contribution pension system. We show this in a calibrated model of the Spanish economy, by comparing the effect of its ageing transition under these different pension systems and by showing how a front-loaded reform-transition, from the PAYG to the BP system can be Pareto improving, while minimizing the cost of the reform.Read more

We study the welfare effects of both existing and counter-factual European unemployment insurance (UI) policies using a rich multi-country dynamic general equilibrium model with labour market frictions. The model successfully replicates several salient features of European labor markets, in particular the cross-country differences in the flows between employment, unemployment and inactivity, as a result of labour market and UI policy differences across euro area countries. We find that mechanisms like the recently introduced European instrument for temporary support to mitigate unemployment risks in an emergency (SURE), which allows national governments to borrow at low interest rates to cover expenditures on unemployment risk, yield sizeable welfare gains.  Furthermore, we find that, in spite of the calibrated heterogeneity across euro area countries, there is a common direction in which they can improve their UI policies; in particular, a harmonized benefit system that features a one-time payment of around three quarters of income upon separation is welfare improving in all euro area countries relative to the status quo.Read more

In an overlapping generations economy with incomplete insurance markets, the introduction of an employment fund—akin to the one introduced in Austria in 2003, also known as ‘Austrian backpack’—can enhance production efficiency and social welfare. It complements the two classical systems of public insurance: pay-as-you-go (PAYG) pensions and unemployment insurance (UI). We show this in a calibrated dynamic general equilibrium model with heterogeneous agents of the Spanish economy in 2018. A ‘backpack’  (BP) employment fund is an individual (across jobs) transferable fund, which earns a market interest rate as a return and is financed with a payroll tax (a BP tax). The worker can use the fund while unemployed or retired. Upon retirement, backpack savings can be converted into an (actuarially fair) retirement pension. To complement the existing PAYG pension and UI systems with a welfare maximizing 6% BP tax would raise welfare by 0.96% of average consumption at the new steady state, if we model Spain as an open economy. As a closed economy, there are important general equilibrium effects, and as a result, the social value of introducing the backpack is substantially greater: 16.14%, with a BP tax of 18%. In both economies, the annuity retirement option is an important component of the welfare gains.Read more


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

This eBook provides an overview of the findings and proposals of the Horizon 2020 ADEMU research project (June 2015 to May 2018), which aimed at reassessing the fiscal and monetary framework of the European Economic and Monetary Union in the wake of the euro crisis.

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