Research/2

Current works and working papers

 

Financial Stability Fund set by a union of sovereign countries can improve countries’ ability to share risks, borrow and lend, with respect to the standard instrument used to smooth fluctuations: sovereign debt financing. Efficiency gains arise from the ability of the fund to offer long-term contingent financial contracts, subject to limited enforcement (LE) and moral hazard (MH) constraints. In contrast, standard sovereign debt contracts are uncontingent and subject to untimely debt roll-overs and default risk. We develop a model of the Financial Stability Fund (Fund) as a long-term partnership with LE and MH constraints. We quantitatively compare the constrained-efficient Fund economy with the incomplete markets economy with default. In particular, we characterize how (implicit) interest rates and asset holdings differ, as well as how both economies react differently to the same productivity and government expenditure shocks. In our economies, `calibrated’ to the euro area `stressed countries’ , substantial effciency gains are achieved by establishing a well-designed Financial Stability Fund; this is particularly true in times of crisis. Our theory provides a basis for the design of a Fund – for example, beyond the current scope of the Euroepan Stability Mechanism (ESM) – and a theoretical and quantitative framework to assess alternative risk-sharing (shock-absorbing) facilities, as well as proposals to deal with the euro area ‘debt overhang problem’.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 pensions and unemployment insurance (UI). We show this in a calibrated dynamic general equilibrium model with heterogeneous agents of the Spanish economy (2014). A ‘backpack’ (BP) employment fund is an individual (across jobs) transferable fund, which earns the economy interest rate as a return and is financed with a payroll tax (a BP tax). The worker can use the fund if he or she becomes unemployed or retires. To complement the existing Spanish pension and UI systems with a welfare maximising 19% BP tax would raise welfare by 1.3% of average consumption at the new steady state, and would be preferred to the status quo by most economic and demographic groups. Our model also provides a framework where other reforms – e.g. a partial, or complete, substitution of current unsustainable pension systems – can be quantitatively assessed.Read more

We study the introduction, and possible design, of a European Unemployment Insurance System (EUIS) using a multi-country dynamic general equilibrium model with labour market frictions. Our calibration provides a novel diagnosis of European labour markets, revealing the key parameters – in particular, job-separation and job-arrival rates – that explain their different performance in terms of unemployment (or employment) and its persistence. We show that there are small welfare gains from insuring against country-specific cyclical fluctuations in unemployment expenditures. However, we find that there are substantial gains from reforming currently suboptimal unemployment benefit systems. In spite of country differences, it is possible to unanimously agree on a (minimal) EUIS, which countries can complement by additional national benefits. The EUIS features an unlimited duration of eligibility, which eliminates the risk of not finding a job before the receipt of benefits ends, and a low replacement rate of 10%, which stabilizes incentives to work. Country-specific payroll taxes eliminate cross-country persistent transfers. The resulting tax differences across countries may be the best statistic of their structural labour market differences, in terms of job creation and destruction, providing clear incentives for reform. Read more

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

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.

Two core principles of economics are that welfare can be enhanced with stronger commitment to individual arrangements (contracts) and with more competition. However, in the presence of search frictions, commitment may deter entry with consequent reduction in the reallocation of human resources. We study these tradeoffs when there are different degrees of commitment in a model with on-the-job search. Since the degree of commitment depends on the organizational structure of a firm, we contrast the equilibrium of an industry where firms are organized in the form of partnerships with the equilibrium where firms are public companies. We show that in the equilibrium with public companies there is more investment in high return but uncertain activities (risk-taking), 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. 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

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