Efficient Risk Sharing with Limited Commitment and Storage

743 views

Published on

Sarolta Laczó (IAE and Barcelona GSE)
Presented at Barcelona GSE Trobada X

Published in: Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
743
On SlideShare
0
From Embeds
0
Number of Embeds
3
Actions
Shares
0
Downloads
7
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Efficient Risk Sharing with Limited Commitment and Storage

  1. 1. Efficient Risk Sharing with Limited Commitment and Storage Árpád Ábrahám Sarolta Laczó EUI IAE and Barcelona GSE Barcelona GSE Trobada October 26, 2012Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  2. 2. Risk sharing Consider two agents who each receive a risky endowment. For example, suppose that each may receive 2 or 8 euros each period (and the aggregate endowment is always 10). Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  3. 3. Risk sharing Consider two agents who each receive a risky endowment. For example, suppose that each may receive 2 or 8 euros each period (and the aggregate endowment is always 10). Agents may share the (idiosyncratic) risk they face by making transfers. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  4. 4. Risk sharing Consider two agents who each receive a risky endowment. For example, suppose that each may receive 2 or 8 euros each period (and the aggregate endowment is always 10). Agents may share the (idiosyncratic) risk they face by making transfers. First-best/Unconstrained-efficient outcome: lucky agent makes a transfer of 3 and both consume 5 in each period, for example. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  5. 5. Limited commitment However, the agent who is lucky today might be unwilling to make a large transfer... He might be better off in autarky, i.e., consuming 8 today and then his endowment in all future periods. He will not make a transfer of 3 without commitment. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  6. 6. Limited commitment However, the agent who is lucky today might be unwilling to make a large transfer... He might be better off in autarky, i.e., consuming 8 today and then his endowment in all future periods. He will not make a transfer of 3 without commitment. But he might voluntarily make a smaller transfer in order to benefit from future risk sharing. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  7. 7. Limited commitment However, the agent who is lucky today might be unwilling to make a large transfer... He might be better off in autarky, i.e., consuming 8 today and then his endowment in all future periods. He will not make a transfer of 3 without commitment. But he might voluntarily make a smaller transfer in order to benefit from future risk sharing. More precisely, he is willing to make a transfer that still leaves him at least as well off as being in autarky (2 euros, say). Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  8. 8. Limited commitment The limited commitment friction generates partial risk sharing. Income fluctuations partially translate into consumption fluctuation. When an agent earns 8 he consumes 6, and when he earns 2 he consumes 4. This outcome is constrained efficient. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  9. 9. Limited commitment The limited commitment friction generates partial risk sharing. Income fluctuations partially translate into consumption fluctuation. When an agent earns 8 he consumes 6, and when he earns 2 he consumes 4. This outcome is constrained efficient. Applications: Households in villages (Ligon, Thomas, and Worrall, 2002) Households in the United States (Krueger and Perri, 2006) Members of a household (Mazzocco, 2007) Countries (Kehoe and Perri, 2002) Partnerships such as law firms A farmer and a thief (Schechter, 2007) Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  10. 10. Storage In all these applications, agents are likely to have access to some storage technology, both public and private/hidden. Households in villages may keep grain or cash around the house or use community grain storage facilities. Households in the United States may keep savings in cash or ‘hide’ their assets abroad. Spouses in a household may accumulate both joint assets and savings for personal use. Partners in a law firms may have both common and private assets. The European Stability Mechanism has public funds for euro area countries. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  11. 11. Storage In all these applications, agents are likely to have access to some storage technology, both public and private/hidden. Households in villages may keep grain or cash around the house or use community grain storage facilities. Households in the United States may keep savings in cash or ‘hide’ their assets abroad. Spouses in a household may accumulate both joint assets and savings for personal use. Partners in a law firms may have both common and private assets. The European Stability Mechanism has public funds for euro area countries. If so, agents can also use storage to improve insurance. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  12. 12. What we do in this paper We investigate what are the consequences if both a public and a private storage technology are available, and risk sharing is imperfect because of limited commitment. We provide a thorough analytical characterization of this environment. In particular, we study the implications of the availability of storage on aggregate asset accumulation, individual consumption dynamics, and welfare. We also show that any constrained-efficient allocation can be decentralized as a competitive equilibrium with endogenous borrowing constraints similar to Alvarez and Jermann (2000). Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  13. 13. Literature In the existing models of risk sharing with limited commitment, only public and/or observable and contractible individual intertemporal technologies have been considered. Marcet and Marimon (1992), Ligon, Thomas, and Worrall (2000), Kehoe and Perri (2002), Ábrahám and Carceles-Poveda (2006), Krueger and Perri (2006) Both public and private storage technologies have been considered when the deep friction that limits risk sharing is imperfect information (hidden income or effort). Cole and Kocherlakota (2001), Werning (2001), Ábrahám and Pavoni (2008), Ábrahám, Koehne, and Pavoni (2010) Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  14. 14. Setup Our starting point is the two-sided lack of commitment framework of Kocherlakota (1996). Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  15. 15. Setup Our starting point is the two-sided lack of commitment framework of Kocherlakota (1996). Two (types of) infinitely-lived, risk-averse, ex-ante identical agents. Income has discrete support (S states), is i.i.d. over time, and is perfectly negatively correlated across the two agents, i.e. there is no aggregate risk in the sense that the aggregate endowment is constant. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  16. 16. Setup continued We consider a storage/saving technology with exogenous return −1 ≤ r ≤ 1/β − 1. Borrowing is not allowed. The planner can use this storage technology. – public storage Agents have access to the same technology in a hidden (non-observable and/or non-contractible) way. – private storage (later) Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  17. 17. Model with public storage The planner’s problem is ∞ max λi β t Pr st u ci st ci (s ),B(st ) t i t=1 st s.t. ci st ≤ Y + (1 + r)B(st−1 ) − B(st ), B(st ) ≥ 0, ∀st , i Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  18. 18. Model with public storage The planner’s problem is ∞ max λi β t Pr st u ci st ci (s ),B(st ) t i t=1 st s.t. ci st ≤ Y + (1 + r)B(st−1 ) − B(st ), B(st ) ≥ 0, ∀st , i ∞ β r−t Pr sr | st u (ci (sr )) ≥ Uiau (st ) , ∀st , ∀i, r=t sr where Uiau (st ) is the value function of autarky. (Alternative outside options are possible as long as the value is increasing in current income.) Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  19. 19. Characterization t Define Mi (st ) ≡ λi + τ τ =1 µi (s ), where sτ is the subhistory of t µi (s ) st up to time τ , υi (st ) ≡ Mi (st ) , and M1 (st ) u (c2 (st )) x st ≡ = , M2 (st ) u (c1 (st )) which is the ‘temporary’ relative Pareto weight of agent 1. The law of motion of x is given by 1 − υ2 (st ) x st = x st−1 . 1 − υ1 (st ) Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  20. 20. Characterization t Define Mi (st ) ≡ λi + τ τ =1 µi (s ), where sτ is the subhistory of t µi (s ) st up to time τ , υi (st ) ≡ Mi (st ) , and M1 (st ) u (c2 (st )) x st ≡ = , M2 (st ) u (c1 (st )) which is the ‘temporary’ relative Pareto weight of agent 1. The law of motion of x is given by 1 − υ2 (st ) x st = x st−1 . 1 − υ1 (st ) The planner’s Euler (optimality condition for B t+1 ) is u ci st+1 u ci st ≥ β(1 + r) Pr st+1 |st , 1 − υi (st+1 ) st+1 where 0 ≤ υi st+1 ≤ 1. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  21. 21. Characterization The key variable for the characterization of the model’s dynamics is the time-varying relative Pareto weight of agent 1, x. Given B, the constrained-efficient allocation is described by optimal state-dependent intervals, xj (B), xj (B) , j = 1, ..., S. The lower (upper) limit is determined by the binding participation constraint of agent 1 (agent 2). Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  22. 22. Characterization The key variable for the characterization of the model’s dynamics is the time-varying relative Pareto weight of agent 1, x. Given B, the constrained-efficient allocation is described by optimal state-dependent intervals, xj (B), xj (B) , j = 1, ..., S. The lower (upper) limit is determined by the binding participation constraint of agent 1 (agent 2). The dynamics of the relative Pareto weight is given by  j  x (B) if xt−1 > xj (B) xt = xt−1 if xt−1 ∈ xj (B), xj (B)  j x (B) if xt−1 < xj (B) Similar intervals and dynamics on consumption: cj (B), cj (B) ... Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  23. 23. Characterization β determines the width of the intervals. High β: wide intervals and more risk sharing. Low β: narrow intervals and less risk sharing. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  24. 24. Characterization β determines the width of the intervals. High β: wide intervals and more risk sharing. Low β: narrow intervals and less risk sharing. We say that risk sharing is high if the consumption distribution is time invariant in the long run. This happens when β is above some threshold. We say that risk sharing is low if the consumption distribution varies over time. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  25. 25. Short-run asset dynamics Proposition. Given inherited assets, aggregate storage is greater when consumption inequality is higher. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  26. 26. Short-run asset dynamics Proposition. Given inherited assets, aggregate storage is greater when consumption inequality is higher. Intuition: the planner stores for the agents and to improve risk sharing in the future. When inequality is higher today, the high-income agent has more incentive to store. The planner inherits this incentive. When inequality is higher today, the gains from improving risk sharing in the future are higher. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  27. 27. Long-run behavior of assets Proposition. Assume that β is such that agents obtain low risk sharing in the sense that the consumption distribution is time varying when B = B = 0 is imposed. (i) There exists r1 such that for all r ∈ [−1, r1 ], B = 0 for all income levels, that is, public storage is never used in the long run. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  28. 28. Long-run behavior of assets Proposition. Assume that β is such that agents obtain low risk sharing in the sense that the consumption distribution is time varying when B = B = 0 is imposed. (i) There exists r1 such that for all r ∈ [−1, r1 ], B = 0 for all income levels, that is, public storage is never used in the long run. (ii) There exists a strictly positive r2 > r1 such that for all r ∈ (r1 , r2 ), B remains stochastic but bounded in the long run. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  29. 29. Long-run behavior of assets Proposition. Assume that β is such that agents obtain low risk sharing in the sense that the consumption distribution is time varying when B = B = 0 is imposed. (i) There exists r1 such that for all r ∈ [−1, r1 ], B = 0 for all income levels, that is, public storage is never used in the long run. (ii) There exists a strictly positive r2 > r1 such that for all r ∈ (r1 , r2 ), B remains stochastic but bounded in the long run. (iii) For all r ∈ [r2 , 1/β − 1), B converges almost surely to a strictly positive constant where the consumption distribution is time invariant but perfect risk sharing is not achieved. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  30. 30. Long-run behavior of assets Proposition. Assume that β is such that agents obtain low risk sharing in the sense that the consumption distribution is time varying when B = B = 0 is imposed. (i) There exists r1 such that for all r ∈ [−1, r1 ], B = 0 for all income levels, that is, public storage is never used in the long run. (ii) There exists a strictly positive r2 > r1 such that for all r ∈ (r1 , r2 ), B remains stochastic but bounded in the long run. (iii) For all r ∈ [r2 , 1/β − 1), B converges almost surely to a strictly positive constant where the consumption distribution is time invariant but perfect risk sharing is not achieved. (iv) Whenever r = 1/β − 1, B converges to a strictly positive constant and perfect risk sharing is self-enforcing. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  31. 31. Long-run behavior of assets Proposition. Assume that β is such that agents obtain low risk sharing in the sense that the consumption distribution is time varying when B = B = 0 is imposed. (i) There exists r1 such that for all r ∈ [−1, r1 ], B = 0 for all income levels, that is, public storage is never used in the long run. (ii) There exists a strictly positive r2 > r1 such that for all r ∈ (r1 , r2 ), B remains stochastic but bounded in the long run. (iii) For all r ∈ [r2 , 1/β − 1), B converges almost surely to a strictly positive constant where the consumption distribution is time invariant but perfect risk sharing is not achieved. (iv) Whenever r = 1/β − 1, B converges to a strictly positive constant and perfect risk sharing is self-enforcing. If β is such that the consumption distribution is time invariant when B = B = 0 is imposed, then only (i), (iii), and (iv) occur. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  32. 32. Long-run behavior of assets Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  33. 33. Long-run behavior of assets Intuition: There is a trade-off between improving future risk sharing, and using an inefficient storage technology. As r increases, the first becomes relatively more important. No trade-off when β(1 + r) = 1. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  34. 34. Decentralization/Competitive equilibrium Public storage can be interpreted as a special case of capital ⇒ decentralization is a special case of Ábrahám and Carceles-Poveda (2006). Agents trade Arrow securities subject to endogenous borrowing constraints (as in Alvarez and Jermann, 2000). Intermediaries issue Arrow securities to finance storage (i.e., agents do not own it directly) and make zero profits. Asset prices take into account future binding borrowing constraints. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  35. 35. Decentralization/Competitive equilibrium Public storage can be interpreted as a special case of capital ⇒ decentralization is a special case of Ábrahám and Carceles-Poveda (2006). Agents trade Arrow securities subject to endogenous borrowing constraints (as in Alvarez and Jermann, 2000). Intermediaries issue Arrow securities to finance storage (i.e., agents do not own it directly) and make zero profits. Asset prices take into account future binding borrowing constraints. Our model provides a theory of endogenously growing (and shrinking) Lucas trees in equilibrium. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  36. 36. Model with both public and private storage The planner’s problem is ∞ max λi β t Pr st u ci st ci (s ),B(st ) t i t=1 st s.t. ci st ≤ Y + (1 + r)B(st−1 ) − B(st ), B(st ) ≥ 0, ∀st , i ∞ ˜ β r−t Pr sr | st u (ci (sr )) ≥ Uiau (st ) , ∀st , ∀i, r=t sr Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  37. 37. Model with both public and private storage The planner’s problem is ∞ max λi β t Pr st u ci st ci (s ),B(st ) t i t=1 st s.t. ci st ≤ Y + (1 + r)B(st−1 ) − B(st ), B(st ) ≥ 0, ∀st , i ∞ ˜ β r−t Pr sr | st u (ci (sr )) ≥ Uiau (st ) , ∀st , ∀i, r=t sr u ci st ≥ β(1 + r) Pr st+1 u ci st+1 , ∀st , ∀i. st+1 Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  38. 38. Model with both public and private storage The planner’s problem is ∞ max λi β t Pr st u ci st ci (s ),B(st ) t i t=1 st s.t. ci st ≤ Y + (1 + r)B(st−1 ) − B(st ), B(st ) ≥ 0, ∀st , i ∞ ˜ β r−t Pr sr | st u (ci (sr )) ≥ Uiau (st ) , ∀st , ∀i, r=t sr u ci st ≥ β(1 + r) Pr st+1 u ci st+1 , ∀st , ∀i. st+1 (We show that the first-order condition approach is valid.) Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  39. 39. Characterization Proposition. When the planner’s Euler is satisfied, the agents’ Eulers are satisfied as well. Therefore, the solution of the model with both public and hidden storage corresponds to the solution of the problem with only public storage, as long as the outside option is the same. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  40. 40. Characterization Proposition. When the planner’s Euler is satisfied, the agents’ Eulers are satisfied as well. Therefore, the solution of the model with both public and hidden storage corresponds to the solution of the problem with only public storage, as long as the outside option is the same. u ci st+1 Planner: u ci st ≥ β(1 + r) Pr st+1 |st . 1 − υi (st+1 ) st+1 Agent: u ci st ≥ β(1 + r) Pr st+1 |st u ci st+1 . st+1 Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  41. 41. Characterization Proposition. When the planner’s Euler is satisfied, the agents’ Eulers are satisfied as well. Therefore, the solution of the model with both public and hidden storage corresponds to the solution of the problem with only public storage, as long as the outside option is the same. u ci st+1 Planner: u ci st ≥ β(1 + r) Pr st+1 |st . 1 − υi (st+1 ) st+1 Agent: u ci st ≥ β(1 + r) Pr st+1 |st u ci st+1 . st+1 Intuition: public storage relaxes future participation constraints, thus improves risk sharing – only the planner internalizes this externality. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  42. 42. Does access to hidden storage matter? We have just seen that hidden storage does not matter in our model with public storage. In other words, agents’ Euler inequalities are satisfied. Does hidden storage matter in the basic model without storage? Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  43. 43. Does access to hidden storage matter? We have just seen that hidden storage does not matter in our model with public storage. In other words, agents’ Euler inequalities are satisfied. Does hidden storage matter in the basic model without storage? Proposition. Suppose that partial insurance occurs. There exists ˜ 1 r < β − 1 such that for all r > r, agents’ Euler inequalities are ˜ violated at the constrained-efficient allocation of the basic model. r can even be negative ˜ Intuition: under bounded support of income and imperfect risk sharing, high income agents face weakly decreasing consumption next period. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  44. 44. Individual consumption dynamics We overturn 3 counterfactual predictions of the basic model with respect to consumption dynamics (Attanasio, 1999; Broer, 2011). In our model, the amnesia property does not hold in general. the persistence property does not hold in general. agents’ Euler inequalities hold. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  45. 45. Long-run welfare Proposition. (i) There exists r1 such that for all r ∈ [−1, r1 ] storage is not used even in autarky, therefore access to storage is welfare neutral. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  46. 46. Long-run welfare Proposition. (i) There exists r1 such that for all r ∈ [−1, r1 ] storage is not used even in autarky, therefore access to storage is welfare neutral. (ii) There exists a strictly positive r2 > r1 such that for all r ∈ (r1 , r2 ] storage is used in autarky but not in equilibrium, therefore consumption dispersion increases and welfare deteriorates as a result of access to storage. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  47. 47. Long-run welfare Proposition. (i) There exists r1 such that for all r ∈ [−1, r1 ] storage is not used even in autarky, therefore access to storage is welfare neutral. (ii) There exists a strictly positive r2 > r1 such that for all r ∈ (r1 , r2 ] storage is used in autarky but not in equilibrium, therefore consumption dispersion increases and welfare deteriorates as a result of access to storage. (iii) There exists a strictly positive r3 > r2 such that for all r ∈ (r2 , r3 ) public storage is (at least sometimes) positive, but access to storage is still welfare reducing. Access to storage is welfare neutral in the long run at the threshold r = r3 . Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  48. 48. Long-run welfare Proposition. (i) There exists r1 such that for all r ∈ [−1, r1 ] storage is not used even in autarky, therefore access to storage is welfare neutral. (ii) There exists a strictly positive r2 > r1 such that for all r ∈ (r1 , r2 ] storage is used in autarky but not in equilibrium, therefore consumption dispersion increases and welfare deteriorates as a result of access to storage. (iii) There exists a strictly positive r3 > r2 such that for all r ∈ (r2 , r3 ) public storage is (at least sometimes) positive, but access to storage is still welfare reducing. Access to storage is welfare neutral in the long run at the threshold r = r3 . (iv) For all r ∈ (r3 , 1/β − 1] access to storage is welfare improving in the long run. Consumption dispersion may or may not be lower than in the basic model without storage. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  49. 49. Long-run welfare Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  50. 50. Big picture Hidden storage has been considered in models with hidden income or effort (Cole and Kocherlakota, 2001; Ábrahám, Koehne, and Pavoni, 2010). The problem is a similar joint deviation: storage and shirking/misreporting vs. storage and default. Limited commitment: storage by the planner both improves insurance and relaxes the incentive problem, hence access to storage may be welfare improving. Hidden income/effort: public asset accumulation would make incentive provision more expensive, so it does not take place in the optimal allocation, and access to storage is detrimental to welfare. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage
  51. 51. Applications Quantitative implications of storage on the dynamics of consumption. Risk sharing in villages – rationale for public storage facilities. Partnerships – rationale for ‘common’ capital. Couples – economic reasons for not providing rights to accumulated capital for initiator of divorce. Economic unions – rationale for building up stability funds. Ábrahám (EUI) & Laczó (IAE & Barcelona GSE) Limited Commitment and Storage

×