CLO replenishment regarded as linear optimisation problem

Synthetic collateralised loan obligations (CLOs) often have a replenishment feature: if the securitised assets amortise, the unused CLO volume can be replenished (refilled). While this replenishment problem usually is not a linear optimisation problem, we show that under additional assumptions it can be converted into a linear optimisation problem. Thus, the replenishment problem becomes numerically tractable even for a large number of assets.     

Competitive equilibria in economies with multiple indivisible and multiple divisible commodities

In this paper we consider a general equilibrium model with a finite number of divisible and a finite number of indivisible commodities. In models with indivisibilities it is typically assumed that there is only one divisible good, which serves as money. The presence of money in the model is used to transfer the value of certain amounts of indivisible goods. For such economies with only one divisible commodity Danilov et al. showed the existence of a general equilibrium if the individual demands and supplies belong to a same class of discrete convexity. For economies with multiple divisible goods and money van der Laan et al. proved existence of a general equilibrium if the divisible goods are produced out of money using a linear production technology and no other producers are present in the model.     

Club theory and household formation

The relationship between our general equilibrium model with multi-member households and club models with multiple private goods is investigated. The main distinction in the definitions consists in the equilibrium concepts. As a rule, competitive equilibria among households where no group of consumers can benefit from forming a new household and valuation equilibria prove equivalent in the absence of consumption externalities, but not in their presence.     

Reduction-consistency in collective choice problems

We consider the problem of choosing a subset of a feasible set over which each agent has a strict preference. We propose an invariance property, reduction-consistency, of choice rules and study its implications. The property is a natural expression for the problems of a general principle of consistency having been studied extensively in resource allocation problems. We show that no scoring rule satisfies reduction-consistency, and base a characterization of the top rule on the property. We also investigate the minimal extension of a rule needed to recover reduction-consistency, and identify the minimal extensions of several rules including the Borda and plurality rules.     

Separability of stochastic production decisions from producer risk preferences in the presence of financial markets

Separation results, as they are usually understood, refer to conditions under which a firm’s production decisions are independent of its risk attitudes. Well-understood situations where separation occurs typically include those where technically feasible production opportunities are replicable in financial markets. This paper gives necessary and sufficient conditions for separation that go beyond these well-understood spanning conditions. To do so, we present a unified treatment of the production and financial decisions available to a firm facing frictionless financial markets and a stochastic production technology under minimal assumptions about the firm’s technology and objective function.     

Constrained inefficiency in GEI: A geometric argument

In this paper we use global analysis to study the welfare properties of general equilibrium economies with incomplete markets (GEI). Our main result is to show that constrained Pareto optimal equilibria are contained in a submanifold of the equilibrium set. This result is explicitly derived for economies with real assets and fixed aggregate resources, of which real numéraire assets are a special case. As a by product of our analysis, we propose an original global parametrization of the equilibrium set that generalizes to incomplete markets the classical one, first, proposed by Lange [Lange, O., 1942. The foundations of welfare economics. Econometrica 10, 215–228].     

Contractual solutions to hold-up problems with quality uncertainty and unobservable investments

Consider a seller and a buyer who write a contract. After that, the seller produces a good. She can influence the expected quality of the good by making unobservable investments. Only the seller learns the realized quality. Finally, trade can occur. It is always ex post efficient to trade. Yet, it may be impossible to achieve the first best, even though the risk-neutral parties are symmetrically informed at the contracting stage and complete contracts can be written. The second best is characterized by distortions that are reminiscent of adverse selection models (i.e., models with precontractual private information but without hidden actions).     

Mechanisms that efficiently verify the optimality of a proposed action

The best known achievement of the literature on resource-allocating mechanisms and their message spaces is the first rigorous proof of the competitive mechanism's informational efficiency. In an exchange economy withN persons andK+1 commodities (including a numeraire), that mechanism announcesK prices as well as aK-compenent trade vector for each ofN−1 persons, making a total ofNK message variables. Trial messages are successively announced and after each announcement each personprivately determines, usingprivate information, whether she finds the proposed trades acceptable at the announced prices. When a message is reached with which all are content, then the trades specified in that message take place, and they satisfy Pareto optimality and individual rationality. The literature shows that no (suitably regular) mechanism can achieve the same thing with fewer thanNK message variables. In the classic proof, all the candidate mechanisms have the privacy property, and the proof uses that property in a crucial way. ‘Non-private’ mechanisms are, however, well-defined. We present a proof that forN>K,NK remains a lower bound even when we permit ‘non-private’ mechanisms. Our new proof does not use privacy at all. But in a non-private mechanism, minimality of the number of message variables can hardly be defended as the hallmark of informational efficiency, since a non-private mechanism requires some persons to know something about the private information of othersin addition to the information contained in the messages. The new proof of the lower boundNK invites a new interpretation of the competitive mechanism's informational efficiency. We provide a new concept of efficiency which the competitive mechanism exhibits and which does rest on privacy even whenN>K. To do so, we first define a class ofprojection mechanisms, wherein some of the message variables are proposed values of the action to be taken, and the rest are auxiliary variables. The competitive mechanism has the projection property, with a trade vector as its action and prices as the auxiliary variables. A projection mechanism proposes an action; for each proposal, the agents then use the auxiliary variables, together with their private information, to verify that the proposed action meets the mechanism's goal (Pareto optimality and individual rationality for the competitive mechanism) if, indeed, it does meet that goal. For a given goal, we seek projection mechanisms for which theverification effort (suitably measured) is not greater than that of any other projection mechanism that achieves the goal. We show the competitive mechanism to be verification-minimal within the class of private projection mechanisms that achieve Pareto optimality and individual rationality; that proofdoes use the privacy of the candidate mechanisms. We also show, under certain conditions, that a verification-minimal projection mechanism achieving a given goal has smallest ‘total communication effort’ (which is locally equivalent to the classic ‘message-space size’) among all private mechanisms that achieve the goal, whether or not they have the projection property.     

Inter-temporal preference for flexibility and risky choice

We derive an inter-temporal theory of choice, in the spirit of Kreps and Porteus [Kreps, D.M., Porteus, E.L., 1978. Temporal resolution of uncertainty and dynamic choice theory. Econometrica 46, 185–200], where decision makers have incomplete preferences. This can be used to model indecisiveness as well as unforeseen contingencies. The key to our approach is a time consistency condition and therefore the normative connection between ex-ante and ex-post choice. The time consistency condition enables a representation that is a straight forward extension of recursive utility with the exception that it features an inter-temporal ‘utility for flexibility’.     

On financial equilibrium with intermediation costs

This paper studies the set of competitive equilibria in financial economies with intermediation costs. We consider an arbitrary dividend structure, which includes options and equity with limited liabilities. We show a general existence result and upper-hemi continuity of the equilibrium correspondence. Finally, we prove that when intermediation costs approach zero, unbounded volume of asset trades is a necessary and sufficient condition, provided that, there is no financial equilibrium without intermediation costs.     

Recognizing one-dimensional Euclidean preference profiles

A preference profile has a one-dimensional Euclidean representation if it can be derived from an arrangement of individuals and alternatives on a line, with each individual preferring the nearer of each pair of alternatives. We provide a polynomial-time algorithm that determines whether a given preference profile has a one-dimensional Euclidean representation and, if so, constructs one. This result has electoral and mechanism design applications.     

On economies of scope in communication

A classic puzzle in the economic theory of the firm concerns the fundamental cause of decreasing returns to scale. If a plant producing product quantityX at costC can be replicated as often as desired, then the quantityrX need never cost more thanrC. Traditionally the firm is imagined to take its identity from a fixednon-replicable input, namely a ‘top manager’; as more plants or divisions are added, the communication and computation burden imposed on the top manager (who has information not possessed by the divisions) grows more than proportionately. Decreasing returns are experienced as the top manager hires more variable inputs to cope with the rising burden. Suppose it turns out, however, that when the divisions are assembled, and are given exactly the same totally independent tasks that they fulfilled when they were autonomous, then asaving can be achieved if they adopt a joint procedure for performing those tasks rather than replicating their previous separate procedures. Then the top manager's rising burden must be shown to be particularly onerous—otherwise there may actually beincreasing returns. We show that for a certain model of the information-processing procedure used by the separate divisions and by the firm, there may indeed be such an odd unexpected saving. The saving occurs with respect to the size of the language in which members of each division, or of the firm, communicate with one another, provided that language is finite. If instead the language is a continuum then the saving cannot occur, provided that the procedures used obey suitable ‘smoothness’ conditions. We show that the saving for the finite case can be ruled out in two ways: by requiring the procedures used to obey a regularity condition that is a crude analogue of the smoothness conditions we impose on the continuum procedures, or by insisting that the procedure used be a ‘deterministic’ protocol. Such a protocol prescribes a conversation among the participants, in which a participant has only one choice, whenever that participant has to make an announcement to the others. The results suggest that a variety of information-processing models will have to be studied before the traditional explanation for decreasing returns to scale is understood in a rigorous way.     

Core equivalence and welfare properties without divisible goods

We study an economy where all goods entering preferences or production processes are indivisible. Fiat money not entering consumers’ preferences is an additional perfectly divisible parameter. We establish a First and Second Welfare Theorem and a core equivalence result for the rationing equilibrium concept introduced in Florig and Rivera (2005a). The rationing equilibrium can be considered as a natural extension of the Walrasian notion when all goods are indivisible at the individual level but perfectly divisible at the level of the entire economy.     

Dispersed initial ownership and the efficiency of the stock market under moral hazard

We generalize a standard general equilibrium framework extended for moral hazard to allow for a dispersed initial ownership distribution of firms. We show that the market allocation is constrained-efficient only when in each firm the entrepreneur who generates payoffs through unobservable effort has full initial ownership in his firm.     

Wealth Accumulation and Factors Accounting for Success

We use detailed income, balance sheet, and cash flow statements constructed for households in a long monthly panel in an emerging market economy, and some recent contributions in economic theory, to document and better understand the factors underlying success in achieving upward mobility in the distribution of net worth. Wealth inequality is decreasing over time, and many households work their way out of poverty and lower wealth over the seven year period. The accounts establish that, mechanically, this is largely due to savings rather than incoming gifts and remittances. In turn, the growth of net worth can be decomposed household by household into the savings rate and how productively that savings is used, the return on assets (ROA). The latter plays the larger role. ROA is, in turn, positively correlated with higher education of household members, younger age of the head, and with a higher debt/asset ratio and lower initial wealth, so it seems from cross-sections that the financial system is imperfectly channeling resources to productive and poor households. Household fixed effects account for the larger part of ROA, and this success is largely persistent, undercutting the story that successful entrepreneurs are those that simply get lucky. Persistence does vary across households, and in at least one province with much change and increasing opportunities, ROA changes as households move over time to higher-return occupations. But for those households with high and persistent ROA, the savings rate is higher, consistent with some micro founded macro models with imperfect credit markets. Indeed, high ROA households save by investing in their own enterprises and adopt consistent financial strategies for smoothing fluctuations. More generally growth of wealth, savings levels and/or rates are correlated with TFP and the household fixed effects that are the larger part of ROA.     

A characterization and an impossibility of finite length anonymity for infinite generations

In the context of ranking infinite utility streams, the impartiality axiom of finite length anonymity requires the equal ranking of any two utility streams that are equal up to a finite length permutation ( Fleurbaey and Michel, 2003). We first characterize any finite length permutation as a composition of a fixed step permutation and an “almost” fixed step permutation. We then show that if a binary relation satisfies finite length anonymity, then it violates all the distributional axioms that are based on a segment-wise comparison. Examples of those axioms include the weak Pareto principle and the weak Pigou-Dalton principle.     

Smooth inequality measurement: Approximation theorems

The main purpose of this paper is to prove that smoothness is not a restrictive assumption in inequality measurement as any inequality measure (preorder) can be approximated in a well defined sense by a smooth inequality measure (preorder).     

Common agency with risk-averse agent

In a common agency model with a risk-averse agent and private information distortion in the equilibrium policy from the first-best is greater compared to the case of a risk-neutral agent. The principals are unable to screen completely the agent’s preferences if he is sufficiently risk-averse: there is bunching in the contract. The contribution schedules keep track of informational externality. However, when the coefficient of risk-aversion goes to zero the contributions become truthful as in the complete information case.