BUSCADOR RECOLECTA

Some high-income countries have total fertility rates as low as one child. Using Spanish administrative data, we document that temporary contracts correlate with lower first birth rates. Also, women with children are less likely to work split-shift jobs with long breaks in the middle of the day. We build a life-cycle model where women decide on labor supply and fertility. We show that reforms eliminating duality or split-shift jobs raise women's labor participation, narrow the employment gap between mothers and nonmothers, and boost fertility for working women. These reforms, together with childcare subsidies, increase married women's fertility to 1.8 children, Guner acknowledges financial support from RecerCaixa, and from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000915-S). Kaya acknowledges financial support from the Spanish Ministry of Science and Innovation through grant “Consolidated Group-C” ECO2008-04756 and FEDER. Sánchez-Marcos acknowledges financial support from the Spanish Government under Grant No. PID2019-108087RB-I00 and from Fundación Ramon Areces. We thank our discussant, Pedro Mira, at the 2018 COSME Gender Economics Workshop in Madrid, and seminar and workshop participants at Bank of Spain, Cardiff Business School, Collegio Carlo Alberto, Stockholm School of Economics, U. de Alicante, U. Autonoma de Barcelona, U. of Bristol, U. of Edinburgh, U. Pablo de Olavide, U. de Zaragoza, 2017 SED Meetings in Edinburgh, 2018 EAE-ESEM Meetings in Cologne, 2019 Workshop in Public Policy Design: Family, Gender Economics at the Universitat de Girona, 2019 Meeting of the Italian Economic Association in Palermo, 2020 Income Dynamics and the Family Workshop in Barcelona, and 2021 GW4 Career Breaks & Gender Equality Workshop.

The final publication is available at Springer via http://dx.doi.org/10.1007/s00355-012-0689-8, We present a model that is closely related to the so-called models of choice under complete uncertainty, in which the agent has no information about the probability of the outcomes. There are two approaches within the said models: the state space-based approach, which takes into account the possible states of nature and the correspondence between states and outcomes; and the set-based approach, which ignores such information, and solves certain difficulties arising from the state space-based approach. Kelsey (Int Econ Rev 34:297–308, 1993) incorporates into a state space-based framework the assumption that the agent has ordinal information about the likelihood of the states. This paper incorporates this same assumption into a set-based framework, thus filling a theoretical gap in the literature. Compared to the set-based models of choice under complete uncertainty we introduce the information about the ordinal likelihood of the outcomes while, compared to Kelsey’s approach, we incorporate the advantages of describing uncertainty environments from the set-based perspective. We present an axiomatic study that includes adaptations of some of the axioms found in the related literature and we characterize some rules featuring different combinations of information about the ordinal likelihood of the outcomes and information about their desirability., We acknowledge financial support
from the Spanish Ministry of Science and Technology (Projects ECO2008-04756, ECO2009-11213,
ECO2009-12836 and Ramón y Cajal program), the Junta de Castilla y León (Project VA092A08), FEDER,
and the Barcelona Economics Program of CREA.

The final publication is available at Springer via http://dx.doi.org/10.1007/s10888-011-9165-4, Rankings to evaluate opportunity distributions present in most of the literature judge a policy (change from one distribution of opportunities to another) on the basis of the changes created and, thus, independently of the original situation. This paper proposes a group of axioms capturing the idea that rankings of equality of opportunities might consider not only the changes promoted, but also the initial situation in society. The combination of this group of axioms with other well-established properties enables us to characterize two families of new opportunity distribution rankings. The first family weighs each individual’s percentage share in the total number of opportunities, while the second weighs opportunities depending on how many agents have them available., Financial support
from the Spanish Ministry of Education through grants ECO2008-04756, ECO2009-
11213, ECO2009-12836, Juan de la Cierva and Ramon y Cajal programs, FEDER, and
the Barcelona Economics Program of CREA is gratefully acknowledged.

This essay deals with the notion and content of freedom of choice proposing a new set up and a new family of measures for this concept which is, indeed, an ethical value of paramount importance in a well ordered and open society. Following some ideas of John StuartMill, we propose that freedom of choice has to be understood not in a single stage of choice, but in the ordered collection of choices that a person can make in her life.We then suggest to represent a life in a tree structure, where each node
represents a state of life and the edges between nodes will represent possible decisions in life. In this new framework, we propose a set of axioms that imply the following family of measures of lifetime’s freedom of choice: the lifetime’s freedom of choice has to be evaluated by a weighted sum of all possible states of life an individual might visit, with weights representing the number of decisions the individual took to reach that state., Financial support
from the Spanish Ministry of Education through grants ECO2008-04756, ECO2009-11213, ECO2009-
12836, Ramon y Cajal program, FEDER, and the Barcelona Economics Program of CREA is gratefully
acknowledged.

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. Most of the literature has implicitly assumed that all divisions are feasible. In this paper we consider the division problem when each agent has a maximal capacity due to an objective and verifiable feasibility constraint which imposes an upper bound on his share. Then each agent has a feasible interval of shares where his preferences are single-peaked. A rule has to propose to each agent a feasible share.We focus mainly on strategy-proof, efficient and consistent rules and provide alternative characterizations of the extension of the uniform rule that deals explicitly with agents' maximal capacity constraints

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this paper we consider the division problem when agents participation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are single-peaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agents shares. We study a subclass of e¢ cient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents voluntary participation.

A multiple-partners assignment game with heterogeneous sales and multi-unit demands consists of a set of sellers that own a given number of indivisible units of potentially many different goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by using only linear programming. In particular, we show how to compute equilibrium price vectors from the solutions of the dual linear program associated to the primal linear program defined to find optimal assignments. Using only linear programming tools, we also show (i) that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all optimal assignments, and vice versa; (ii) that the set of (restricted) equilibrium price vectors has a natural lattice structure; and (iii) how this structure is translated into the set of agents' utilities that are attainable at equilibrium

We consider the general many-to-one matching model with ordinal preferences and give a procedure to partition the set of preference profiles into subsets with the property that all preference profiles in the same subset have the same Core. We also show how to identify a profile of (incomplete) binary relations containing the minimal information needed to generate as strict extensions all the (complete) preference profiles with the same Core. This is important for applications since it reduces the amount of information that agents have to reveal about their preference relations to centralized Core matching mechanisms; moreover, this reduction is maximal.

The Blocking Lemma identifies a particular blocking pair for each non-stable and individually rational matching that is preferred by some agents of one side of the market to their optimal stable matching. Its interest lies in the fact that it has been an instrumental result to prove key results on matching. For instance, the fact that in the college admissions problem the workers-optimal stable mechanism is group strategy-proof for the workers and the strong stability theorem in the marriage model follow directly from the Blocking Lemma. However, it is known that the Blocking Lemma and its consequences do not hold in the general many-to-one matching model in which firms have substitutable preference relations. We show that the Blocking Lemma holds for the many-to-one matching model in which firms' preference relations are, in addition to substitutable, quota q-separable. We also show that the Blocking Lemma holds on a subset of substitutable preference profiles if and only if the workers-optimal stable mechanism is group strategy-proof for the workers on this subset of profiles

Es presenten els dos teoremes d'impossibilitat més importants de la moderna teoria de l'elecció social: el teorema d'Arrow per a funcions de benestar social no dictatorials que satisfan el principi de Pareto i la propietat de la independència d'alternatives irrellevants, i el teorema de Gibbard-Satterthwaite per a funcions d'elecció social no trivials i no manipulables. Es descriuen set exemples de problemes concrets d'elecció social en què l'estructura particular del conjunt d'alternatives socials permet restringir el domini de preferències individuals i dissenyar, per a cada un d'aquests, funcions d'elecció social no manipulables en els corresponents dominis de preferències restringits., We present the two most important impossibility theorems of the modern social choice theory: Arrow's theorem for social welfare functions satisfying the Pareto principle and the independence of irrelevant alternatives property, and Gibbard-Satterthwaite's theorem for non-trivial and strategy-proof social choice functions. We describe seven examples of specific social choice problems where the particular structure of the set of social alternatives allows to restrict the domain of individual preferences and to design for each of them strategy-proof social choice functions on the corresponding restricted preference domains

We study cooperative and competitive solutions for a many-to-many generalization of Shapley and Shubik's (1971) assignment game. We consider the Core, three other notions of group stability, and two alternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related to the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated with the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of matrices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view.

This essay deals with the notion and content of freedom of choice proposing a new set up and a new family of measures for this concept which is, indeed, an ethical value of paramount importance in a well ordered and open society. Following some ideas of John StuartMill, we propose that freedom of choice has to be understood not in a single stage of choice, but in the ordered collection of choices that a person can make in her life.We then suggest to represent a life in a tree structure, where each node represents a state of life and the edges between nodes will represent possible decisions in life. In this new framework, we propose a set of axioms that imply the following family of measures of lifetime's freedom of choice: the lifetime's freedom of choice has to be evaluated by a weighted sum of all possible states of life an individual might visit, with weights representing the number of decisions the individual took to reach that state.

We document recent trends in gender equality in employment and wages in Spain. Despite an impressive decline in the gender gap in employment, females are still less likely to work than males: about 76% of working age males and 63% of working age females were employed in 2010. If females work they are more likely to be employed part time and with temporary contracts. The large increase in female employment, from 28% in 1977 to 63% in 2010, was accompanied by a significant decline in fertility. The gender gap in wages, after controlling for worker and job characteristics as well as for selection, is high. It was about 20% in 2010, quite close to its value in 1994. Furthermore, the gender gap in wages is driven mainly by differences in returns to individual characteristics. While women are more qualified than men in observable labor market characteristics, they end up earning less. There have been several important policy changes that try to help families reconcile family responsibilities with market work. The existing literature suggests that households do react to incentives generated by different policies and policy changes are at least partly responsible for changes in female labor supply. In recent decades, the large inflow of immigrants, who provided relatively cheap household services, allowedmore educated women to enter the labor market. Policy challenges, however, remain.

We study the possibilities for agenda manipulation under strategic voting for two prominent sequential voting procedures: the amendment procedure and the successive procedure. We show that a well known result for tournaments, namely that the successive procedure is (weakly) more manipulable than the amendment procedure at any given preference profile, extends to arbitrary majority quotas. Moreover, our characterizations of the attainable outcomes for arbitrary quotas allow us to compare the possibilities for manipulation across different quotas. It turns out that the simple majority quota maximizes the domain of preference profiles for which neither procedure is manipulable, but at the same time neither the simple majority quota nor any other quota uniformly minimizes the scope of manipulation once this becomes possible. Hence, quite surprisingly, simple majority voting is not necessarily the optimal choice of a society that is concerned about agenda manipulation.

We present a model that is closely related to the so-called models of choice under complete uncertainty, in which the agent has no information about the probability of the outcomes. There are two approaches within the said models: the state space-based approach, which takes into account the possible states of nature and the correspondence between states and outcomes; and the set-based approach, which ignores such information, and solves certain diculties arising from the state space-based approach. Kelsey [?] incorporates into a state space-based framework the assumption that the agent has ordinal information about the likelihood of the states. This paper incorporates this same assumption into a set-based framework, thus lling a theoretical gap in the literature. Compared to the set-based models of choice under complete uncertainty we introduce the information about the ordinal likelihood of the outcomes while, compared to Kelsey's approach, we incorporate the advantages of describing uncertainty environments from the set-based perspective. We present an axiomatic study that includes adaptations of some of the axioms found in the related literature and we characterize some rules featuring different combinations of information about the ordinal likelihood of the outcomes and information about their desirability.

Many salient rules to allocate private goods are not only strategyproof, but also group strategy-proof, in appropriate domains of definition, hence diminishing the traditional conflict between incentives and efficiency. That is so for solutions to matching, division, cost sharing, house allocation, and auctions, in spite of the substantive disparity between these cases. In a general framework encompassing all of them, we prove that the equivalence between the two forms of strategy-proofness is due to an underlying common structure that transcends the many differences between the contexts and the mechanisms for which it holds. (JEL C78, D44, D63, D71, D82).

The rule of k names can be described as follows: given a set of candidates for office, a committee chooses k members from this set by voting, and makes a list with their names. Then a single individual from outside the committee selects one of the listed names for the office. Different variants of this method have been used since the distant past and are still used today in many countries and for different types of choices. After documenting this widespread use by means of actual examples, we provide a game theoretical analysis. We concentrate on the plausible outcomes induced by the rule of k names when the agents involved act strategically. Our analysis shows how the parameter k, the screening rule and the nature of candidacies act as a means to balance the power of the committee with that of the chooser.

When members of a voting body exhibit single peaked preferences, pair-wise majority voting equilibria (Condorcet winners) always exist. Moreover, they coincide with the median(s) of the voters' most preferred alternatives. This important fact is known as the median voter result. Variants of it also apply when single-peakedness fails, but preferences verify other domain restrictions, such as single-crossing, intermediateness or order restriction. Austen-Smith and Banks (1999) also proved that the result holds under single-peakedness, for a wide class of voting rules that includes the majority rule as a special case, and conveniently redefined versions of a median. We extend and unify previous results. We propose a new domain condition, called top monotonicity, which encompasses all previous domains restrictions, allows for new ones and preserves a version of the median voter result for a large class of voting rules. We also show that top monotonicity arises in interesting economic environments.

We characterize the set of all individual and group strategy-proof rules on the domain of all single-dipped preferences on a line. For rules defined on this domain, and on several of its subdomains, we explore the implications of these strategy-proofness requirements on the maximum size of the rules' range. We show that when all single-dipped preferences are admissible, the range must contain two alternatives at most. But this bound changes as we consider different subclasses of single-dipped preferences: we provide examples of subdomains admitting strategy-proof rules with larger ranges. We establish exact bounds on the maximal size of strategy-proof functions on each of these domains, and prove that the relationship between the sizes of the subdomains and those of the ranges of strategy-proof functions on them need not be monotonic. Our results exhibit a sharp contrast between the structure of strategy-proof rules defined on subdomains of single-dipped preferences and those defined on subsets of single-peaked ones