On the observational equivalence of random matching

Random matching is often used in economic models as a means of introducing uncertainty in sequential decision problems. We show that random matching processes that satisfy standard proportionality laws are not unique. We give conditions on the payoffs and transition functions of sequential decision models that insure that economic models are robust to the nonuniqueness of the matching process. Under these conditions, the information contained in the proportionality laws is all that is needed to know about the matching process to formulate the model.     

The labor wedge as a matching friction

We use a search and matching model to decompose the labor wedge into three classes of labor market frictions and evaluate their role for the labor wedge and unemployment. We find that there is an asymmetric effect of labor market frictions on the labor wedge and unemployment. While the wedge is to a large extent explained by changes in matching efficiency, unemployment is accounted for by the combination of frictions to matching efficiency, job destruction and bargaining. If search and matching frictions give rise to the labor wedge, then it is relevant for explaining unemployment mainly through changes in matching efficiency.     

数据交易市场双边匹配模型与决策方法研究

针对平台视角下的数据交易供需双边匹配问题,基于双边匹配理论,提出了考虑模糊语言评价信息、区间数评价信息和0-1评价信息的混合型多属性匹配决策方法并定义了属性匹配满意度函数。以供需主体最大匹配满意度为目标,构建了数据交易供需双边匹配的多目标优化模型,并设计模型求解算法,将多目标化模型转化为单目标线性规划模型进行求解,以获取匹配结果。结果表明,通过对供需双方需求信息的详细分析,双边匹配结果能在最大程度上满足双方需求,同时,优化模型具有合理性及有效性。     

The exact law of large numbers for independent random matching

This paper provides a mathematical foundation for independent random matching of a large population, as widely used in the economics literature. We consider both static and dynamic systems with random mutation, partial matching arising from search, and type changes induced by matching. Under independence assumptions at each randomization step, we show that there is an almost-sure constant cross-sectional distribution of types in a large population, and moreover that the multi-period cross-sectional distribution of types is deterministic and evolves according to the transition matrices of the type process of a given agent. We also show the existence of a joint agent-probability space, and randomized mutation, partial matching and match-induced type-changing functions that satisfy appropriate independence conditions, where the agent space is an extension of the classical Lebesgue unit interval.     

Matching with preferences over colleagues solves classical matching

In this note, we demonstrate that the problem of “many-to-one matching with (strict) preferences over colleagues” is actually more difficult than the classical many-to-one matching problem, “matching without preferences over colleagues.” We give an explicit reduction of any problem of the latter type to a problem of the former type. This construction leads to the first algorithm which finds all stable matchings in the setting of “matching without preferences over colleagues,” for any set of preferences. Our construction directly extends to generalized matching settings.     

Global public goods and coalition formation under matching mechanisms

This paper links coalition theory with matching mechanisms in the presence of global public goods among heterogeneous players. This matching coalition may achieve Pareto‐improving outcomes while avoiding side payments. The paper characterizes conditions of coalition profitability and stability at both interior and corner equilibria. It is generally much harder to satisfy stability conditions than profitability conditions. A matching coalition is more profitable but less stable with a larger matching rate. Empirically there is no stable coalition but this can be overcome by introducing reputation mechanisms. There always exists a stable grand matching coalition if players value their reputation. The matching coalition faces a trade‐off between matching depth and breadth.     

旅游区域的城市与景区空间匹配及其实践意义

城市和景区是区域旅游网络中两个基本节点,它们之间关系紧密,包含多种空间匹配关系。数量关系上由一对一匹配、一对多匹配、多对一匹配、多对多匹配构成;等级关系上由正位匹配和倒位匹配构成;距离关系上由城区城郊型、一日游型、离散型构成;几何分布关系上由点轴匹配和面状匹配构成;管理匹配关系上由同位管理匹配和异位管理匹配构成。分析城市与景区空间匹配组合特征,对于寻找合理的景区依托城镇、采取正确的区域旅游发展战略等都具有重要的实践意义。     

Bilateral Search and Vertical Heterogeneity

Just like perfect (frictionless) matching models, a search model is proposed that is characterized by bilateral search and vertical heterogeneity. It allows for a generally specified utility function. The equilibrium allocation is unique and exists in iterated strict dominance. The model is robust with the perfect matching model as frictions disappear. Nonetheless, the equilibrium allocations are surprisingly odd. For multiplicatively separable preferences, the distributions are partitioned endogenously. And for a wide range of preferences, matching sets are naturally disconnected.     

AN EXAMPLE OF THE USE OF STATISTICAL MATCHING IN THE ESTIMATION AND ANALYSIS OF THE SIZE DISTRIBUTION OF INCOME*

This paper focuses on the use of statistical matching in the estimation and analysis of the size distribution of family unit personal income. The paper begins with a brief discussion of data on the size distribution of income in the U.S. and their limitations. Several methods of improving or augmenting those data are described, and earlier examples of statistical matching for that purpose are mentioned. A brief summary of the types of statistical matching methods which have been used is also presented. Then a recent example of statistical matching carried out at the Office of Research and Statistics, Social Security Administration, is described, and the effects on the size distribution of adjusting and augmenting the initial data using the statistically matched data from that example are shown. Material relating to the accuracy of that statistical match is presented in the appendix.     

能力柔性与知识管理战略匹配对竞争优势的影响

能力柔性与知识管理战略相互影响形成匹配，对企业战略选择而言，匹配模式及其对竞争优势的影响至关重要。基于匹配及战略管理理论，构建知识管理战略与能力柔性匹配模式，运用独立样本T检验探究匹配对竞争优势的影响。研究发现，能力柔性与知识管理战略存在两种一致性匹配模式，即高能力柔性与积极知识管理战略匹配、低能力柔性与保守知识管理战略匹配。匹配对竞争优势产生积极影响，即高能力柔性与积极知识管理战略匹配能够增强企业灵活性、提升顾客优势、增强创新优势，而低能力柔性与保守知识管理战略匹配更有利于提升顾客优势及创新优势。     

Coarse matching with incomplete information

We study two-sided markets with heterogeneous, privately informed agents who gain from being matched with better partners from the other side. Our main results quantify the relative attractiveness of a coarse matching scheme consisting of two classes of agents on each side, in terms of matching surplus (output), an intermediary’s revenue, and the agents’ welfare (defined as the total surplus minus payments to the intermediary). Following Chao and Wilson (Am Econ Rev 77: 899–916, 1987) and McAfee (Econometrica 70:2025–2034, 2002), our philosophy is that, if the worst-case scenario under coarse matching is not too bad relative to what is achievable by more complex, finer schemes, a coarse matching scheme will turn out to be preferable once the various transaction costs associated with fine schemes are taken into account. Similarly, coarse matching schemes can be significantly better than random matching, while still requiring only a minimal amount of information.     

Participation constraints of matching mechanisms

Matching mechanisms have been proposed to improve public good provision in voluntary contributions. However, such decentralized subsidizing mechanisms may not be Pareto‐improving and may suffer from incomplete information and incredible commitment. This paper examines participation constraints of matching mechanisms with small matching rates in two cases of equilibria. At interior equilibria, there always exist small Pareto‐improving matching schemes regardless of preferences. This universal existence is useful for cooperation among heterogeneous players in the context without global information of preferences or at the international level without central governments. At corner equilibria, matching schemes work in different ways and have distinct welfare effects in certain cases, and the existence of Pareto‐improving matching schemes is not universal but is possible under certain conditions. The paper further characterizes Pareto‐improving matching schemes, and shows that it is easier to reach Pareto‐improving matching outcomes if players value more on public goods and have stronger substitution between private and public goods.     

Matching and anonymity

This work introduces a set-theoretic foundation of deterministic bilateral matching processes and studies their properties. In particular, it formalizes a link between matching and informational constraints by developing a notion of anonymity that is based on the agents’ matching histories. It also explains why and how various matching processes generate different degrees of “informational isolation” in the economy. We illustrate the usefulness of our approach to modeling matching frameworks by discussing the classical turnpike model of Townsend.This research is supported in part by the NSF grants EIA-0075506, SES-0128039, DMS-0437210, and ACI-0325846. We thank two anonymous referees for constructive comments that improved the exposition of the paper. We also thank the participants in seminars at the University of Aarhus, Purdue University, University of Texas at Austin, and at the XI Meeting on Real Analysis and Measure Theory in 2004, the spring 2004 Midwest Economic Theory Meeting, the summer 2004 North American and European Econometric Society meetings.     

Wage-Tenure Contracts in a Frictional Labour Market: Firms' Strategies for Recruitment and Retention

A common assumption in equilibrium search and matching models of the labour market is that each firm posts a wage, to be paid to any worker hired. This paper considers the implications of firms posting contracts , in a random matching model with on-the-job search. More complex contracts enable firms to address both recruitment and retention problems by, for example, increasing the wage with tenure. The effect on the labour market is to reduce turnover, below the level required for efficient matching of workers to firms.     

Accounting for endogeneity in matching function estimation

We show that equilibrium matching models imply that standard estimates of the matching function elasticities are exposed to an endogeneity bias, which arises from the search behavior of agents on either side of the market. We offer an estimation method which, under certain structural assumptions about the process driving shocks to matching efficiency, is immune from that bias. Application of our method to the estimation of a basic version of the matching function using aggregate U.S. data from the Job Openings and Labor Turnover Survey (JOLTS) suggests that the bias can be quantitatively important.     

On the existence of a strictly strong Nash equilibrium under the student-optimal deferred acceptance algorithm

This study analyzes a preference revelation game in the student-optimal deferred acceptance algorithm in a college admission problem. We assume that each college's true preferences are known publicly, and analyze the strategic behavior of students. We demonstrate the existence of a strictly strong Nash equilibrium in the preference revelation game through a simple algorithm that finds it. Specifically, (i) the equilibrium outcome from our algorithm is the same matching as in the efficiency-adjusted deferred acceptance algorithm and (ii) in a one-to-one matching market, it coincides with the student-optimal von Neumann–Morgenstern (vNM) stable matching. We also show that (i) when a strict core allocation in a housing market derived from a college admission market exists, it can be supported by a strictly strong Nash equilibrium, and (ii) there exists a strictly strong Nash equilibrium under the college-optimal deferred acceptance algorithm if and only if the student-optimal stable matching is Pareto-efficient for students.     

Equilibria under deferred acceptance: Dropping strategies,filled positions,and welfare

We study many-to-one matching markets where hospitals have responsive preferences over students. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling.Roth and Sotomayor (1990) showed that equilibrium outcomes can be unstable. We prove that any stable matching is obtained in some equilibrium. We also show that the exhaustive class of dropping strategies does not necessarily generate the full set of equilibrium outcomes. Finally, we find that the ‘rural hospital theorem’ cannot be extended to the set of equilibrium outcomes and that welfare levels are in general unrelated to the set of stable matchings. Two important consequences are that, contrary to one-to-one matching markets, (a) filled positions depend on the equilibrium that is reached and (b) welfare levels are not bounded by the optimal stable matchings (with respect to the true preferences).     

Assigning Refugees to Landlords in Sweden: Efficient,Stable, and Maximum Matchings*

In this paper, we investigate the problem of finding housing for refugees once they have been granted asylum. In particular, we demonstrate that market design can play an important role in a partial solution to the problem. More specifically, we investigate a specific matching system, and we propose an easy-to-implement mechanism that finds an efficient, stable, and maximum matching. Such a matching guarantees that housing is efficiently provided to a maximum number of refugees, and that no refugee prefers another specific landlord to their current match when, at the same time, that specific landlord prefers that refugee to their own current match.     

Global public goods and unilateral matching mechanisms

While conventional agreements on international public goods require bilateral or multilateral cooperation, we show that unilateral action through matching mechanisms with a self‐commitment device can possibly generate Pareto‐improving outcomes. Even without commitment, unilateral matching may also benefit both players at corner situations. We further characterize the conditions under which this desirable outcome is achieved, particularly highlighting the role of the income distribution and its interplay with the preferences. Moreover, we propose a variant of unilateral matching that can generate Pareto‐improving outcomes regardless of the preferences and the income distribution, indicating that income inequality may not be an obstacle for improving public good provision through unilateral matching.     

Employer matching and 401(k) saving: Evidence from the health and retirement study

Employer matching of employee 401(k) contributions is often touted as a powerful incentive to save for retirement and is a key component in pension-plan design in the United States. Using detailed administrative contribution, earnings, and pension-plan data from the Health and Retirement Study, this analysis formulates a life-cycle-consistent econometric specification of 401(k) saving and estimates the determinants of saving accounting for non-linearities in the household budget set induced by matching. The participation estimates indicate that an increase in the match rate by 25 cents per dollar of employee contribution raises 401(k) participation by 5 percentage points. The parametric and semi-parametric estimates for saving indicate that an increase in the match rate by 25 cents per dollar of employee contribution raises 401(k) saving by $365 (in 1991 dollars). Overall, the analysis reveals that the 401(k) saving response to matching is quite inelastic, and, hence, matching is a rather poor policy instrument with which to raise retirement saving.