Monotonicity and Nash implementation in matching markets with contracts

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (2005) and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable (Theorems 1 and 3). Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence (Theorem 2). In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.matching with contracts, (Maskin) monotonicity, Nash implementation, stability.

Contracts versus Salaries in Matching

Firms and workers may sign complex contracts that govern many aspects of their interactions. I show that when firms regard contracts as substitutes, bargaining over contracts can be understood as bargaining only over wages. Substitutes is the assumption commonly used to guarantee the existence of stable matchings of workers and firms

Inside the Black Box: Partnerships in Rio de Janeiro, 1870-1891

We use newly-constructed individual-level data on partnership contracts in late nineteenth century Rio de Janeiro to examine differences between limited and unlimited liability firms and partners, and to assess the impact of a major institutional reform that facilitated the formation of joint stock companies on the terms of partnership contracts. Contrary to expectation, we find that most unlimited partners contributed capital and received profit shares, and most non-managing limited partners received salaries. Limited partners contributed more capital and received lower salaries and profit shares than their unlimited partners; unlimited partners in limited firms received more favorable terms than those in unlimited firms. Finally, we find suggestive evidence that the reforms reduced the extent of income smoothing for the limited partner and increased the average quality of unlimited liability partners in limited liability firms. These findings highlight the role of incentives and the desire for income smoothing in shaping contract terms.Partnerships, Brazil

Self-Promoting Investments

When human capital skills differ in their ability to attract offers from alternative employers, a potential inefficiency in human capital investment arises. If a worker's ability and investments are observed by the labour market only when the worker invests in self-promoting activities, then high-ability workers overinvest in self-promotion. No bond is posted in the contract that both attains efficient investment and minimizes the bond subject to individual rationality constraints and the zero profit condition. The contract is one in which the firm (i) offers to match outside offers strategically and (ii) guarantees a minimum wage. The model predicts that, under both the spot market contract and the efficient contract, wage declines with seniority even when conditioning on high ability. This prediction is consistent with the stylized fact regarding the decline of wages with seniority in academia. The model can also explain how the seniority wage premium may vary across disciplines, time, and schools.microeconomic theory, negative seniority wage premium, spot market contract, efficient contract, general human capital, multi-tasking

Self-Promoting Investments

When human capital skills differ in their ability to attract offers from alternative employers, a potential inefficiency in human capital investment arises. If a worker's output is observed by the labour market only when the worker invests in self-promoting activities, then high-ability workers overinvest in self-promotion. No bond is posted in the contract that both attains efficient investment and minimizes the bond subject to individual rationality constraints and the zero profit condition. The contract is one in which the firm (i) offers to match outside offers strategically and (ii) guarantees a minimum wage. The model predicts that, under both the spot market contract and the efficient contract, wage declines with seniority even when conditioning on high ability. This prediction is consistent with the stylized fact regarding the decline of wages with seniority in academia. The model can also explain how the seniority wage premium may vary across disciplines, time, and schools.negative seniority wage premium, spot market contract, efficient contract, general human capital

A Call to Action: Reconnecting College Sports and Higher Education

Revisits the findings of a series of reports on the state of college athletics and evaluates progress made in the intervening ten years, finding that the NCAA has moved a long way toward achieving the goals laid out in the commission's earlier reports

Employment conditions in the scottish social care voluntary sector : impact of public funding constraints in the context of economic recession

This report uses data to assess the impact of public funding constraints on employment conditions in the Scottish social care voluntary sector, in the context of the recent economic recessionand future public expenditure cuts

The Financial and Professional Impact of Anterior Cruciate Ligament Injuries in National Football League Athletes.

BACKGROUND: Anterior cruciate ligament (ACL) injuries can have negative consequences on the careers of National Football League (NFL) players, however no study has ever analyzed the financial impact of these injuries in this population. PURPOSE: To quantify the impact of ACL injuries on salary and career length in NFL athletes. STUDY DESIGN: Cohort study; Level of evidence, 3. METHODS: Any player in the NFL suffering an ACL injury from 2010 to 2013 was identified using a comprehensive online search. A database of NFL player salaries was used to conduct a matched cohort analysis comparing ACL-injured players with the rest of the NFL. The main outcomes were the percentage of players remaining in the NFL and mean salary at 1, 2, 3, and 4 years after injury. Cohorts were subdivided based on initial salary: group A,$2,000,000. Mean cumulative earnings were calculated by multiplying the percentage of players remaining in the league by their mean salaries and compounding this each season. RESULTS: NFL athletes suffered 219 ACL injuries from 2010 to 2013. The 7504 other player seasons in the NFL during this time were used as controls. Significantly fewer ACL-injured players than controls remained in the NFL at each time point (P \u3c .05). In group A, significantly less ACL-injured players remained in the NFL at 1 to 3 seasons after injury (P \u3c .05), and in group B, significantly less ACL-injured players remained in the NFL at 1 and 2 seasons after injury (P \u3c .05). There was no significant decrease in group C. Players in groups A and B remaining in the NFL also had a lower mean salary than controls (P \u3c .05 in season 1). The mean cumulative earnings over 4 years for ACL-injured players was$2,070,521 less per player than uninjured controls. CONCLUSION: On average, ACL-injured players earned $2,070,521 less than salary-matched controls over the 4 years after injury. Players initially earning less than$2 million per year have lower mean salaries and are less likely to remain in the league than uninjured controls. The careers of players initially earning over $2 million per year, meanwhile, are not negatively affected. This demonstrates the degree of negative impact these injuries have on the careers of NFL players. It also indicates that a player\u27s standing within the league before injury strongly influences how much an ACL injury will affect his career

Concave many-to-one matching

We propose a notion of concavity in two-sided many-to-one matching, which is an analogue to the balancedness condition in cooperative games. A stable matching exists when the market is concave. We provide a class of concave markets. In the proof of the existence theorem, we use Scarf's algorithm to find a stable schedule matching, which is of independent interest