Unbalanced Random Matching Markets with Partial Preferences

Properties of stable matchings in the popular random-matching-market model have been studied for over 50 years. In a random matching market, each agent has complete preferences drawn uniformly and independently at random. Wilson (1972), Knuth (1976) and Pittel (1989) proved that in balanced random matching markets, the proposers are matched to their $\ln n$th choice on average. In this paper, we consider markets where agents have partial (truncated) preferences, that is, the proposers only rank their top $d$ partners. Despite the long history of the problem, the following fundamental question remained unanswered: \emph{what is the smallest value of $d$ that results in a perfect stable matching with high probability?} In this paper, we answer this question exactly -- we prove that a degree of $\ln^2 n$ is necessary and sufficient. That is, we show that if $d < (1-\epsilon) \ln^2 n$ then no stable matching is perfect and if $d > (1+ \epsilon) \ln^2 n$, then every stable matching is perfect with high probability. This settles a recent conjecture by Kanoria, Min and Qian (2021). We generalize this threshold for unbalanced markets: we consider a matching market with $n$ agents on the shorter side and $n(\alpha+1)$ agents on the longer side. We show that for markets with $\alpha =o(1)$, the sharp threshold characterizing the existence of perfect stable matching occurs when $d$ is $\ln n \cdot \ln \left(\frac{1 + \alpha}{\alpha + (1/n(\alpha+1))} \right)$. Finally, we extend the line of work studying the effect of imbalance on the expected rank of the proposers (termed the ``stark effect of competition''). We establish the regime in unbalanced markets that forces this stark effect to take shape in markets with partial preferences

An Approximate "Law of One Price" in Random Assignment Games

Assignment games represent a tractable yet versatile model of two-sided markets with transfers. We study the likely properties of the core of randomly generated assignment games. If the joint productivities of every firm and worker are i.i.d bounded random variables, then with high probability all workers are paid roughly equal wages, and all firms make similar profits. This implies that core allocations vary significantly in balanced markets, but that there is core convergence in even slightly unbalanced markets. For the benchmark case of uniform distribution, we provide a tight bound for the workers' share of the surplus under the firm-optimal core allocation. We present simulation results suggesting that the phenomena analyzed appear even in medium-sized markets. Finally, we briefly discuss the effects of unbounded distributions and the ways in which they may affect wage dispersion

The size of the core in assignment markets

Assignment markets involve matching with transfers, as in labor markets and housing markets. We consider a two-sided assignment market with agent types and stochastic structure similar to models used in empirical studies, and characterize the size of the core in such markets. Each agent has a randomly drawn productivity with respect to each type of agent on the other side. The value generated from a match between a pair of agents is the sum of the two productivity terms, each of which depends only on the type but not the identity of one of the agents, and a third deterministic term driven by the pair of types. We allow the number of agents to grow, keeping the number of agent types fixed. Let $n$ be the number of agents and $K$ be the number of types on the side of the market with more types. We find, under reasonable assumptions, that the relative variation in utility per agent over core outcomes is bounded as $O^*(1/n^{1/K})$, where polylogarithmic factors have been suppressed. Further, we show that this bound is tight in worst case. We also provide a tighter bound under more restrictive assumptions. Our results provide partial justification for the typical assumption of a unique core outcome in empirical studies

Resolving Conflicts by a Random Device

We examine conflict resolution via a random device. We model conflict as a two-agent rent-seeking contest for a fixed prize. Before conflict arises, both agents may agree to allocate the prize by coin flip to avoid the costs of conflict. In equilibrium, risk-neutral agents with relatively symmetric conflict capabilities agree to resolve the conflict by randomization. However, with sufficiently asymmetric capabilities, conflicts are unavoidable because the stronger agent prefers to fight. Laboratory experiments confirm that the availability of the random device partially eliminates conflicts when agents are relatively symmetric; however, the device also reduces conflict between substantially asymmetric agents.Beauty contest, conflict resolution, experiments

The collapse of a medical clearinghouse (and why such failures are rare)

The collapse of the clearinghouse for the entry-level gastroenterology labor market offers a unique opportunity to study how stable clearinghouses succeed and fail. To explore the reasons for the failure of the clearinghouse (and why failures of this kind of clearinghouse have been so rare), we conduct an experimental investigation of demand shocks of the kind that occurred in the gastroenterology market. We find that a reduction in demand for positions leads to the collapse of the match only when it is detectable by firms before being detected by workers (as in the unexpected shock that took place in 1996, which could be seen by firms in their reduced applicant pools). Simple demand and supply imbalances do not seem to interfere with the operation of the centralized match. Our results suggest an affirmative answer to the question posed by market participants about whether the clearinghouse could be successfully restarted, and that this would relieve some of the distress now reported in that market, by allowing it to operate later, at a more uniform time, and with more national scope.

Do Exports Raise Productivity? Plant-level Evidence from the Colombian Agri-food Industries

Using detailed plant-level manufacturing Census data from the Colombian Agri-food industries, we show that exports raise plant-level productivity by about 15 to 20 percent. However, the estimates reveal that efficiency in plants that become persistent exporters, i.e. plants that service foreign markets at least 30 percent of the time during our sample years 1981-1991, increases about 30 percent upon their entry into foreign markets, while productivity in plants that become only occasional exporters does not change at all. Hence, the positive impact of exports on productivity for is driven by the large positive impact on persistent exporters. To identify the effect of exports on plant-level productivity we employ the Levinsohn-Petrin (2003) measure of total factor productivity and a difference-in-differences propensity score matching estimator. The estimates reveal that productivity in plants that become persistent exporters, i.e. plants that service foreign markets at least 30 percent of the time during our sample years 1981-1991, rises about 30 percent upon their entry into foreign markets. Productivity in plants that become only occasional exporters, on the other hand, does not change. We perform a number of robustness checks, all of which confirm our baseline results.exports, productivity, difference-in-differences, propensity score matching, International Development, International Relations/Trade, Production Economics, Productivity Analysis, Q17, F12, Q12, O33,

Determinants of farm diversification and interaction with the CAP. An application to FADN of Marche region (Italy)

This work analyzes farm diversification activities in an Italian region (Marche). The study examines 387 farms from Farm Accountancy Data Network (FADN) over a six-year period (2000-2005), applying Discrete Choice Models to identify their business. Recognizing the driving forces of such diversification strategy can be useful to better design those agricultural policies explicitly aimed at promoting agricultural multifunctionality as well as social and environmental sustainability. The linkage between diversification choices and CAP payments is thus also investigated.Farm diversification, Discrete Choice Models, Multifunctionality, Agricultural and Food Policy, Farm Management,

International Trade and Productivity: Firm-Level Evidence from Ukraine

The paper empirically assesses microeconomic exporting-productivity nexus using the data for Ukrainian manufacturing firms for the years 2000-2005. The results of the estimation show that firms with higher total factor productivity (TFP) levels in the period prior to entry are much more likely to enter export markets. Also age, size and intangible assets of the firm have significant positive influence on the probability of exporting. In testing learning-by-exporting effect I employ propensity score matching to address issues of endogeneity and sample selection. When the estimation is done for the whole universe of firms in the dataset, the results go in line with common trends and suggest significant positive post-entry productivity effect for the firms that enter export markets for the first time (in the t, t+1 and t+2 periods). At the industry level the results confirm the presence of learning-by-exporting effect in some industries. However the effect is not universal and varies between different types of exporting firms.exports, TFP, control function, matching, sample selection, endogeneity