We develop an alternative theory to the aggregate matching function in which workers search for jobs through a network of firms: the labor flow network. The lack of an edge between two companies indicates the impossibility of labor flows between them due to high frictions. In equilibrium, firms' hiring behavior correlates through the network, generating highly disaggregated local unemployment. Hence, aggregation depends on the topology of the network in non-trivial ways. This theory provides new micro-foundations for the Beveridge curve, wage dispersion, and the employer-size premium. We apply our model to employer-employee matched records and find that network topologies with Pareto-distributed connections cause disproportionately large changes on aggregate unemployment under high labor supply elasticity.
Whether it is for the whole economy or for submarkets, there are a number of problems that arise from viewing matching in aggregate terms, and here we mention a few. First, when an AMF is responsible of pairing up workers and vacancies, it is assumed that all matches are equally likely. This neglects the importance that specific firms have in reallocating labor within a submarket. Second, defining a submarket is an arbitrary choice that might be well suited for a specific problem, but not necessarily for a broader context. Since these classifications are usually built for taxonomic purposes, they are not designed to minimize inter-submarket flows and maximize intra-submarket, which would capture the structural information of labor market frictions. This problem has been pointed out by @cite_17 in their classical paper on structural unemployment:
@cite_17
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A number of labor markets and student placement systems can be modeled as many-to-one matching markets. We analyze the scope for manipulation in many-to-one matching markets under the student-optimal stable mechanism when the number of participants is large. Under some regularity conditions, we show that the fraction of participants with incentives to misrepresent their preferences when others are truthful approaches zero as the market becomes large. With an additional condition, truthful reporting by every participant is an approximate equilibrium under the student-optimal stable mechanism in large markets. (JEL C78) We analyze a decentralized trading process in a basic labor market where heterogeneous firms and workers meet directly and randomly, and negotiate salaries with each other over time. Firms and workers may not have a complete picture of the entire market and can thus behave myopically in the process. Our main result establishes that, starting from an arbitrary initial market state, there exists a finite sequence of successive myopic (firm-worker) pair improvements, or bilateral trades, leading to a stable matching between firms and workers with a scheme of competitive salary offers. An important implication of this result is that a general random process where every possible bilateral trade is chosen with a positive probability converges with probability one to a competitive equilibrium of the market. We study a labor market with finitely many heterogeneous workers and firms to illustrate the decentralized (myopic) blocking dynamics in two-sided one-to-one matching markets with continuous side payments (assignment problems, Shapley and Shubik, 1971). A labor market is unstable if there is at least one blocking pair, that is, a worker and a firm who would prefer to be matched to each other in order to obtain higher payoffs than the payoffs they obtain by being matched to their current partners. A blocking path is a sequence of outcomes (specifying matchings and payoffs) such that each outcome is obtained from the previous one by satisfying a blocking pair (i.e., by matching the two blocking agents and assigning new payoffs to them that are higher than the ones they received before). We are interested in the question if starting from any (unstable) outcome, there always exists a blocking path that will lead to a stable outcome. In contrast to discrete versions of the model (i.e., for marriage markets, one-to-one matching, or discretized assignment problems), the existence of blocking paths to stability cannot always be guaranteed. We identify a necessary and sufficient condition for an assignment problem (the existence of a stable outcome such that all matched agents receive positive payoffs) to guarantee the existence of paths to stability and show how to construct such a path whenever this is possible. We report on the design of the new clearinghouse adopted by the National Resident Matching Program, which annually fills approximately 20,000 jobs for new physicians in the United States. Because that market exhibits many complementarities between applicants and between positions, the theory of simple matching markets does not apply directly. However, computational experiments reveal that the theory provides a good approximation, and furthermore the set of stable matchings, and the opportunities for strategic manipulation, are surprisingly small. A new kind of core convergence' result is presented to explain this; the fact that each applicant can interview for only a small fraction of available positions is important. We also describe in detail engineering aspects of the design process.