Urn-Ball Matching Function with Elastic Search Effort

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In Simple Words

Picture job seekers as throwing balls randomly into a set of urns representing job openings. If multiple workers throw their balls into the exact same urn, only one gets hired, while the extra balls represent wasted effort (congestion). At the same time, urns that receive no balls remain empty vacancies. Increasing the number of balls thrown per worker increases overall hits, but at a diminishing rate due to higher collision odds.

Research question

Standard Cobb-Douglas matching functions assume constant returns to scale and smooth substitution, which fails to capture discrete coordination failure and congestion when job seekers independently direct search effort toward an endogenous pool of firm vacancies.

Participants

Theoretical framework fitted via Indirect Inference onto Danish experimental data of N = 40,403 unemployed workers across 14 county markets.

Study Design

Structural equilibrium matching model explicitly integrating non-linear contact probabilities, elastic worker search effort costs, and firm entry costs.

Results

The urn-ball functional form micro-founds crowding-out externalities, yielding structural elasticity estimates where increased search intensity of treated workers directly depresses the contact rate per unit of search effort for non-treated workers.

Takeaway

Utilize micro-founded matching functions with variable coordination frictions rather than aggregate Cobb-Douglas forms when predicting labor policy effects across regional markets.

Source and citation

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