Urn-Ball Matching Function with Elastic Search Effort
Expert TheoryReview
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.
Picture this
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.
What the evidence says
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.
- Who was studied
- Theoretical framework fitted via Indirect Inference onto Danish experimental data of N = 40,403 unemployed workers across 14 county markets.
- How
- Structural equilibrium matching model explicitly integrating non-linear contact probabilities, elastic worker search effort costs, and firm entry costs.
What to do
Utilize micro-founded matching functions with variable coordination frictions rather than aggregate Cobb-Douglas forms when predicting labor policy effects across regional markets.
From the source
"We model the matching process between workers and vacancies using an urn-ball matching function... this matching function microfounds the presence of congestion externalities among searchers."
816b5187-9076-4043-aba7-184043b2e524-Estimating Equilibrium Effects of Job Search Assistance.pdf