We provide bounds on the parameters of matching functions such that the job-finding rate and the vacancy-filling rate are below 1. We do that in the context of the canonical search and matching model with a Pissarides-type free-entry condition. We find that the restrictions for a Cobb–Douglas matching function with increasing returns to scale are rather restrictive, involving an upper bound to future expected profits and the number of job searchers. In contrast, for functional forms with constant returns to scale (Cobb–Douglas, CES) the restrictions involve only parameters or an upper bound to the future expected profits. The paper also investigates when a job-finding rate (vacancy filling rate) below one can restrict the vacancy filling rate (job-finding rate) to be below and strictly bounded away from one. We provide the bounds implied by these “interior equilibria.”

中文翻译：

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匹配功能的不同功能形式的限制

我们为匹配函数的参数提供了界限，以使求职率和空缺填补率低于1。我们在具有Pissarides型自由进入条件的规范搜索和匹配模型的情况下做到了这一点。我们发现，随着规模收益的增加，对Cobb–Douglas匹配函数的限制相当严格，涉及到未来预期利润和求职者数量的上限。相反，对于具有固定规模收益的功能形式（Cobb–Douglas，CES），限制仅涉及参数或未来预期利润的上限。本文还研究了什么时候低于1的求职率（职位空缺率）可以限制职位空缺率（职位空缺率）在1以下并严格限制。