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I'm currently reading up on matching models in terms of their ability to describe frictional unemployment, they generally follow a cobb-douglas form.

$$M(u,v)=m=\mu u^\alpha v^{1-\alpha}$$

Where $M(u,v)$ or $m$ is the number of employed, $u$ is the number of unemployed, $v$ is the number of job vacancies, $\mu$ is a constant and $0<\alpha<1$.

moving around the formula we obtain vacancy rate.

$$v=\left(\frac{m}{\mu u^\alpha}\right)^{\frac{1}{1-\alpha}}$$

Economterically estimating job vacancy would seem to be much more difficult for countries which do not have a history of report it.This is mainly due to omitted variable bais, which would skew our estimates for $\alpha$.

How does one estimate job vacancy in countries that only report employment and unemployment?

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