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I want to calculate market concentration (HHI and C4) but I don't have sales data. Is it accurate to use the share of establishments of each firm as a proxy for market power?

Could you list some references that use this or a similar method?

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Why not using the number of workers? And simply replacing sales (or output) by workers in the HHI or C4 indices. I saw this in the literature, but where? May be in a report of the German "Monopolkomission"...

EDIT: I found an example for France. The share $C_{10}$ of the production of the 10 biggest firms is very correlated with their share in total employment (at the sectoral level). The correlation coefficient is about 0.96. Note, however, that their production share often tend to be higher than their employment share, maybe due to increasing returns to scale.
Source: Insee, GR2 – Concentration des groupes : part des 4 ou 10 premiers groupes (NES 114 postes)
https://www.insee.fr/fr/statistiques/2381764?sommaire=2381775&q=concentration

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