An economic audit in crypto is a type of check that is conducted by an external organization to validate the economic claims made by a crypto currency. It typically involves mathematically verifying the economic claims made by the project.
An example of an economic audit is the economic audit that was carried out by Coinfabrik on HEX, an ERC-20 token that replicates bank term deposits in the crypto space. The essential claim of HEX was that by staking longer and larger users of the system would get higher returns. The economic audit proved this mathematically.