<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:

def _set_id_variable_by_entity_key(self) -> Dict[str, str]:
        '''Identify and set the good ids for the different entities'''
        if self.id_variable_by_entity_key is None:
            self.id_variable_by_entity_key = dict(
                (entity.key, entity.key + '_id') for entity in self.tax_benefit_system.entities)
            log.debug("Use default id_variable names:\n  {}".format(self.id_variable_by_entity_key))

        return self.id_variable_by_entity_key