Which type of nerve injury causes an inability to extend the thumb in a hitchhiker's sign?

The hitchhike sign represents the extension of the thumb and it is used to identify two different conditions: radial nerve or posterior interosseous nerve palsy and diastrophic dwarfism.
If there is radial nerve lesion then weakness of brachioradialis and finger flexion occurs. If there is a posterior interosseous nerve lesion then weakness of finger extension occurs.