Batman's origins resemble those of The Shadow

Rating: Null/10 (26 June 2005)

Has anyone noticed how similar Batman has become to that other pulp-era crimefighter of book and radio fame, The Shadow? The Shadow's alter-ego was a millionaire who disappeared into the mysterious East for several years. He led a criminal life but was found and reformed by a master of mystical and martial arts. The Shadow then returns to his home city (in this case New York City) to use his skills to fight crime.
While there are some differences between the origins of these two characters, the similarity in the overall structure seems not coincidental.
I am not saying that this is bad (I always loved The Shadow). However, it does seem like an homage of sorts to the pulp-era (which also spawned Batman).