Thank you for the time you put into this query and for your answer. Interestingly enough, this same jar showed up on eBay this week and in addition to the ink stamp mark it has a gold foil label that reads:
A.A. Importing CO St. Louis, MO Made in Japan
A.A. Importing is still in business and after speaking with them I found out they had imported many ceramic pieces from Japan back in the 1960's and early 1970's that were based on or copies of old German and Bavarian powder and dresser jars. This is one of those copies.
The ink stamp on its base is the mark of the Japanese ceramic company (he believes the company's name was Nippon) that made the jar. However, the company is no longer in business, so I have no way of verifying this information nor does A.A. Importing have records that go back to the 1960's.
Mark solved, eh? And it was never intended as a cookie jar, afterall. At least we can now remove it from the unknown maker pages of all the cookie jar books and place it under MIJ.