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I've read several articles on the internet about famed hat designer William J (aka Bill Cunningham).
This hat (seen below) doesn't appear to be outlandish as others I've seen on the internet that were designed by Bill Cunningham, but the tag on this hat does say William J (though it doesn't match other tags I've seen from other Bill Cunningham designed hats).
From what I have come across, he had different labels for different time periods, or designs. The Typed WILLIAM J. New York label is the only one I have seen duplicated. In terms of the hat itself, he had a couple "low key" hats out there, so I would not be surprised. Like this one ON THE RIGHT :)
You've given me hope !
These hats certainly exhibit the style that I've read indicate they were made by William J.