If the movie was set any later than 1940 it seems like there would be references to World War II, and it looks like the years after WWII would be too far away, and there would be some post war references. That makes me lean toward thinking the movie was very late 30's or 1940, but no later. According to Wikipedia Jean Shepherd was born in 1921 and the story wasn't actually based on his life. If it had been the time should have been about 10 years earlier.