Gbeatty is right. According to the novel analysis here on eNotes, the time period for this is "probably in the late 1910s. The setting does not seem dated, however, because the characters and situations in Ginger Pye are, in large part, universal to childhood."

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A good question. You aren't every really told specifically, but from the level of the technology, you can assume it is early in the 20th century, say just before World War I.