Tense: back-shifted version of present perfect or past?

Hi. Would you say the past perfect tense is correct for a backshifted-version tense for both the past tense and present perfect tense?

eg,

John says, "Joe went to school."

Reported speech:

John said that Joe had gone to school.

John says, "I think Joe has gone to school."

Reported speech:

John said that he thought Joe had gone to school.