"The reason is climate change."

The reason isn't climate change.

The Central African Republic has just come out of a civil war. Of course things are going to improve rapidly, because that farmer that was in a refugee camp can now go home and grow enough to barely feed his family.

You can't extrapolate that out to the CAR overtaking first world countries in a generation simply because that farmer hasn't been educated to do the jobs that the economy would require, neither probably will his children.

That's before getting into things like infrastructure, rule of law, etc, etc, etc.

Edit: To clarify, I don't disagree that climate change will probably hurt the poorest countries disproportionately though.