In any case, though, do these graphs really show that voters reward presidents for results? Hardly. Almost all economists agree that the president has only a mild effect on the macroeconomy. Much of the credit and blame for economic performance should go to other political actors - the Fed, Congress, state governments, etc., and a lot is outside the control of any political actor.
As Achen and Bartels memorably wrote:
If jobs have been lost in a recession, something is wrong, but is that the president’s fault? If it is not, then voting on the basis of economic results may be no more rational than killing the pharaoh when the Nile does not flood, as some scholars believe occurred in ancient Egypt, or voting against Woodrow Wilson when sharks attack the Jersey shore, as we believe happened in 1916. [footnote omitted]
Hibbs' results do little to vindicate voter rationality. What they really show is that you don't have to live in ancient Egypt to mistake a mortal man for a God-King.