So, each president is criticised and applauded for how the economy does during their term, and after it.
Each is also praised for what they've done to fix the country.
Really well written arguments as well. Anyway, all of these people are convinced that some president or the other had a really large role on helping or hurting the economy.
That's wrong. There are so many other factors that make such a claim incorrect. The most basic one is that the president is less powerful than Congress, so they have more power about laws than he does. They arguably also have a comparable amount of power in the executive, simply because the senate approves executive nominations. So, a president will likely do less to affect the economy during his term than his congress.
Secondly, the global market is so large, complex, and powerful that our economy can be hurt or helped dramatically in a short time by conditions completely outside America's and Americans' control. For instance, if China were to have a revolution, we would have severe economic problems since we would lose a source of cheap consumer goods. If somewhere in the middle east has a civil war about their religion or culture, and blows up our oil pipelines, then we suddenly lose a source of transportation and also many consumer goods and much of our electricity. If the euro goes up dramatically, the dollar will be hurt badly (i think). The president can't control these things, and in addition, there are many subtler changes than the ones I described above that can't even be understood very well and that are also outside the president's control.
Thirdly, people (Americans) are very complex. Modern science hasn't done much to improve people's morals or work ethics, in contrast to the immense progress in physical sciences. Whether this is because people are just more complex than other organisms and objects, or because they have souls, free will, or something like that, they can't be understood or manipulated very well. So, if most americans are lazy and incompetent, no amount of government intervention can save the problems that will be caused by their laziness and incompetence. For instance, let's say that everyone manufacturing cars in the U.S wastes 99% of the resources that go into their cars. The auto industry and also most people's daily lives (at least those who rely on cars) would be damaged seriously. The government can't do much to fix that, at least in the short term. A good economy relies on competent, motivated people and there is no effective social science that can create people like that.
Fourthly, the current state of the economy depends on things that happened five, ten and twenty years ago. A recession now doesn't necessarily implicate the current president in whatever happened. If political figures can be blamed for a current recession, we must remember that previous leaders are partly responsible as well.
The economy is very flexible and responds quickly and dynamically to events in America. For instance, the september 11th attacks destabilised the economy badly, and caused a recession. Yet some people blamed Bush for how bad the economy was during his first term.
Of course, we can still talk a little about presidents' affect on the economy. If a president does something that obviously has a specific and observed result, then it's clearly reasonable to say that he caused that result. However, we shouldn't blame presidents for everything that happens in the economy during their term, the way some of the partisan writers above have done.