2. But, it wasn't just "an accident of history." Those resources were worthless until we applied ingenuity, sweat and freedom. The Indians had the same resources, and didn't do much with them.
3. I think most economists would say that we had caught up with the "advanced european economies" by the 1880s, if not the 1850s.
4. You can have an export based economy, even if you are very rich, if you have a great comparative advantage,either in making something, or having some resource that is peculiar to your location (oil in the middle east, hydro power in Norway, etc).
2. I describe the settlement of this nation as an "accident of history" because it was so unusual at the time. Because the U.S. was able to clear the land of its existing occupants at a relatively low cost (in essence, we simply took the land away from people who didn't understand our Western notion of "ownership"), we were effectively able to "start from scratch" in a manner that no other country in the developed world could possibly have done (particularly with regard to land titles).
3. I guess that is largely a function of how you define "catching up." I think it is safe to say that the U.S. caught up to Europe in terms of technological and industrial development by the period you described, but the average American had a lower standard of living than the average resident of the countries I identified well into the 20th century. In fact, the U.S. was still looked upon as an agrarian nation almost until the time of World War II.
4. How often does this kind of thing occur in the world today? I would even make the case that "peculiar" resource wealth may not be such a good thing, because the focus of a nation's economy is turned to the possession and protection of that resource (hence the constant civil wars in resource-rich countries in sub-Saharan Africa). Ironically, some of the countries in this world with the highest standards of living are those with no resource wealth at all (Japan and Singapore are good examples of this). This is because they are effectively forced into a position of high efficiency -- because the only real source of revenue their governments have is the taxation of their labor.
One important point. In contrast with the Latin America (where top families own the most) the land taken from Indians was GIVEN FOR FREE to the all citizens in order to create the independent middle class. Freed blacks on the other hand did not get their "mule and forty acres" - results show until today.