In college I had an econ friend who said that there's basically only three ways to grow an economy: more workers, better technology or more capital.

If you look at technology, then I think "yes!" it has improved the economy. Look at engines and trains and telecommunications. The first world economy today, per person, is rip-roarin' compared to 100 years ago.

Many western economies haven't noticed the decline in the birth rate yet because of so many immigrants. Japan is unique in that they are a modern country, with a declining birth rate, but very low immigration.