Growth and stagnation happen at all income levels. There are low income countries, middle-income countries, and rich countries whose growths slow down and stop before they catch up with the world leader, often after a period of rapid growth. The non-convergence pattern is interesting and generally difficult to explain in the existing literature. This is because a country's growth is often considered as a process of efficiency improvement for this country, and its impact on other countries is either ignored or only considered positive. Therefore, many different theories are needed to explain stagnation at different levels: poverty trap, middle-income trap, Japanese syndrome, etc.. In this paper, I propose a theory in which growth also contains a process of creative destruction, which may negatively influence the outputs of some other countries. A multi-country growth model with vertical innovation is built to study the cross-country income distribution and its slow evolution. In this model, two types of technological progress drive growth: efficiency improvement and innovation with creative destruction. A relatively poor country can grow initially through efficiency improvement, however, after reaching certain income level, every step of growth requires obtaining the frontier technology of a more advanced product through innovation with creative destruction. Growth becomes harder because the incumbent country is also competing for the leading technology of this product. Creative destruction leads to a stable income distribution among middle- and high-income countries. Stagnation always occur, in one or another country. Poverty trap is also incorporated into this framework as a lack of innovation to improve efficiency. This theory also explains why capital flows to the rich countries, and why an advanced technology does not flow to the low-income countries or other rich countries. The externalities and potential inefficiencies of growth are discussed, and corresponding development strategies to correct them are suggested.
