> However, once you have (mostly) caught up, it becomes less obvious what the next thing to do is.

Chinese economy is not about catching up with the west anymore. If you ever lived in China in recent years, you'd see that the Chinese economy is advancing in lots of aspects, and many of those in ways vastly different from western societies. The government plays an important part in it, but private companies are just as important. For example, the tech industry in China (which comprised of mostly private companies) evolved into its own ecosystem, and is iterating faster than that of silicon valley.