Does the Chinese government take a strong role in today's Chinese economy?
Yes, the Chinese government does take a strong role in today's Chinese economy, often to the consternation of the United States. In the recent past, President Barack Obama's team has accused the Chinese government of manipulating the Chinese currency. This currency is called the yuan.
The Chinese government doesn't control all aspects of their economy. However, their influence is extensive. There is give and take in the Chinese economy. Top business leaders often secure top government economic positions. Some government officials end up in business in leadership positions.
Another way that some believe the Chinese government controls their national economy is the fact that they own a significant portion of it. They own a great deal of the companies in the major sectors of their economy. Many of these sectors are of substantial strategic importance. One sector is Rare Earth Elements (REEs), which China has a world monopoly on.
Some people believe that China represents a frightening marriage of capitalism and communism. They believe there is no oversight. They believe a very small group of people in the Chinese government are making significant and vital economic decisions and there's no one to oversee this - in effect, they have free rein to control the Chinese economy. These people desire a public forum for discussion so the government cannot just impose their will on the economy without input from other stakeholders.