私有制 is a formal term, primarily used in written language and serious discussions.
Economic and Political Discourse: You will frequently encounter it in news articles, academic papers, and government reports discussing economic policy, legal reforms, and the structure of the Chinese economy. For example, a news report might analyze the “contribution of the private ownership economy” (私有制经济) to GDP.
Business and Finance: When comparing business models, analysts will distinguish between private enterprises (私营企业) operating under a 私有制 framework and state-owned enterprises (国有企业).
Historical Discussions: The term is essential when talking about the economic history of modern China, especially the transition from a planned economy to a market-based one.
Connotation: In modern, mainstream usage, the connotation is generally neutral to positive, as it's associated with efficiency, job creation, and economic dynamism. However, among those who hold a more orthodox socialist viewpoint, it can still carry negative connotations of inequality, exploitation, and capitalism.