What does the efficiency and cost-effectiveness of the public or private sector have to do with a centrally-planned economy?
Or, let me be charitable (because I think I know what you were getting at...) and instead put it to you this way:
Let's say government-financed or government-run health care is more efficient or more cost-effective than privately-run health care, because there's no privately-run insurance company that exists to extract a bit of dosh from every doctor-patient transaction.
(And safe money's on government-financed/run health care buying better health care for its citizens, dollar for dollar and measuring on a variety of health outcomes. I've seen a lot of arguments from theory that "more free markets, less regulation" would do as good a job, or better, but I haven't seen evidence of that, just arguments from theory.)
Does this mean that a country that adopts a single-payer or government-run health care system for its citizens has _also_ adopted a centrally planned--or in your words, "government-directed"--economy?