BEIJING—Chinese consumer inflation is rising at its fastest rate in nearly a decade. Economic growth, meantime, is at its lowest level in three decades.

That picture might look similar to stagflation, the toxic combination of stagnating growth and soaring prices that plagued the U.S. from 1970 to 1981. At that time, U.S. inflation neared 15% while the economy fell into recession and unemployment climbed sharply.

There...