[영문]It is generally believed that chaining reduces the Paasche?Laspeyres spread if prices and quantities are monotonic over time. I consider three alternative definitions of monotonicity and show that none provide either necessary or sufficient conditions for chaining to reduce the Paasche?Laspeyres spread. What matters is the interaction between prices and quantities both in the same period and lagged one period. Sufficient conditions are derived, and the implications of these conditions for the measurement of inflation are considered. The paper concludes with an empirical illustration using scanner data.