RDP 9810: The Distribution and Measurement of Inflation Equation (A2)

\begin{array}{l} S_{1} = \frac{\sum_{i = 1}^{n} w_{i}^{2} P_{i k_{1}}}{\sum_{i = 1}^{n} w_{i}^{1} P_{i k_{1}}} • \frac{\sum_{i = 1}^{n} w_{i}^{3} P_{i k_{2}}}{\sum_{i = 1}^{n} w_{i}^{2} P_{i k_{2}}} \\ S_{2} = \frac{\sum_{i = 1}^{n} w_{i}^{3} P_{i k_{2}}}{\sum_{i = 1}^{n} w_{i}^{2} P_{i k_{2}}} \\ S_{3} = 1, \\ S_{4} = \frac{\sum_{i = 1}^{n} w_{i}^{3} P_{i k_{3}}}{\sum_{i = 1}^{n} w_{i}^{4} P_{i k_{3}}} \end{array}