Index Numbers and Time Series
What the exam tests
Index-number questions test simple and weighted price indices, especially Laspeyres, Paasche and Fisher, plus interpretation of base and current years. Time-series questions test the components of a series and trend estimation by moving averages or least squares.
Core rules
- A price index is (\frac{\sum p_1q}{\sum p_0q}\times100), with the choice of (q) distinguishing the methods.
- Laspeyres uses base-year quantities: (\frac{\sum p_1q_0}{\sum p_0q_0}\times100). Paasche uses current-year quantities: (\frac{\sum p_1q_1}{\sum p_0q_1}\times100).
- Fisher’s ideal index is the geometric mean of Laspeyres and Paasche: (\sqrt{L\times P}).
- Time-series components are trend, seasonal, cyclical and irregular variation.
- A moving average smooths short-term fluctuations to reveal trend; its period should match the seasonal cycle.
Worked example
Base prices are 10 and 20, with base quantities 5 and 2. Current prices are 12 and 25. Laspeyres (=\frac{12(5)+25(2)}{10(5)+20(2)}\times100=\frac{110}{90}\times100\approx122.22). This means the weighted price level rose by about 22.22% from the base year.
Traps
Match the weights to the method: Laspeyres uses (q_0), Paasche uses (q_1). Do not average Laspeyres and Paasche arithmetically when Fisher is asked. An index of 122 is not a price of 122. In moving averages, a centred average is needed for an even period. Do not label a seasonal movement as the long-term trend.