Törnqvist index

In economics, the Törnqvist index is a price or quantity index. In practice, Törnqvist index values are calculated for consecutive periods, then these are strung together, or "chained". Thus, the core calculation does not refer to a single base year.

The price index for some period is usually normalized to be 1 or 100, and that period is called "base period."

A Törnqvist or Törnqvist-Theil price index is the weighted geometric average of the price relatives using arithmetic averages of the value shares in the two periods as weights.

The data used are prices and quantities in two time-periods, (t-1) and (t), for each of n goods which are indexed by i.

If we denote the price of item i at time t-1 by ${\displaystyle p_{i,t-1}}$, and, analogously, we define ${\displaystyle q_{i,t}}$ to be the quantity purchased of item i at time t, then, the Törnqvist price index ${\displaystyle P_{t}}$ at time t can be calculated as follows:

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