Teaching Index Numbers to economists

Figures & data

Table 1. Index Number formulae

Formula name	Formula
Carli	$\frac{1}{N}{\sum }_{i=1}^N\frac{P_{i1}}{P_{i0}}$
Jevons	${\left(\frac{P_{i1}}{P_{i0}}\right)}^{1/N}$
Dutot	$\frac{\frac{1}{N}{\sum }_{i=1}^N{P}_{i1}}{\frac{1}{N}{\sum }_{i=1}^N{P}_{i0}}$
Laspeyres	$\frac{{\sum }_{i=1}^N{P}_{i1}{Q}_{i0}}{{\sum }_{i=1}^N{P}_{i0}{Q}_{i0}}$
Paasche	$\frac{{\sum }_{i=1}^N{P}_{i1}{Q}_{i1}}{{\sum }_{i=1}^N{P}_{i0}{Q}_{i1}}$
Fisher	$\sqrt{\text{Laspeyres}\times \text{Paasche}}$

Table 2. Example data for an Index Numbers exercise

	2010		2014
Item	Quantity	Price	Quantity	Price
Book	10	10	6	11
Notepad	4	5	12	6
Ebook	6	9	16	8.5
Bookmark	5	1	1	0.5

Table 3. Levels of achievement for Index Numbers learning

Level of understanding	Description of ability outcomes
Basic	Able to use data to estimate index numbers from a formula and able to state the main finding resulting from the index
Intermediate	In addition to the Basic level skills, students are able to manipulate and interpret different forms of index numbers, also able to describe different methods for choosing between formulae.
Higher	In addition to Intermediate, able to discuss and analyse the relative properties of various index numbers as well as identify appropriate real-world applications of the technique.
Advanced	In addition to Higher, able to discuss the practical trade-offs which might affect the use of index numbers in practice and able to assess uses of index numbers as appropriate or not.