1. Econ 332 Spring 2013 © copyright 2013 by Casey B. Mulligan
Index Numbers
Econ 332
Spring 2013
© copyright 2013 by Casey B. Mulligan

2. Index Numbers as Summary Statistics
example: how much did aggregate consumption change?
some goods were consumed more over time
others were consumed less
could look at a weighted-average growth rate, but what are the “right” weights?
answer: use the consumer’s utility function, defined over the commodity vector v

4. Quantity and Price Indices
log consumption quantity index percentage change is the weighted average of log component changes, using expenditure shares as weights
weights can be initial period shares (Laspeyres), or final period shares (Paasche), or the average of the two (Marshall-Edgeworth)
For more than two periods, there are at least two changes:
each change can have its own weights (chained weight), or
each change can have the same weights (fixed weight)
a quantity index changes only if at least one of the component quantities change

5. Price Indices implicit price index = expenditure/q index
price index can be formed using the above procedure, but using component price changes rather than component quantity changes
implicit quantity index = expenditure/p index
a price index changes only if at least one of the component prices change

6. Other Uses of Index Numbers
Use index numbers any time you want to summarize many components and can quantify the relative importance of the components
e.g., statutory generosity index summarizes changes from benefit and eligibility rules from various safety net programs