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

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

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

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

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