Academic journal article Atlantic Economic Journal

Aggregation of Multiperiod Index Numbers

Academic journal article Atlantic Economic Journal

Aggregation of Multiperiod Index Numbers

Article excerpt

Suppose several commodities have been classified in three groups, food (f), clothing (c), and the aggregate (a) of food and clothing together. A time series of T observations on the individual prices and quantities is available. Let exp (vfrt) denote the total value of the food group when the prices of period r are applied to the quantities of period t. To estimate price and quantity indices for the food group, Blankmeyer [AEJ, June 1990] proposes the two-way analysis of variance (ANOVA):

vfrt = pfr + qft + zf + efrt, r, t = 1, . . ., T, (1)

where zf is the general mean and efrt is a spherical error. The log-linear contrasts pfr - pft and qfr-qft are best linear unbiased estimates of the percent change in the food price level and food quantity level. Indices for the clothing group and for the aggregate group are estimated analogously.

If, in some reference period, wf and wc are the shares of food and clothing in total expenditures (wf + wc = 1), then

wf (pfT - pf1) + wc(pcT - pc1) - (paT - pa1) = 0 (2)

is a linear restriction on the parameters of the three ANOVA equations. …

Search by... Author
Show... All Results Primary Sources Peer-reviewed

Oops!

An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.