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The Marshall-Edgeworth index, credited to Marshall (1887) and Edgeworth (1925), [11] is a weighted relative of current period to base period sets of prices. This index uses the arithmetic average of the current and based period quantities for weighting. It is considered a pseudo-superlative formula and is symmetric. [12]
For example, a Törnqvist index summarizing labor input may weigh the growth rate of the hours of each group of workers by the share of labor compensation they receive. [7] The Törnqvist index is a superlative index, meaning it can approximate any smooth production or cost function. "Smooth" here means that small changes in relative prices for ...
Index numbers are used especially to compare business activity, the cost of living, and employment. They enable economists to reduce unwieldy business data into easily understood terms. In contrast to a cost-of-living index based on the true but unknown utility function, a superlative index number is an index number that can be calculated. [1]
The Malmquist Index (MI) is a bilateral index [a] that can be used to compare the production technology of two economies. It is named after Professor Sten Malmquist, on whose ideas it is based. It is also called the Malmquist Productivity Index. The MI is based on the concept of the production function. This is a function of maximum possible ...
However, more practical formulas can be evaluated based on their relationship to the true cost of living index. One of the most commonly used formulas for consumer price indices, the Laspeyres price index, compares the cost of what a consumer bought in one time period (q 0) with how much it would have cost to buy the same set of goods and ...
PPP levels will also vary based on the formula used to calculate price matrices. Possible formulas include GEKS-Fisher, Geary-Khamis, IDB, and the superlative method. Each has advantages and disadvantages. Linking regions presents another methodological difficulty.
The new measure, called a "superlative" index, is designed to be a closer approximation to a "cost-of-living" index than the other measures. The use of expenditure data for both a base period and the current period in order to average price change across item categories distinguishes the C-CPI-U from the existing CPI measures, which use only a ...
For two univariate distributions and with the same standard deviation, it is denoted by ′ ('dee-prime'): ′ = | |. In higher dimensions, i.e. with two multivariate distributions with the same variance-covariance matrix , (whose symmetric square-root, the standard deviation matrix, is ), this generalizes to the Mahalanobis distance between the two distributions: