Given that an index formula is a mathematical function, what statistical properties make it a ‘good’ index ? A number of tests have been developed, and are used to understand the advantages and disadvantages of one formula over another.
Proportionality – If all prices changes by x percentage, the price index should also change by x percentage.
Commensurability – The price index should be invariant to changes in the unit of measure. E.g., if both sets of prices are measured in dollars and then in pesos, the index should show the same development.
Time reversal – If prices between periods are reversed, then the second period index change should be the reciprocal of the first period index change.
Monotonicity – If one or more prices are rising in the current period, and non is decreasing, then the price index should increase.
Circularity – The product of the price index change going from period 1 to 2 times the price index change going from period 2 to 3 should equal the price index change going directly from period 1 to 3.
Factor Reversibility – a price index multiplied by a corresponding quantity index should equal the ratio of the values for the two comparison periods.
All of the above tests appear to be reasonable criteria; however, no single index passes all of the tests. The proportionality, the commensurability and the time reversal test are all critical tests for price indices, while circularity and factor reversibility are nice but restrictive tests – and are failed by the most commonly used index formulas.
Furthermore, economic theory should be used to evaluate the different index formulas. For instance; According to consumer utility theory, consumers will maximize their utility under given constraints (household budgets). If relative prices change, consumers will tend to move towards relatively cheaper goods and away from relatively more expensive goods. Thus, indices with base period fixed weights (e.g., the Laspeyres) will serve as an upper bound in the measurement of inflation since it assumes that purchases are made in fixed quantities based on the optimal decisions from some previous periods experience – no substitution is taking place. Vice versa, indices with current period based weights (e.g., the Paasche) will represent the lower boundary on inflation because it assumes that that purchases are made in the past following the most resent pattern. It follows an average of an index based on current period weights and an index based on base period weights should be preferred. However, the use of a formula based on base period weights can be close to the ideal (an index based on both base period and current period weights) if the weights are updated regularly – monthly, quarterly or annually – and the indices chain linked to form time-series.
Thus, as a user check:
(i) What kind of index-formula is used,
(ii) Whether it represents an upper or a lower bound to true inflation, and
(iii) Whether its coverage is relevant for the purpose (e.g., CPI vs PPI).
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