WHEN DOES CHAINING REDUCE THE PAASCHE-LASPEYRES SPREAD? AN APPLICATION TO SCANNER DATA

Robert Hill

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Monetary Policy and Economic Impact Income, Poverty, and Inequality Consumer Market Behavior and Pricing

Abstract

It is generally believed that chaining reduces the Paasche–Laspeyres spread if prices and quantities are monotonic over time. I consider three alternative definitions of monotonicity and show that none provide either necessary or sufficient conditions for chaining to reduce the Paasche–Laspeyres spread. What matters is the interaction between prices and quantities both in the same period and lagged one period. Sufficient conditions are derived, and the implications of these conditions for the measurement of inflation are considered. The paper concludes with an empirical illustration using scanner data.

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References

1978Superlative Index Numbers and Consistency in Aggregation 1983World Product and Income: International Comparisons of Real Gross Product.1936Annual Survey of General Economic Theory: The Problem of Index Numbers 1936Annual Survey of General Economic Theory: The Problem of Index Numbers 1936Composite Commodities and the Problem of Index Numbers 1988The Early History of Price Index Research 1887Remedies for fluctuations of general prices 2004Superlative index numbers: not all of them are super

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