Seasonal Commodities, High Inflation and Index Number Theory

This paper studies the problems of measuring economic growth under conditions of high inflation. Traditional bilateral index number theory implicitly assumes that variations in the price of a commodity within a period can be ignored. In order to justify this assumption under conditions of high inflation, the accounting period must be shortened to a quarter, month or possibly a week. However, once the accounting period is less than a year, the problem of seasonal commodities is encountered, i.e., in some subannual periods, many seasonal commodities will be unavailable, and hence the usual bilateral index number theory cannot be applied. The present paper systematically reviews the problems of index number construction when there are seasonal commodities and high inflation. Various index number formulae are justified from the viewpoint of the economic approach to index number theory by making separability assumptions on consumers? intertemporal preferences. We find that accurate economic measurement under conditions of high inflation is very complex. Statistical Agencies should produce at least three different types of index: (i) year over year ?monthly? price and quantity indexes; (ii) a short term ?month to month? price index of non-seasonal commodities; and (iii) annual Mudgett-Stone quantity indexes that use the short term price index in (ii) to deflate the seasonal prices. In section 8, it is shown how the annual Mudgett-Stone quantity indexes can be calculated for moving years as well as for calendar years. These moving year indexes can be centered, and the centered indexes can serve as ?monthly? seasonally adjusted indexes at annual rates. In section 9, this index number method of seasonal adjustment is compared with traditional time series methods of seasonal adjustment. The paper is also related to the accounting literature on adjusting for changes in the general price level