Effect of Weight-Period Selection on Measurement of Agricultural Production Inputs

Choice of weights is basic to construction of index numbers that are designed to measure change over time. The analysis in this article develops criteria for selection of weights and examines the results of using different periods as a basis for measuring change in the volume of selected inputs in farm production from 1910 to 1955. Laspeyres' weighted aggregative formula was considered the most appropriate formula for use in this analysis. Average cost rates were used as weighting units. The various indexes of combined inputs that are described here were developed for testing purposes. It is believed that the index of total farm inputs that will result when the aggregate production inputs of agriculture are measured and analyzed will differ substantially from any of the index-number series of selected agricultural inputs shown here. This paper is a report on the first phase of the project. It does not pretend to be an exhaustive study of the many problems that arise in the construction of an index of agricultural inputs. For instance, the problems associated with selection of weighting units and an index formula are not discussed. However, it is a reasonably thorough analysis of the problem of how to aggregate the different inputs in a meaningful way to show change over time when the composition, relative prices, and quantities of inputs change. The advice and leadership of Glen T. Barton in the preparation of this article is acknowledged by the author.