The Effects of Sample Size on Variances of the Producer Price Index

The PPI is a modified Laspeyres index which estimates a fixed input output price index model. Since the 1978 revision of the PPI, the industry output indexes have been based on the Standard Industrial Classification (SIC). Samples are drawn separately for four digit SIC industries, where each industry is assigned a publication structure prior to sampling. The publication structure partitions the SIC into detailed cells which generally make up the different homogeneous (with respect to price-determining characteristics) product categories within that SIC. These detailed cells are combined into higher level cells which eventually aggregate to the four digit SIC. The sample design is a two-stage systematic sample with item probabilities assigned proportionally to measures of size. In the first stage, the primary sample unit (PSU) is a profit maximizing center. This profit maximizing center is one or more establishments within which prices are set and records kept. The first stage sample is drawn in the Washington Office using a frame derived from the Unemployment Insurance file. Employment, as a proxy for company revenue, is used as the measure of size. The second stage of the sample is performed at each selected company using a sampling procedure known as disaggregation. Unique products are selected and information concerning each PSU is obtained. Subsequently, monthly price data on the selected unique products are obtained and used to measure price change in the PPI. These are published as the monthly price indexes. The current sample design process permits the computation of variances using balanced halfsample replication as described in Collia (1988). The sampling frame is divided into n variance strata, where n is dependent on the sample size and the number of self-representing PSUs and where (n+l) is a multiple of 4. The first-stage sample is then drawn by taking two independent half-samples within each variance stratum. Each of these strata must contain at least one certainty unit or two probability units. During the second-stage sampling process, items from self-representing PSU's and PSU's selected in both first-stage half samples are divided between half-samples. Using a Hadamard matrix, (n+l) orthogonal replicates are formed from unique combinations of price quotes. The remainder of the quotes are formed into corresponding complements. Indexes are then calculated for each replicate and its complement and the variance is computed as a function of these indexes. McCarthy (1969) provides a clear discussion of the use of the complement in this type of variance estimation. The first stage sample allocation for a four digit SIC is presently determined by examining such industry characteristics as industry concentration and product diversity and by considering the importance to PPI users of specific lower level indexes. The second stage allocation is usually determined using a formula based on the expected diversity of production within each first stage sample unit. The final two criteria for determining sample allocations are user need and budgetary constraints. Both first and second stage allocations may be supplemented in order to ensure publication of cell indexes which are of particular interest to PPI users and whose monthly publication might otherwise be in jeopardy. However, these enhancements must be balanced against cost considerations. The PPI operates on a fixed overall budget; when sample allocation enhancements are made in one industry, compromises in sample size may be necessary in others. This tradeoff between quality and quantity gives rise to a crucial question: What are the effects of sample size on variance levels and index quality in the PPI?