Cost-of-Living Index Based on an Estimated Generalized Constant-Elasticity-of-Substitution Utility Function

• Activity Number: 413
• Type: Topic Contributed
• Date/Time: Wednesday, August 5, 2009 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Peter Zadrozny*+
• Companies: Bureau of Labor Statistics
• Keywords: multi-step perturbation solution of nonlinear equations ; trend, cycle, and seasonality in time-series models

Abstract

We estimate parameters of a generalized constant-elasticity-of-substitution (GCES) utility function by applying MLE to price and quantity data for 8 categories of expenditures by U.S. consumers. GCES generalizes the familiar CES utility function. The estimating equations are a linear-in-variables VARMA process, subject to nonlinear first-order conditions on parameters which reflect maximization of the GCES utility function. The equations account for trend, cycle, and seasonality, which are interpreted in terms of consumer preferences. We also compute monthly changes in the cost-of-living index (COLI), based on the estimated GCES utility function by applying multi-step perturbation (MSP) to the first-order conditions. Resulting computed COLI should more accurately reflect substitution in consumer expenditures due to relative price changes than commonly used "superlative" indexes.