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Abstract:
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Using monthly price-quantity data for eight categories of consumer expenditures, we obtain ML parameter estimates of a variable-elasticity-of-substitution utility function, a generalization of the CES utility function. Estimating equations are a linear-in-variables VARMA process, subject to nonlinear parameter restrictions representing VES utility maximization. We also account for trend, cycle, and seasonality, which represent time-varying consumer preferences. Then, we use the multistep perturbation method---for solving nonlinear equations---to compute month-to-month changes in the cost-of-living index based on the estimated VES utility function for the price-quantity data. The resulting COLI should reflect substitution in aggregate consumer expenditures more accurately than commonly publicized, so-called superlative indexes---such as Tornqvist---due to relative price changes.
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