An Additive Double-Logarithmic Consumer Demand System


The University of Arizona is an equal opportunity, affirmative action institution. The University does not discriminate on the basis of race, color, religion, sex, national origin, age, disability , veteran status, or sexual orientation in its programs and activities. Abstract An Additive Double-Logarithmic Consumer Demand System Despite obvious theoretical shortcomings, the double-logarithmic function, because of ease of estimation and generally superior fit, is often the demand function of choice in applied demand analysis. However, the drawback to double-logarithmic demand functions is that they are not theoretically plausible, in that they are neither consistent with an underlying utility function nor additive (in the sense of satisfying the budget constraint). The purpose of this paper is to introduce a double-logarithmic demand system that is additive. This is accomplished through an extension of the Houthakker's indirect addilog model that allows for all prices, not just the own-price of a good, to be included in each of the demand functions. The system is applied to a cross-sectional data set consisting of six exhaustive categories of consumption expenditure from the four quarterly BLS consumer expenditure surveys for 1996 augmented with price data collected in quarterly cost-of-living surveys conducted by ACCRA. I am grateful to Sean McNamara of ACCRA for making EXCEL files of ACCRA surveys available to me and to the Cardon Chair Endowment in the Department of Agricultural and Resource Economics at the University of Arizona for financial support. Construction of data sets and econometric estimation have all been done in SAS. 2 1 This paper is the third in an ongoing investigation into the feasibility of integrating price information into the BLS quarterly consumer expenditure surveys. The first (2004a) analyzes 16 quarters of CES and ACCRA data (1996-1999) using only simple double-logarithmic equations, while the second (2004b) compares, using only the four quarters for 1996, price and total expenditure elasticities obtained from four " theoretically plausible " demand systems, AIDS, LES, and the Indirect and Direct Addilog models.

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taken from the on-going price surveys of the 62 items of consumer expenditure listed in Table A1 above in more than 300 cities in the U.S. that are conducted quarterly by ACCRA 14