Decomposition analysis of consumers' demand changes: an application to Greek consumption data

Abstract

A decomposition analysis for consumer demand functions is developed. Changes in Marshallian demand or expenditure shares functions over time are decomposed into a total substitution effect, an income effect, and a habit effect. This framework is applied to post-war Greek consumption patterns through a habit persistence version of the Quadratic Almost Ideal Demand System (QUAIDS). It is found that for all commodity categories (i.e., food, beverages and tobacco, footwear and clothing, settling and housing, and others) the income effect was the main driving force in explaining changes in both quantity demanded and expenditure shares, followed by habit and total substitution effects.

Notes

¹ Most complicated forms of habit formation can also be used instead of the lagged quantity demanded (see for example Ray, 1985) even though this does not change the qualitative nature of the following analysis.

² This framework has previously been used by Karagiannis and Velentzas (1997) to explain food consumption patterns in Greece during the post-war period.

³ In this procedure, it is implicitly assumed that the representative consumer has no monopsony power over the consumption commodity bundles and that minimum expenditure equals income (ignoring savings). Equation 5b is also proved by Silberberg (1992, p. 340).

⁴ Lewbel (1990, 1991) defines the rank of any demand system to be the dimension of the space spanned by its Engle curves. The maximum possible rank of any exactly aggregable demand system is 3. Notice that both AIDS and translog demand systems are of rank 2.

⁵ For Greece, such a linear habit version of AIDS has been estimated by Mergos and Donatos (1989) and by Karagiannis and Velentzas (1993) using data for the periods 1960–1986 and 1958–1989, respectively.

⁶ When λ(p) is independent of commodity prices, the QUAIDS may be nested to a quadratic formulation of AIDS, used by Blundell et al. (1993).

⁷ In order to identify the parameter α₀ in Equation 9a, Deaton and Muellbauer (1980) original discussion is followed and is chosen to be 0.95 of the minimum value of ln M. Several other values have been used but this choice did not affect the results.

⁸ The corresponding eigen values are −0.0029, −0.0009, −0.0006, −0.0001, and −0.00005.

⁹ In all cases, the explained changes (i.e., the sum of the total substitution, the income and the habit effect) in quantity demanded and expenditure shares is greater than 87% of the corresponding observed changes, leaving the unexplained residual within a reasonable range.

¹⁰ A storage effect often makes the habit effect in consumer durables negative, i.e., a large consumption this period lowers the demand for the subsequent periods.