Food Prices and Overweight Patterns in Italy

estimate elasticities of demand, we assumed a multistage decision process (Edgerton,
1997). The estimated system is conditional on the choice of purchasing goods that
consists of non-durables in a previous non-modelled stage and is determined as part
of consumers’ overall decision regarding how to allocate expenditure across the full
range of goods. In fact as the expenditure is allocated within non-durables, only
in the second (conditional) stage consumers decide how to allocate across healthy
foods, unhealthy foods, and other foods and non-durables⁸ . In this case, income
elasticity and Hicksian price elasticities are computed as follows:

= ∂qi y = ∂wi 1 + i
^ηi   ∂y qi   ∂ log ywi

with i = 1, 2, 3. The expression for expenditure elasticity indicates that a good
is a luxury if ηi > 1 and a necessity if ηi < 1. The compensated price elasticities
are given as:

where the partial derivatives in (8) and (9) are obtained from equation (7) and
i,j=1,2,3. Then, the uncompensated price elasticities are obtained from the Slutsky
equation, ε_ij = η_ij - wjη_i .

One formal way of testing the substitution effects between healthy and unhealthy
foods is to calculate their cross-price elasticities. According to Hicks (1936), ηij >
0 indicates substitutability among goods, ηij < 0 complementarity, and ηij = 0
independence.

One important property of the Slutsky equation is that the estimated parameters
of the matrix are symmetric. But unlike Allen’s (1938) elasticity of substitution,
the Hicksian framework does not impose symmetry restrictions in elasticity terms.
In line with the aims of this paper, we can verify how changes in the prices of
unhealthy versus healthy foods simultaneously affect the relative cost of purchasing
quantities of these categories of foods. The framework is therefore close to that of
Auld and Powell (2009). If, as shown in section 2, changes in healthy food prices are
higher than in unhealthy food prices during the last decade in Italy, we can predict
greater total calorie intake, generated by a substitution towards unhealthy foods,
which determines an increase in the consumption of energy-dense foods. In addition,

⁸ In a complete demand system, we should consider previously at least the choice of how to allocate total expen-
diture between goods and services for consumption (Gorman, 1995).

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