Food prices and overweight patterns in Italy

Abstract

In this paper, we examine the role of relative food prices in determining the recent increase in body weight in Italy. Cross-price elasticities of unhealthy and healthy foods estimated by a demand system provide a consistent framework to evaluate substitution effects, when a close association is assumed between unhealthy (healthy) foods and more (less) energy-dense foods. We used a dataset constructed from a series of cross-sections of the Italian Household Budget Survey (1997–2005) to obtain the variables of the demand system, which accounts for regional price variability. The relative increase in healthy food prices was found to produce nontrivial elasticities of substitution towards higher relative consumption of unhealthy foods, with effects on weight outcomes. In addition, these changes were unevenly distributed among individuals and were particularly significant for those who were poorer and had less education.

Appendices

Appendix 1

see Table 6.

Table 6 Food classification

Appendix 2: Identification of long-run AIDS

The cointegration relationships in the VECM equation (6), subject to reduced rank restrictions on the $\Uppi=\alpha \beta^{\ast^{\prime }}$ matrix, are not identified. Following Pesaran and Shin (2002), the identification of the long-run parameters in $\beta^{\ast ^{\prime }}$ requires the imposition of r restrictions on each cointegrating vector, although a necessary and sufficient condition (order condition) for the identification is that the number of the identifying restrictions, k, should be at least equal to r ².

In order to explain these fundamental identifying conditions in our demand system with three categories of goods, we note first that adding up reduces the rank to two, i.e., r = (n − 1). As a formal extension of the ECM vectors in Eq. (6), let us consider two non-identified cointegrating vectors made up of the variables w _1t ,  w _2t ,  lnP _1t ,  lnP _2t ,  lnP _3t ,  ln(y _t /p _t ) and the intercept. The associated parameters are as follows:

$$ \widetilde{\beta}_{U}^{\prime}= \left\{\begin{array}{ccccccc} \beta_{11} &\beta_{21} & \beta_{31}& \beta_{41}& \beta_{51}& \beta_{61}& \beta_{71}\\ \beta_{12}& \beta_{22}& \beta_{32}& \beta_{42} & \beta_{52} & \beta_{62} & \beta_{72} \end{array}\right\} $$

(11)

The exact identifying restrictions r ² = (n − 1)² = 4 assume a diagonal structure because theory suggests that budget shares responds mainly respond to own and cross-price changes and income impulses, but not to (endogenous) changes in other budget shares. Formally,

$$ \left\{\begin{array}{ccc}\beta_{11}=-1, &\beta_{12}=0 \\ \beta_{21}=0, & \beta_{22}=-1 \end{array}\right\} $$

(12)

so that the cointegrating vectors may be written as:

$$ \widetilde{\beta}^{\prime}= \left\{\begin{array}{ccccccc}-1 &0 & \beta_{31}& \beta_{41}& \beta_{51}& \beta_{61}& \beta_{71} \\ 0& -1 & \beta_{32}& \beta_{42} & \beta_{52} & \beta_{62} & \beta_{72} \end{array}\right\} $$

(13)

In order to test theoretical restrictions, long-run parameter restrictions should be included. As discussed in the text, the property of symmetry may be imposed as a cross-equation restriction, β₃₂ = β₄₁. The cointegrating vectors thus assume the following structure:

$$ \widetilde{\beta}_{S}^{\prime}= \left\{\begin{array}{ccccccc}-1 &0 & \beta_{31}& * & \beta_{51}& \beta_{61}& \beta_{71} \\ 0 & -1 & \beta_{32}& \beta_{42} & \beta_{52} & \beta_{62} & \beta_{72} \end{array}\right\} $$

(14)

Estimations of cointegrating vectors subject to symmetry is tested by the LR statistic distributed as a χ² with one degree of freedom. This restriction is not rejected when the log likelihoods of this restricted model is compared with the exact-identified model in Eq. (13), the differences are not significant.

Lastly, as suggested by the demand theory, we impose and test in the cointegration vectors the properties of both symmetry and homogeneity. In addition to the symmetry restriction, β₃₂ = β₄₁, the restriction of homogeneity for each equation is added, that is, (β₃₁ + β₃₂ = −β₅₁) and (β₃₂ + β₄₂ = −β₅₂). Thus, the cointegration vector is given as:

$$ \widetilde{\beta}_{SH}^{\prime}= \left\{\begin{array}{ccccccc}-1 & 0 & \beta_{31}& * & * & \beta_{61}& \beta_{71}\\ 0 &-1 & \beta_{32}& \beta_{42} & * & \beta_{62} & \beta_{72} \end{array}\right\} $$

(15)

As shown in the text, the LR statistic, distributed as a χ² with three degrees of freedom, is then used to test these joint theoretical restrictions.

Appendix 3

see Table 7.

Table 7 Sensitivity analyses of long-run estimated elasticities from the demand system (Eq. 7)

Appendix 4

see Table 8.

Table 8 Johansen’s cointegration rank test statistics for AIDS system applied to subsamples of Italian survey data