Food Prices and Overweight Patterns in Italy

because the elasticity of substitution is the percentage change in the budget share
allocated to good wi , divided by the percentage change in price pj , we can compute
the net effects of healthy and unhealthy budget share responses to changes in prices.
We use η₁₂ to represent the elasticity of substitution of the healthy food to changes
in unhealthy food prices; η₂₁ represents the response of the unhealthy food budget
share to changes in healthy food prices. Recalling that the food prices of both
categories increased in the period 1997-2005, the net effect of this elasticity on the
sample mean is given as:

∆η = η21 - η12                             (10)

If the cointegrated AI is exactly identified, when we extend estimations at each
(monthly) point of the sample, we can use the estimations of the elasticity of substi-
tution to evaluate the dynamics of the response of healthy and unhealthy food con-
sumption to relative price changes by the scaling procedure of estimation discussed
above. In the condition that the concavity condition is satisfied, we consistently
reconstruct the elasticities of substitution (η21 and η12) for both the full sample and
for the subsamples and their confidence intervals by bootstrapping the standard
errors of elasticities.

5 Results and discussion

The long-run AI model considers the share equations in equation (1) as the long-run
equilibrium relationships of a VAR model, Xt = (X1t, X2t). Following the discussion
in Section 4, cointegration test procedures were used to identify the number of
long-run empirically important relationships in our data. We only note that exact
identification requires two cointegrating relations associated with n-1 (3-1) budget
shares among the variables of the model, so that we specify a VAR(3) to evaluate
it⁹.

The test results of the trace statistic of Johansen (1995) and Saikonnen and
Liitkepohl test (SL) (2000) are listed in Table 1. We report both tests from data
obtained by aggregations of good categories across households of national or regional
indices. At the five percent significance level, neither the trace statistic nor the
SL test reject the hypothesis that there are two cointegrating vectors among the

⁹To select the order of the VAR, we used the sequential modified likelihood ratio (LR) test as in Liitkepohl
(1991), while estimations are carried out by including centred seasonal dummies.

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