Equation (1) can be estimated with different estimators, for example using seemingly unrelated regressions (SUR) with iterated feasible generalized nonlinear least-squares estimator (FGNLS) through nonlinear three-stage least squares (Poi, 2012). A preferred alternative is to use the Iterated Linear Least-Squares (ILLS) estimator developed by Browning and Meghir (1991) and later generalized by Blundell and Robin (1999), which is computationally more attractive (Lecocq and Robin, 2015). It is based on the conditional linearity property – i.e. all equations in (1) are linear in all parameters conditional on the price aggregators functions – and it requires linear SUR to obtain consistent and asymptotically normal estimation of the demand system. In order to allow the level of demand to vary according to household heterogeneity, the intercepts _ɑ_ ’s are parametrized with the sociodemographic variables _s_<sup>_h_</sup> from the household survey and described in Table 4, such that: Lecocq and Robin’s model (2015) allows accounting for endogenous prices by using instrumental variable techniques. the error _u_<sup>_h_</sup> _i_ in equation (1) is augmented with the vector _Z_<sup>_h_</sup> predicted from estimating reduced forms for _x_<sup>_h_</sup> and _p_<sup>_h_</sup> : The independent variables in the reduced form equations are the sociodemographic variables in _s_<sup>_h_</sup> plus the instruments. The instruments used are the unit values calculated for each good _i_ , corrected with price indexes for 2015, so to obtain one-year lagged unit values. Finally, price and expenditure elasticities are calculated at the mean of the household sample.

# **6. Results**

Table 5 displays expenditure and own-price elasticities obtained from the estimation of the QUAIDS with 10 goods and services. Column 1 reports expenditure (income) elasticities, while columns 2 and 3 report the uncompansate and compensated price elasticities. Uncompensated (Marshallian) elasticity of demand measures both the substitution (e.g. when the relative price of a good _i_ increases, the household substitutes it with other goods) and the income (e.g. when the relative price of a good _i_ increases, the household’s purchasing power has decreased, therefore the entire bundle is re-optimized further reducing the consumption of the good _i_ ) effects; while compensated price elasticities measures only the substitution effect, ignoring the income effect. Therefore, the uncompensated elasticity of demand is greater than the compensated one and it is the most useful one for observing demand behavior. For this reason, in what follows the discussion will focus on the uncompensated price elasticities.

Starting from expenditure elasticities (table 5 column 1), they are all positive and statistically significant at 1% level. This suggests that all the goods and services considered in the demand analysis are normal – i.e. an increse in budget expenditure is followed by an increase in the quantity consumed of each good and service. However, some of the goods and services are much less responsive to expenditure change than others.

The least responsive, and therefore inelastic, items are food and education, with an expenditure elasticity of 0.458 and 0.556 respectively. An increase in household expenditure (or income) is followed by a halved increase in these items. For example, if household income increases of 1%, the corresponding 16