consumption; the methodology followed in this paper uses the national median values of prices reported by ration agents to value ration items [World Bank (2013)].

Using the quantities and ration-agent’s prices for these ration items to estimate expenditures, on average only 6% of total expenditure is allocated to this type of products by Iraqi households in 2012. This aggregate statistic hides a lot of heterogeneity throughout the consumption distribution. PDS expenditures account for 30 percent of food expenditures for the poorest 10 percent of Iraqi households, and around 17 percent of their total expenditures in 2012. The share of PDS expenditures declines as total household expenditures increase or as households get richer. For instance, it reduces to 12, 7 and 2 percent for the 2<sup>nd</sup> , 5<sup>th</sup> and top deciles of the consumption distribution respectively (Figure 1). Table 1 shows the average shares of ration expenditure with respect to total food expenditure by consumption quintile in urban and rural areas. In urban areas, the richest spend almost 9% of their total food expenditure on ration products, compared to 44% spent by the poorest quintile. These shares are slightly higher in rural areas: 9.4% and 47% for the upper and bottom 20 percent of the consumption distribution respectively.

# **3. Mixed Demand Model**

Estimating the behavioral responses of households to changes in the availability of goods requires the estimation of the demand functions of consumers of these goods. In this setting, the most common empirical specifications involve expressing quantity demanded as a function of total expenditure and market prices, or a direct demand system [Moschini and Rizzi (2006)]. However, standard specifications rely on additional identifying assumptions, in particular, the implicit assumption that prices are predetermined, or in other words, that supply functions for these goods are perfectly elastic. This assumption is not likely to hold in the context under consideration here, where nominally priced PDS items form a significant part of expenditures on food, and are widely consumed. An alternate approach treats quantities as predetermined, with prices adjusting so that demand and supply are equalized in the aggregate. This approach, while appropriate for perishable products, is not appropriate in the scenario considered in this paper either. A third approach, first introduced by Samuelson (1965), considers mixed demand functions. In this approach, while for some goods, prices are predetermined, for others, quantities are given. This allows for more flexibility in assumptions regarding whether prices or quantities are held exogenous for each good, and this is the approach we follow in this paper.

In addition, the presence of a dual system of prices for PDS or ration goods can be incorporated into a mixed demand model specification; whereas Marshallian demand functions using flexible specifications such as the Almost Ideal Demand Systems (AIDS) may not be appropriate. The dual system is one where households have access to quotas of subsidized food products in addition to their free market counterparts. In this setting, a consumer has to simultaneously choose the subsidized consumption segment (i.e., a quantity above or below 6