Next, these monthly quantities of PDS items need to be valued and two key principles guide this valuation procedure. Households who consume (or purchase) a larger quantity of PDS items must be assigned higher consumption and thereby utility. Second, in principle, goods and services ought to be valued equal to their infra-marginal benefit; i.e.; the market price faced for the marginal unit consumed. In Iraq, ration items are rarely traded in the market and a market-equivalent price is non-existent. Few transactions are recorded in the diary and there are two main reasons why market prices or in this case unit values (the ratio of expenditure to quantity) from market transactions are not used as the reference for valuing ration items. The first is the insufficient number of observations per item. For instance; the percentage of households reporting purchases of ration items in the diary questionnaire varies from less than 1 percent in the case vegetable fat, lentils, brown wheat, and sugar to a maximum of less than 3 percent in the case of rice. Furthermore, there are no transactions recorded in some geographical divisions for brown wheat, vegetable fat, vegetable oil, lentils and sugar. Secondly, there is a possibility of selection-bias. In other words, these unit values could be associated with a select few households who are quantity constrained and purchased PDS items on the market because their allocation proved insufficient.

Additionally, the unit values for the nearest free market equivalents are significantly higher for some items. For instance, a significant gap is observed in unit values between market-traded and ration rice. For instance, the difference between the median unit value of ration rice from diary and commercial local rice is 70 percent. This gap doubles when comparing with the median unit value of imported commercial rice. This could be mainly related to important quality differences between these types of goods. This implies that market prices for commercially available items cannot be used to value all ration items because they are not perfect substitutes.

Another possibility is to use official prices for ration items. Again, two main concerns are relevant: the first is that these prices are very low. Using these heavily subsidized prices would artificially suppress the value of food expenditures stemming from rations. The second is that rations should be valued at a price close to that we expect to be traded. But these official prices are not prices at which households can procure unlimited quantities (by design).

The remaining candidate to value rations is the self-reported value of ration items. IHSES asks households how much they would pay for ration-equivalent items in the market.<sup>6</sup> In practice, few households expressed an opinion, and enumerators approached the local ration agent in the cluster, in a manner akin to a price survey. However, there were variations in these prices that may reflect uncertainty, noise and local variations in supply, demand and quality. In order to ensure that all those who consume exactly the same amount of a ration item are assigned the same expenditure, and thereby utility; and that this expenditure increases with higher

> 6 The actual question from the IHSES questionnaire is: “If you could buy this [ITEM] in the market, how much would you have to pay for it?”

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