Misreporting of diary entries affects equation (1) by introducing a disturbance term on the right-hand side.

# **2.3 Recall Interviews**

Many household surveys implemented in the developing world ask respondents to recall quantities in a preselected list of food items consumed over a fixed period and their associated market value. In our case study, the recall period is seven days, ending with the interview (Lyberg and Kasprzyk, 2004, Beegle et al., 2012, and Crossley and Winter, 2014 discuss the effects of changing this time window). Information is collected in two steps. The respondent is first asked if the items in the list were consumed during the past week, going vertically down in the survey form from the first item to the last. For the items for which there is a positive response, the quantity consumed and the unit of measurement are reported. The respondent then must backcast the monetary value of this quantity by reporting estimated expenditures (if market purchased) or market values (if self-produced, received as a gift, or received in barter). The monetary equivalent of recalled consumption (quantity consumed times implicit price per unit, or unit value) is the quantity we consider for the measurement _Y_<sup>_r_</sup> .

Why should one expect differences between _Y_<sup>_∗_</sup> and recalled consumption _Y_<sup>_r_</sup> ? As discussed above, consumption in the week before the interview need not coincide with usual consumption. Arguments can be made in favor of using a longer reference period for recall questions, or asking directly about “usual week” consumption. However, limited cognitive abilities and the difficulty of recalling the timing of events may challenge respondents’ ability to perform the computations. Estimating the monetary equivalent of the quantities consumed from non-market sources adds an additional layer of difficulty. Errors may arise because the respondent solves a prediction problem rather than reporting a noisy measurement. Households may form their answers using the information available, for example including other features of the survey, so that the value _Y_<sup>_r_</sup> is their best predictor of the unobserved value _Y_<sup>_∗_</sup> . Experimental evidence in psychology research supports this interpretation (see Comerford et al., 2009). Rounding errors in providing the quantities consumed or telescoping (the act of recalling consumption occurring over a longer period of time as within the reference period; Neter and Waksberg, 1964) were found to be important factors in the computation. These concerns may be particularly salient in a context such as Iraq, where many households have relatively low educational attainment.

The textbook assumption of classical errors is violated in general, with no obvious direction of bias. For example, if the best prediction is obtained by respondents in terms of quadratic loss, recall errors must be centered at zero and not correlated with _Y_<sup>_r_</sup> but correlated with consumption _Y_<sup>_∗_</sup> . If an absolute value loss is used instead, the household would report the median of _Y_<sup>_∗_</sup> given the information available (see Hyslop and Imbens, 2001, and Hoderlein and Winter, 2010).

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