to value that consumption, irrespective of source, at market prices. Diaries instead collect information on food _acquired_ during the interview period regardless of when the food was consumed. There is little evidence on the best approach for managing the transition to recall interviews, with most countries accepting a break in the series on poverty, food security, and welfare aggregates, given that the survey mode affects indicators of poverty and inequality in the cross-section (Beegle et al., 2012) and over time (Battistin, 2003, Pudney, 2008, Attanasio and Pistaferri, 2016, and Coibion et al., 2020).

This paper studies how to obtain the most accurate measurements of population well-being in household expenditure surveys. Specifically, we define a household’s well-being as their _usual_ (or _average_ ) rate of consumption in a fixed period, which in our application is one week. Usual consumption is a longer-run average of weekly intakes and the quantity grounding welfare comparisons on the theoretical concept of consumption smoothing. The empirical challenge then is to use survey measurements collected as a snapshot, typically covering one week, to infer usual consumption. We develop a strategy to identify the distribution of usual consumption, which is _unobserved_ because of the short-term nature of interviews, without applying any corrections to raw data or assuming _ex ante_ which mode of collection – diaries or recall questions – yields the most accurate measurement.

We frame the identification of consumer welfare in a general setting, encompassing “survey errors” – defined here as differences between survey measurements and usual consumption – related to household preferences and misreporting behavior. Specifically, households with different consumption preferences in the interview week but planning for the same dollar amount of consumption over a longer period (e.g., a month) will have the same well-being. Such _irregularity of consumption_ has implications for welfare analysis even when survey measurements are not misreported (as discussed by Kay et al., 1984, and Deaton and Grosh, 2000, among others). In addition, our analysis allows for survey errors from any of two broad sources. The first source is _infrequency of acquisitions_ , which arises because cash outlays occurred during the interview week may present extreme values resulting from no acquisition or positive acquisition of infrequently purchased items.<sup>2</sup> The second source of survey errors arises because of _misreporting_ , which is the object of a voluminous literature spanning both developed and developing countries (see Deaton and Zaidi, 2002, and Carroll et al., 2015). Our investigation disentangles the relative contribution of any of the above channels in both diary and recall data.

We leverage a unique large-scale experiment on consumption measurement in Iraq designed for the Iraq Household and Socio-Economic Survey (IHSES) in 2012. The survey ran continuously for one year and was administered to approximately 25,000 households across the country. All households filled out a 7-day diary on their acquisitions with the assistance of enumerators during regular visits. One-third of households were randomized to an additional survey module, administered before the diary, that asked them to recall food consumption in the last 7 days. The size of the experimental sample, approximately 8 _,_ 000 households, is of a different order of magnitude compared to other studies on consumption measurement in developing countries. The household diary employed was of the standard acquisition type, with one respondent recording on behalf of the household. Diaries were filled out by the same person

> 2If stocks are observed, one can impute consumption from diaries by measuring stock inflows and outflows (as in Beegle et al., 2012). However, the measurement of stocks is costly, prone to additional measurement concerns (Sharp et al., 2019), and seldom available in empirical work.

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