for poverty measurement.

We conclude our analysis by showing that a recall survey is the best option even in the worst case scenario when no information on _Y_<sup>_∗_</sup> is available.<sup>17</sup> This can be seen from the dashed lines in Figure 9, which are obtained by setting _p_ ( _y_<sup>_∗_</sup> ) = _p_ in (6) and allocating to diaries a _random_ share _p_ of households independently of their consumption. The lines in the four panels suggest that there is no gain from mixing diary and recall interviews without a selective allocation of households that depends on their consumption.

The take-away message from this section is that we do not find evidence of any loss in accuracy from using recall questions compared to a diary. Moreover, the above definition of optimal design does not take into account costs and budget constraints in the optimization. Our conclusions on the value of recall surveys would be strengthened given the much higher costs of running a diary survey.

# **7 Conclusion**

Using a large-scale randomization in Iraq, we found little empirical support for the idea that diaries yield better quality data for assessing household welfare. Diaries provide a more reliable measurement of usual consumption _averages_ , and we have shown that the cognitive errors arising from the process of recalling consumption lead to overstated actual consumption. However, when inequality and poverty measurements are of interest, the benefits of diaries are far less clear-cut. Diary measurements, despite being correct on average, have large variance. We have demonstrated that this is not the consequence of measurement errors but mostly a reflection of heterogeneous frequency of consumption across households. We have found that recall modules provide a more reliable mode of data collection for inequality and poverty. The use of surveys with both diary and recall interviews can yield improved measurements because these two collection modes work best for eliciting consumption in different segments of the distribution. Nevertheless, our calculations have shown that a fully fledged recall survey can yield inequality measurements that are not too different from those that would be obtained from the optimal mix of diary and recall interviews.

The first implication of our research is that the loss in accuracy from using recall questions is minimal compared to the higher costs of using diaries. This finding provides an empirical justification for considering a transition to recall modules in household surveys in developing countries. However, more research is needed to assess what makes a good recall module, given that the length of the recall list will affect the propensity of respondents to engage in the survey. The answer to this question could be given, for example, by randomizing households to recall modules of different length and using our research design. The decision between using diaries or recall modules is not confined to developing economies. For example, the problems associated with the Consumer Expenditure Surveys in the United States have intensified the call for a redesign of the survey, which is underway following the recommendations of a specially appointed panel (the Gemini project).

Diary surveys should collect information on the purchasing behavior of households to correct for the unwelcome effects of infrequent purchases on inequality measurement – which is the second implication

> 17Allocation based on proxies of _Y ∗_ , such as income or residence in areas with homogeneous compositions of household demographics, falls between this case and the one above.

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