distribution arising from this design is: the percent of survey participants filling out a diary being: For example, in a recall survey _p_ ( _y_<sup>_∗_</sup> ) = 0 at all values _y_<sup>_∗_</sup> . We are interested in the effects of the collection mode on functionals of the distribution of usual consumption _FY ∗_ [ _y_<sup>_∗_</sup> ]. Possible choices for these functionals are quantiles, share below the poverty line, and the Gini coefficient. The difference: represents the distance between the true statistic, _ν_ ( _FY ∗_ [ _y_<sup>_∗_</sup> ]), and the same statistic that would be computed under the assignment design described above, _ν_ ( _FY_ [ _y_ ]). In this section, we find the configuration of weights _p_ ( _y_<sup>_∗_</sup> ) that minimizes the distance in (8) at any given choice for the value of _p_ (the algorithm used to obtain the solution is described in the Appendix). In an effort to contain the computational burden, we use _FY d|Y ∗_ [ _y|y_<sup>_∗_</sup> ], _FY r|Y ∗_ [ _y|y_<sup>_∗_</sup> ] and _FY ∗_ [ _y_<sup>_∗_</sup> ] as if they were _known_ quantities and discard the additional variability arising from estimation errors.

Distributions retrieved from a recall survey are closer to the underlying distribution of usual consumption than in a diary survey. This can be seen in Panel A of Figure 9, where the statistic _ν_ represents the Kullback-Leibler distance (KLD) from the consumption distribution and _ν_ ( _FY ∗_ [ _y_<sup>_∗_</sup> ]) = 0. The continuous line here shows the value of (8) at different values of _p_ . The value corresponding to _p_ = 0 is the KLD from a survey with only recall questions. The panel conveys two important messages. First, as more resources are allocated to diaries, the KLD improves until it reaches the value _p_ = 0 _._ 42. In particular, Appendix Figure A.1 shows that weights _p_ ( _y_<sup>_∗_</sup> ) at the value _p_ = 0 _._ 42 are such that households with large values of _Y_<sup>_∗_</sup> should always be assigned to diaries. The second important message is that the KLD is larger at _p_ = 1 than at _p_ = 0. This implies that, in our case study, the data distribution obtained from a fully fledged recall survey has better properties than one obtained from diaries alone.

Distributions obtained from diary data yield worse measurements of poverty and inequality. This can be seen in the remaining panels of Figure 9, where the continuous lines represent alternative definitions for the statistic _ν_ ( _FY_ [ _y_ ]): the Gini coefficient (Panel B), the standard deviation of logged consumption (Panel C), and the share of consumption for households in the bottom decile (Panel D). The horizontal lines in panels represent the value of the true statistic _ν_ ( _FY ∗_ [ _y_<sup>_∗_</sup> ]). Diaries yield more disperse consumption distributions, as shown in Panel B and Panel C. Moreover, the Gini coefficient and the standard deviation computed from a recall survey are closer to their true values than one would obtain by using only diaries. It is also clear that allocating more resources to diaries would improve inequality measurement only until approximately the value _p_ = 0 _._ 10. This suggests that a fully fledged recall survey is almost as close to the optimal design when inequality measurement is of concern. Panel D yields very similar conclusions 26