weakest assumptions needed to address measurement error in empirical work.

Our research design yields a second important finding: the presumption that diaries should be the benchmark for measuring household well-being is an illusion. Although a consumer demand model implies that acquisition is an unbiased estimate of usual consumption, we demonstrate empirically that the difference between these two quantities can be substantial. For example, the likelihood of measuring less than half of the actual value of usual consumption with a diary is 15.1% and 14.1% for households in the first and fourth consumption quartiles, respectively. The likelihood of attributing a value for usual consumption at least twice the size of the actual one is 4.1% and 3.7% for these households, respectively. Importantly, we find that diary errors remain large for perishable components of food, which implies that our conclusions are not mechanically driven by consumption from stocks or large cash outlays. We conclude that, if enumerator visits are effective to reduce misreporting in diary entries, mistaken conclusions about welfare measurement from diary data must primarily depend on how households decide to smooth their consumption rather than on the frequency of acquisitions. This implies that even when error-free measurements of consumption in the interview week are attained, misleading conclusions about actual well-being could still ensue, as well-being is a longer-run average of weekly intakes.

Our investigation does not find evidence of zero-mean or classical errors in recall data, which is a conclusion often conjectured in the literature. Our research design allows us to prove this conjecture, and also provides guidance on how to sign the bias from recall errors in empirical work. Specifically, we show that – in our case study – overreporting of usual consumption is between three and four times more likely than underreporting. This finding is not only consistent with telescoping effects but also with more general cognitive errors by respondents when they compute the market value of their consumption. Moreover, we find that the quality of recall data improves with the actual value of usual consumption, which suggests that errors may be comparatively less important for households with higher permanent income and human capital.

Further, the above properties of survey errors have important consequences for the computation of aggregate welfare statistics in our study. Precisely, we find that diary errors yield poverty rates and inequality figures that are less reliable than those obtained from recall data, which yield uniformly larger probabilities of correct classification for households with low usual consumption. However, we also find that the upper tail of the distribution of usual consumption is closer to that from diary data, suggesting that deciding which survey measurement will work best ultimately depends on the policy question of interest.

What are the implications for the design of household surveys? First, there is no loss in accuracy from using a recall module despite the higher costs of using a diary: a recall survey is almost as close to the optimal design as a diary when inequality measurement is of concern. The choice of the most appropriate collection mode can be seen as the solution to a decision problem in which each household is assigned to a diary or a recall module to minimize the overall impact of survey errors. We therefore study which assignment would make the inequality and poverty measurements computed from raw data as close as possible to their true values. We show that the optimal solution to this problem is a mix of diaries and recall interviews, with relatively more well-off households assigned to diaries. Although a 4