category of consumption (e.g., total expenditure on flour) instead of individual items (e.g., expenditure on corn flour, wheat flour, etc.). However, altering the set of items in the questionnaire can result in a nontrivial change in the reported consumption amount (Olson-Lanjouw and Lanjouw 2001). Both approaches are likely to lead to an underestimation of consumption and overestimation of poverty, as was demonstrated in a study in Tanzania that directly compared various methods of measuring consumption (Beegle et al. 2012).

An alternative approach is to apply methods of cross-survey imputation. In situations where full household expenditure surveys are too costly or impractical to administer, data gaps can be filled using other surveys that have common covariates that are correlated with household expenditure. For example, data from a full consumption survey can be combined with data from shorter and more frequent labor force surveys to generate poverty estimates (Douidich et al. 2013). While such methods may work well even when there is a rapid economic change (Christiaensen et al. 2011), the assumption of a stable structural parameter typically cannot be tested and may not be valid, especially in the context of large and systemic shocks, after implementation of projects, or if a substantial amount of time has passed since the baseline survey was implemented. It is also possible to design a survey such that one sample has a full consumption module and another sample has only the covariates of consumption. Consumption can thus be imputed and poverty estimates can be derived at a reduced cost, even though the magnitude of potential cost reduction may be modest (Fujii and van der Weide 2016). In such a setup, however, the sample for the full consumption module must be chosen randomly to avoid biased estimates of the model parameters. Thus, this approach is only of limited usability in the case of fragile countries as it might not be feasible to administer the full consumption module in particular insecure areas, creating a downward bias in poverty estimates for those areas.

The proposed methodology uses statistical imputations to obtain estimates for deliberately absent consumption values. Statistical imputation techniques are widely used to replace missing values in surveys (Little and Rubin 2019; Ambler, Omar, and Royston 2007; Van Buuren 2007). Straight-forward methods simply replace the missing values with aggregate statistics like a mean. However, this makes the strong and often violated assumption that data are missing at random (Carpenter, Kenward, and White 2007). Model-based approaches can take into account covariates and often use a regression framework to estimate missing values but distort the variance if based on point-estimates. Multiple imputations help to mitigate this by drawing multiple estimates from the posterior distribution using a Bayesian approach (Rubin 2004).

This paper is organized as follows. We first present the proposed methodology with its statistical properties as well as the data in Section 2. In Section 3, we apply the methodology to different scenarios showing the trade-offs between the performance and parameters of the approach, and then compare it to a reduced consumption approach as well as a more sophisticated reduced consumption approach adjusting the poverty line. The section ends with a real-world example based on a pilot survey in Kenya, assessing the performance of the new methodology and comparing it to a cross-survey imputation approach. The paper finishes with Section 4 concluding the findings and discussing some of the limitations of the new approach.

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