# **1. Introduction**

The estimation of poverty in any given country relies on household surveys that contain information on income, consumption or expenditure (Household Expenditure Surveys, or HESs for short). This information is complex to collect and requires elaborated and time consuming questionnaires that result in costly surveys. For this reason, statistical agencies worldwide have taken to the practice of administering relatively small surveys (usually in between 5,000 and 10,000 households) at intervals of several years (usually every 4-5 years).

This practice is sensible from a logistics- and cost perspective but has two main drawbacks for the measurement of poverty. The first is that small surveys can provide statistically reliable statistics only for highly aggregated areas such as rural and urban areas or large sub-national regions. And the second is that poverty statistics can only be produced in conjunction with the HES surveys every several years, leaving researchers with no information on poverty for the periods between any two surveys or beyond the most recent survey.

To address these two shortcomings, we advocate the use of imputation methods to fill these data gaps. Imputation methods have a long history in statistics and economics and have been used to address a variety of missing data problems; see e.g. Rubin (1978 and 1987). While originally conceived to fill data gaps within surveys, these methods have also been extended to cross-survey imputation where one survey is used to fill data gaps of another survey belonging to the same population. A recent review of these methodologies by Ridder and Moffit (2007) shows how widespread these methodologies have become, and how they can be adapted to respond to different types of missing data problems. See also Fujii and van der Weide (2013) and the references therein.

In the context of poverty analyses, imputation methods have found numerous applications to address statistical inference problems across space and time. For example, Elbers et al. (2002, 2003, 2005) combine census and survey data to estimate poverty and inequality for areas considered too small for statistical inference with survey data alone, an exercise known as “poverty mapping”. For an overview of the statistics literature on small area estimation, see Rao (2003). One could alternatively also work with large surveys instead of censuses such as Demographic and Health Surveys (DHSs) to obtain imputationbased poverty estimates. Examples of the latter are Stifel and Christiaensen (2007) and Grosse et al. (2009) who used DHSs to respectively estimate poverty in Kenya and Bolivia. More recently, Christiaensen et al. (2012) used data from Vietnam and China to create a pseudo-panel out of repeated cross-section HESs using imputation methods.

Cross-survey imputation techniques have also been used to resolve problems of comparability between surveys of the same type over time, for example due to changes in the questionnaires. Kijima and Lanjouw (2003) and Tarozzi (2007) have re-estimated poverty rates in India using imputed data in an effort to validate the official figures on poverty during what became known as the “great Indian poverty debate” (see e.g. Deaton and Kozel, 2005).

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