Haslett (2016). Still, ELL’s is arguably the most frequently used poverty mapping approach combining survey and census data. According to Elbers and van der Weide (2014), it has been applied in more than 60 countries. Some examples for the application of ELL, including in areas other than poverty mapping, are Healy et al. (2003), Demombynes and Ozler (2005), Elbers et al. (2007), Araujo et al. (2008), Agostini<sup> ̈</sup> et al. (2010), Bui and Nguyen (2017) and Gibson (2018).

A key assumption for the applicability of ELL is that the distribution of the explanatory variables is the same in both census and survey. This assumption will often be violated if time has passed between data collection for the census and survey, i.e., only a dated census and a more recent survey are available, a common situation as censuses are usually conducted less frequently than surveys. Reasons for a violation of this assumption may include demographic trends, migration, natural disasters, and conflicts. If the population parameters, including the regression coefficients, remain unchanged but the distributions of the explanatory variables change over time, ELL results in an outdated poverty map, namely a poverty map at the time of the census. If both the population parameters and the explanatory variables change over time, it is not quite clear what is obtained, but generally not an up-to-date poverty map.

The discussed assumptions on the explanatory variables can be relaxed if household characteristics from the census are used to explain consumption values from the survey in the first stage to obtain parameter estimates. These can then be used to predict consumption values using the census data in the second stage. As it is usually impossible to match households between a census and a survey, the estimation needs to be conducted at a higher geographical level, for instance at the level of census enumeration areas. Throughout this paper, we will refer to the generic term of clusters as the lowest level at which census and survey information can be matched. If the assumptions on the explanatory variables hold, this aggregation may worsen the prediction accuracy vis-`a-vis ELL, with the magnitude of the loss of precision hinging on the regression model in the first stage. Note that ELL also propose the additional use of census means to explain location effects, i.e. cluster-specific effects. In this regard, our approach can be considered as a variant of ELL without the use of household-level variables included in both census and survey and without reliance on the associated assumptions. When we refer to the ELL method throughout this paper, we have in mind an estimator that combines survey and census variables at the household-level, the central idea of the approach.

In the case that at least one of the underlying assumptions of ELL is violated, our new approach will still produce up-to-date poverty maps with unbiased poverty estimates. The key assumption we introduce is that _aggregate_ household characteristics from the old census relate to consumption the same way in clusters covered by the new survey as in clusters not covered by the new survey. This assumption will hold (on average) if clusters are randomly drawn. Note that a similarly weak assumption has to be made for the applicability of the ELL method if the census and survey are conducted at the same time, namely 3