combined-sample <mark>imputation following Rendall et al. (2013). Initially, this te</mark> chnique was developed to correct for missing values on items from survey data. The method was expanded to cases where variables are not present by design because the question was not asked at all. To still allow for the same adequacy definition across the sample of 64 countries (all seven adequacy dimensions aggregated into _AHI_ <mark>), we pool two nationally representative surveys (a) the countries</mark> HCES <mark>and (b) the respective De</mark> mographic and Health Survey (DHS) which both provide standardized information on a range of housing conditions to impute existing DHS data into HCES. We consider <mark>DHS as the “donor” survey and the H</mark> CES <mark>as the “recipient” survey. We take variables in common between the two data sets (i.e., location and wealth quintile of HH) to identify HHs with common characteristics in both samples to then impute on the</mark> _<mark>missing</mark>_ <mark>dimension.</mark> <mark>Two conditions must be satisfied for unbiased estimates (Rendall et al. 2013). First, the two pooled samples must be drawn from the same underlying population or “universe”</mark> (Carrig et al. 2015, Rendall et al. 2013; Rubin 1986). This assumption allows to treat the unobserved variable in the recipient survey as missing by design since the question has not been asked, which justifies the imputation across surveys (e.g., Gelman et al. 1998). <mark>Second, a number of variables must be “jointly observed” in both the donor and the recipient samples. Van Hook and colleagues (2015) demonstrate that the violation of the latter condition results in severe bias both in magnitude and direction.</mark> <mark>For our purpose, both conditions are satisfied: Both DHS and H</mark> CES <mark>are nationally representative household surveys that collect a large range of variables on housing conditions. Further, location and household size are jointly observed in DHS and H</mark> CES <mark>. While DHS does not collect information on expenditure or income</mark> _<mark>per se</mark>_ <mark>, the survey still calculates a wealth quintile based on other available data collected which are closely correlated with wealth.</mark> <mark>Countries where DHS data were imputed include Albania (structural quality and cooking), Bangladesh (structural quality and cooking), Colombia (cooking), Ethiopia (structural quality), Indonesia (overcrowding), Nepal (structural quality), Pakistan (structural quality and cooking), Philippines (structural quality and cooking), and Senegal (cooking). For India and Mali, due to data quality issues in the H</mark> CES combined with rather old survey data (2011 and 2009 respectively <mark>), we reverted to DHS for all seven adequacy dimensions. For five countries</mark> (Kazakhstan, Russian Federation, Ukraine, Uzbekistan, and Vietnam <mark>) imputation was impossible due to missing data in both the H</mark> CES <mark>and DHS surveys and one dimension remains missing. Overall, this implies that we are potentially underestimating the inadequacy for those countries where data on one adequacy dimension is missing as a stricter definition of adequacy has shown to increase housing deficit estimations (cf. World Bank 2021).</mark>