differences between the two groups. Propensity scores are often estimated to address this issue of noncomparability. A propensity score is the probability of selecting a sample household or individual into the treatment group from the population, conditional on covariates. If a set of assumptions is satisfied (see Rosenbaum and Rubin 1983 and 1984 for details), a comparison of the weighted average of the outcome indicators between the control and treatment groups provides an unbiased estimate for the treatment effect.

Taylor (2000) and Lee (2006) adopted the propensity score matching technique to adjust sampling weights and correct for sampling bias in a web survey. First, they chose a reference survey representative of the population of interest (e.g., the entire population of a country, the urban population, or all refugees in a country). They combined the reference and web surveys and estimated propensity scores using this combined sample. They then divided the combined sample into quintiles based on the propensity scores and adjusted the sampling weights of the web survey to equate the sum of the weights of the web survey with those of the reference survey in each quintile.

Another type of propensity score weighting method is “inverse probability approach,” which uses propensity scores to construct the odds of a sample being selected for a reference survey, and the odds are further used as a sampling weight of a web or phone survey (Morgan and Todd 2008, Schafer and Kang 2008, and Austin 2011). This paper classifies these types of reweighting techniques based on propensity scores as Propensity Score Weighting (PSW) methods. If the assumptions in Rubin and Rosembaum (1983 and 1984) are satisfied, then summary statistics applying PSW-based weights in a web or phone survey become representative of the population of interest.

A second category of reweighting techniques, which we refer to as non-PSW approaches, matches indicators between a phone or web survey and a reference survey at a more aggregate level than at the household/individual level. This group of approaches includes raking, post-stratification, and maxentropy. The non-PSW approaches select a set of indicators and adjust sampling weights so that weighted averages of the selected indicators are closely/exactly matched between a phone/web survey and a reference survey.

PSW and non-PSW adjustments are often conducted together. We consider two advantages of the combined applications of PSW and non-PSW approaches. First, for PSW to eliminate sampling bias, a set of assumptions, like strong ignorability, need to be satisfied, which cannot be easily tested, for which non-PSW serves as a complement for weighting purposes. Second, non-PSW approaches match the means of key indicators between a phone/web survey and a reference survey, but there is no guarantee that the distributions of these indicators are also matched. PSW approaches, by contrast, match the distribution of propensity scores. Since both approaches have their own strengths, conducting both PSW and non-PSW adjustments is reasonable.

This paper investigates whether reweighting can correct the bias of poverty projections produced by the SWIFT methodology. The performance of reweighting techniques differs by data and target indicators that were matched, and there is agreement in the literature that reweighting techniques reduce the biases in target statistics yet do not eliminate them (Lee (2006) and Dreze and Somanchi (2023)). Dreze and Somanchi (2023) created biased samples by dropping poorer households from a household survey and tested whether a non-PSW reweighting technique (maximum entropy reweighting, or maxentropy) can reduce biases in poverty rates and mean household expenditures. Although the biases in poverty rate estimates and means of household expenditures declined, substantial proportions remained.

However, existing literature lacks an assessment of how well reweighting techniques can reduce the biases of poverty projections produced by SWIFT or any other poverty projection method. Using phone or web surveys to estimate poverty necessitates the use of poverty projection methods. Dreze and Somanchi (2023) used actual consumption and income data and showed that a large bias in the poverty rate and mean household expenditure remains even after reweighting but did not assess if reweighting combined with poverty projection methods is 3