This combined approach of (1) PSW, (2) maxentropy/raking, and (3) post-stratification preserves the target variable distributions within each region (cell), meanwhile ensuring that the cross-region (cell) household shares are identical to the reference survey.

# **III. Experimental studies on how reweighting procedures and SWIFT poverty projections affect poverty estimates**

This section conducts a series of experiments to examine how reweighting procedures and SWIFT modeling affect poverty estimates and other statistics.

First, we create artificially biased subsamples by selecting phone owners from the following reference surveys: Rwanda Integrated Household Living Conditions Survey (EICV) 5, Saint Lucia Household Budget Survey (HBS) 2016, and Uganda Refugee and Host Communities Household Survey (URHS) 2018. These surveys were selected because they are representative of the population of interest in each context and were used as the reference surveys for the pilot of the high-frequency phone surveys implemented by the World Bank (see more details in Yoshida et al., 2022b). Second, we estimate poverty rates among these biased subsamples by applying each of the following methods: 1) selected reweighting procedures alone among the actual consumption data in the phone survey (without SWIFT), 2) SWIFT poverty projection models trained with the reference data,<sup>7</sup> and 3) combinations of SWIFT and reweighting procedures. Finally, we compare each generated poverty rate with the actual poverty rates estimated using the consumption data in the reference survey. A smaller difference suggests better performance of the method in adjusting for the bias in poverty estimates produced using phone owner samples.

We separately examine the following reweighting procedures: (i) original weights; (ii) PSW proposed by Lee (2006), (iii) inverse propensity score approach, and (iv) PSW (Lee 2006) with non-PSW adjustments (maxentropy, raking and/or post-stratification).

Second, we conduct the experiment above using a sample of Ethiopia HFPS7, which was collected based on the ESS4 sample. The subsample is subject to both sampling and nonresponse biases. Using this subsample, we examine whether reweighting procedures and the SWIFT poverty projections combined can reduce sampling and nonresponse biases in poverty estimates.<sup>8</sup>

# _III.1 Results from experiments with Rwanda EICV5_

Phone ownership is 65.8 percent in Rwanda (9,589 out of 14,574 households own a mobile phone, according to EICV5). As shown in Table 2, the phone owner subsample is significantly wealthier in terms of asset ownership and housing conditions. For example, bicycle ownership among phone owners is 18 percent compared to 13 percent in the full national sample. However, the average household size, which is usually negatively correlated with household welfare, is about 6.8 percent higher in the phone owner subsample than in the full sample (Table 2). While these two effects offset each other, the actual poverty rate of the phone subsample (29.3 percent) is significantly lower than the national average (38.2 percent), indicating that the phone owner subsample is wealthier than the entire population (Figure 2).

Three types of weights were calculated to adjust for the sampling bias in the phone owner sample of Rwanda EICV5, namely, PSW (Lee), PSW (Inverse), and PSW & non-PSW. The first subfigure in Figure 2 compares the poverty rates of the phone owner sample by applying the abovementioned weights to the actual consumption data. The poverty rates among the phone owners applying original weights, PSW (Lee) weights, PSW (Inverse) weights, and PSW & non-PSW weights are 29.3%, 31.4%, 32.0%, and 31.9%, respectively. While the last three poverty rates with adjusted weights are higher than the poverty rate of the phone owner sample

> 7 In the COVID-19 HFPS for Rwanda, we prepare models for urban and rural areas separately; for Saint Lucia and Uganda (refugees), we prepare only one national SWIFT model.

> 8 This analysis is added based on suggestions from peer reviewers of the World Bank’s quality enhancement review.

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