The set of covariates typically includes similar demographic variables to those used in traditional poststratification adjustment. Harris Interactive, a market research agency, includes demographic and nondemographic variables in the propensity models (Terhanian et al., 2000; Taylor et al., 2001). Rubin and Thomas (1996) suggested including all covariates, even if some are not statistically significant in predicting the outcome variables unless they are unrelated to the treatment outcomes or inappropriate for the model. By the same token, Li, Morgan, and Zaslavsky (2018) proposed that a rich propensity score model, rather than a parsimonious one, is desirable, especially in causal inference applications, because the ignorability assumptions are likely to be violated if the propensity score is only a simple logistic-linear function of the covariates, but both the outcome and assignment mechanism are functions of more complex interactions or nonlinear terms. On the other hand, Lee (2006) suggested that the importance of including non-demographic variables in PSW for web surveys is unclear due to two facts: (1) the inclusion of more variables automatically increases the predictive power of the model, but (2) non-demographic covariates can often be explained by demographic variables, to some degree.

While there has not been a rule of thumb on what variables should be included in the PSW procedure, in the simulation study by Drake (1993), the impact of specifying incorrect propensity score models, such as mistakenly adding a quadratic term or dropping a covariate, was not very serious. In fact, the misspecification of the propensity score model led to only a small bias compared to the misspecification of the response model that was used to simulate the response distribution (Drake 1993).

However, if the reference survey was collected a few or more years before the phone survey, it is recommended not to include covariates that are likely to change drastically over time. PSW balances the phone survey with the reference survey using propensity scores estimated with household-level covariates from both surveys. Some covariates, such as asset ownership or employment conditions, may have changed over the period. For example, if a country grows rapidly, asset ownership and employment conditions can change greatly in only one to two years. If these time-varying indicators were included in the propensity score regression, PSW would match these indicators as if they were constant over the interval between the reference and phone surveys. Such false matching could cause a significant bias in poverty projections. Therefore, we recommend using timeinvariant covariates for the propensity score regression, particularly if the interval between the phone and reference surveys is long. Variables that are usually included in the PSW procedure are household size, dependency ratio, and household locality (urban/rural). If applicable, additional variables such as the highest educational attainment of the household head, age of the household head, sex of the household head, geographical characteristics of the household, and dwelling characteristics of the household can also be included in the PSW procedure as predictors of a household’s probability of being reached by phone.

# _II.3. Non-PSW adjustments_

PSW has good statistical properties in correcting for sampling biases by adjusting sampling weights to match the distribution of target indicators at the household level. Nevertheless, even with PSW-based weight adjustments, the means of time-invariant indicators, such as average household size, can still differ between a phone survey and a reference survey. PSW makes the two surveys comparable, but not perfectly so; some presumably time-invariant variables may still exhibit significant differences in means between the reweighted phone survey and the reference survey. Such remaining non-negligible differences can also cause bias in poverty projections.

Another limitation of PSW is that it cannot be executed if household unit records are unavailable in reference data. Although some statistics representative of a population interest are easily available from official sources, the source data may not be readily available. For example, regional population shares are updated frequently by the Bureau of Statistics of many countries, but the source data is not readily available on a timely basis. Under this circumstance, PSW cannot be used for reweighting.

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