Variables in the matching conditions (1) need to be time-invariant between the reference and phone surveys if the phone survey is carried out a few or more years after the reference survey. If the socioeconomic environment is changing rapidly and the summary statistics of some variables are likely to change after the reference survey was conducted, these variables should not be included in the matching conditions as if they were constant. Therefore, we recommend including only time-invariant or slowly changing variables in the matching conditions. For example, the average household size or the dependency ratio usually takes time to change. Also, housing conditions cannot be changed quickly, even if a large shock like the COVID-19 pandemic occurs.<sup>4</sup> On the other hand, employment conditions and economic sentiments can change very quickly and are therefore not recommended to be included as matching conditions for the maxentropy command.<sup>5</sup>

# <u>Raking</u>

Raking, also referred to as “iterative proportional fitting,” is an algorithm that consists of an outer cycle that checks convergence criteria and an inner cycle that iterates over the control variables. Once the phone survey with updated weights shows convergence along a certain control variable, the algorithm moves to the next control variable and adjusts the weights until convergence on that variable. The process continues until the weights achieve convergence along all specified variables (Kolenikov 2014).

Capacci et al. (2018) recommended raking after PSW to balance the means of key variables between a survey of interest and a reference survey. This subsection introduces raking as a way of balancing the means of key variables after PSW is conducted.

Like maxentropy, variables included in the raking procedure need to be time-invariant between the reference and phone surveys. Some examples include household size (discretized into 3 to 4 categories), dependent share (discretized into 4 to 5 categories), household locality (rural/urban), highest educational attainment of household head, gender of household head, age of household head, geographic variables, and time-invariant asset/dwelling characteristics (wall, roof, fuel, toilet conditions, etc.).<sup>6</sup> For the detailed Stata codes for implementing raking, we recommend referring to Kolenikov (2014), which describes this procedure in more detail. The Stata codes are readily available as user-written commands.

4 Some potential candidates for the maxentropy procedure include, but are not limited to, polynomials of household size, dependency ratio, household locality (urban/rural), the highest educational attainment of the household head, age of household head, sex of household head, geographical characteristics, dwelling characteristics (roof/wall/fuel type/toilet type), and occasionally assets that cannot be easily replaced (refrigerator, washing machine, etc.).

> 5 As a sidenote on the implementation of maxentropy in STATA, incorporating too many matching constraints (1) to the maxentropy procedure may result in non-convergence errors and the STATA command may fail to find optimal weights. If so, some matching constraints must be dropped. To minimize the impact on the national averages for the population of interest, it is recommended to drop the matching conditions involving only a limited number of households. For example, if household shares are considered time invariant, they can be matched between the reference and phone surveys. However, including all district level household shares in the matching conditions may result in non-convergence of the algorithm. As a remedy, one can drop the least populous district in each attempt until the maxentropy algorithm converges. This procedure makes the household shares from the most populous districts exactly matched with the reference survey, leaving those in the least populous districts not necessarily matched. However, since the impact of the least populous districts on the national average is minimal, the resulting bias in the national statistics is also minimal.

6 Since raking can only include discrete variables, continuous variables always need to be discretized before including them in the raking procedure. If raking does not perform well with the discretized variables, such as household size, making the categories finer and redoing the raking process may yield better results.

10