# **4.1. Methodology**

The pass-through rate is estimated using equation 5 above. Following Ravallion (2003), the regression is estimated without an intercept. Improving on the earlier literature, we only include growth spells between household survey rounds that are comparable in order to focus on real changes between two survey rounds and ignore any spurious changes. Survey comparability is assessed according to various characteristics, including the method of sampling, the questionnaire design, the methodology used in the construction of welfare aggregates and the price deflation used over time and space.<sup>19</sup> We use the growth in per capita HFCE as opposed to growth in per capita GDP, as HFCE aims to capture household private consumption in national accounts, and so it is, in principle, more aligned with the consumption captured in surveys than GDP (Ravallion (2003), Deaton (2005)). Similarly, to derive reference-year estimates in the absence of a new household survey, PovcalNet uses HFCE over GDP in most countries, including India (Prydz, et al. (2019)).<sup>20</sup> A crucial question is how to define the relevant sample of survey growth spells. The existing literature has partitioned the sample along various dimensions, for instance by income level, level of inequality or by geographic regions. See, for example, Birdsall et al. (2014), Chen and Ravallion (2010), Chandy et al. (2013) and Corral, et al. (2020). Given that different choices of partitioning variables yield different pass-through rates, a systematic approach of partitioning the data is necessary.

To that end, we follow an approach that is identical to the machine learning algorithm used in Lakner et al. (forthcoming).<sup>21</sup> Here, we use per capita HFCE growth instead of per capita GDP growth as the main independent variable. The partitioning algorithm, referred to as model-based recursive partitioning (MOB), takes equation 1 as the starting point and subsequently adds various input variables interacted with the growth in per capita HFCE, gNAS. Each interaction is added one at a time. For each interaction a Wald test is conducted to determine whether the coefficients on these interactions are statistically significant (at the 5 percent significance level). The input variables are geographical region, a dummy for whether consumption or income is used in the survey, mean consumption, median consumption, the Gini index, population, per capita GDP, and the year of the survey.<sup>22</sup> When a significant interaction is found, the sample is partitioned using that input variable as a splitting variable and the algorithm is applied on each of the sub-samples separately. Splits are only made if at least 10 observations will be in each subsample. For non-

> 19 The precise assessment of comparability is country-dependent, compiled from the World Bank’s economists who are in close dialogue with national data producers and have intimate knowledge of the survey design and methodology. More details on the comparability metadata can be found in Atamanov et al. (2019). The comparability data set can be accessed here: https://datacatalog.worldbank.org/node/506801.

> 20 The exception is Sub-Saharan Africa, where GDP per capita is preferred.

> 21 The algorithm is a variant of Classification and Regression Tree (CART), pioneered by Breiman, et al. (1984).

> 22 We consider two regional definitions. First, the standard World Bank regions, in which all countries are classified according to geography. Second, the regions used by PovcalNet, where most high-income countries form a separate region.

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