# **Appendix 1: Comparison with Deaton (2005) and Ravallion (2003)**

In this appendix, we compare our estimates of the gaps between household surveys and national accounts with earlier studies by Deaton (2005) and Ravallion (2003). Before discussing the differences, we discuss several reasons for why the methods and data differ.

The most important difference is that our analysis is based on significantly more countries and years. Since the time of the Deaton (2005) and Ravallion (2003) papers, there have been significantly more household surveys accessible for comparisons. We match 2,020 household survey means to estimates of HFCE from national accounts, and 2,052 surveys to estimates of GDP. Deaton (2005) presents estimates from matching 543 survey means to HFCE (277 consumption and 266 income surveys) and 272 income means surveys to GDP. Ravallion (2003) uses only 88 observations when assessing differences in levels, 52 for consumption surveys and 36 for income, matched to both GDP and HFCE.

Our analysis covers four decades, from 1977 to 2019, a much longer and more recent time period than previous assessments. Ravallion uses surveys from a little more than a decade, spanning from 1985 to 1998, while Deaton uses surveys from 1979 to 2000. Although our time periods overlap, we have data from different years and surveys in the overlapping periods, so reconstructing the exact same samples used by previous studies with our data is not possible. One reason for this is that since the time of the previous studies, data have been revised, removed or added to both national accounts and household survey collections. National accounts series are revised with irregular intervals, and past HFCE and GDP estimates are recomputed using new methods and data. Therefore, we use a vintage of the national accounts data that is different, even for the same years and countries. Similarly, survey data is sometimes revised, or could also be removed. Deflators – both for surveys and national accounts are also often revised – but are not a concern in our assessment of gaps levels, as we rely on survey and national accounts data in the current values.

In terms of methodology, in our analysis we use weights that differ from those used in Deaton. Our preferred weighting scheme is to give each country equal weight within each sub-sample for which we provide estimates. Ravallion uses only one observation per country and thus also give each country equal weight. Deaton uses two weighting schemes. The first is unweighted – giving each observation equal weight regardless of the number of observations per country, and a second uses population weights.

Given the differences in both the time periods covered, data sources, and weighting methods, it is useful to try to understand the source of the differences. To this end, we examine our estimates by decade. About three-quarters of our observations are from the period after 2000, a period not covered by either of the previous studies. Thus, our overall estimates are heavily weighted towards a time period not covered by earlier studies. The HHS-NAS gap estimated separately for each decade (see Table 1) reveal much smaller gaps for the periods prior to 2000 also in our data. Comparing survey and HFCE means, we estimate a gap of about -15% in the 1980s and 1990s and about -25% for the 2000s and 2010s, a difference which is statistically significant (t=2.38 when comparing 1990s and 2000s samples). Our point estimates of around -15% for 1980s and 1990s are similar to the corresponding estimates of gaps of -12% and -17% for Deaton and Ravallion, respectively. The fact that our sample is heavily weighted towards more recent years than previous studies, contribute to our overall finding of larger gaps than those established by Ravallion (2003) and Deaton (2005).

To further compare our findings with those of Ravallion and Deaton, we next subsample from our data only those observations where we have an exact year match for each country and survey type (i.e., income or consumption) with the analysis of theirs. The resulting match is far from complete, reflecting the revision and removal of many data points during the 1980s and 1990s. For the sample used by Deaton, we