metadata: authors: 0: author: Mahler,Daniel Gerszon
1: author: Schoch,Marta
2: author: Lakner,Christoph
3: author: Minh Nguyen Nguyet Do
count: World
docna: 0: docna: Predicting Income Distributions from Almost Nothing
docty: Policy Research Working Paper
abstracts: cdata!: This paper develops a method to predict
            comparable income and consumption distributions for all
            countries in the world from a simple regression with a
            handful of country-level variables. To fit the model, the
            analysis uses more than 2,000 distributions from household
            surveys covering 168 countries from the World
            Bank&#x2019;s Poverty and Inequality Platform. More than
            1,000 economic, demographic, and remote sensing predictors
            from multiple databases are used to test the models. A model
            is selected that balances out-of-sample accuracy,
            simplicity, and the share of countries for which the method
            can be applied. The paper finds that a simple model relying
            on gross domestic product per capita, under-5 mortality
            rate, life expectancy, and rural population share gives
            almost the same accuracy as a complex machine learning model
            using 1,000 indicators jointly. The method allows for easy
            distributional analysis in countries with extreme data
            deprivation where survey data are unavailable or severely
            outdated, several of which are likely among the poorest
            countries in the world.
display_title: Predicting Income Distributions from
            Almost Nothing
listing_relative_url: /research/2025/01/34445442/predicting-income-distributions-almost-nothing
topicv3: Poverty Measurement and Analysis m1326941 707,Household Surveys m1504071 2761
publishtoextweb_dt: 2025-01-13T00:00:00Z
dois: 10.1596/1813-9450-11034
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 41
author_keys: 0: author_key: 1539953
1: author_key: 1857360
2: author_key: 1206398
3: author_key: NA
model_extractions: Policy Research Working Paper 11034

# Predicting Income Distributions from Almost Nothing

_Daniel Gerszon Mahler_ _Marta Schoch Christoph Lakner Minh Nguyen Jose Montes_ Development Data Group & Poverty and Equity Global Department January 2025
Policy Research Working Paper 11034

# **Abstract**

This paper develops a method to predict comparable income and consumption distributions for all countries in the world from a simple regression with a handful of country-level variables. To fit the model, the analysis uses more than 2,000 distributions from household surveys covering 168 countries from the World Bank’s Poverty and Inequality Platform. More than 1,000 economic, demographic, and remote sensing predictors from multiple databases are used to test the models. A model is selected that balances out-ofsample accuracy, simplicity, and the share of countries for which the method can be applied. The paper finds that a simple model relying on gross domestic product per capita, under-5 mortality rate, life expectancy, and rural population share gives almost the same accuracy as a complex machine learning model using 1,000 indicators jointly. The method allows for easy distributional analysis in countries with extreme data deprivation where survey data are unavailable or severely outdated, several of which are likely among the poorest countries in the world.

This paper is a product of the Development Data Group and the Poverty and Equity Global Department. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/ prwp. The authors may be contacted at dmahler@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Predicting Income Distributions from Almost Nothing

Daniel Gerszon Mahler, Marta Schoch, Christoph Lakner, Minh Nguyen, Jose Montes<sup>1</sup>

## **JEL classification** : C53, D31, I32, O10

**Keywords** : Income, consumption, data deprivation, machine learning, poverty, measurement

> 1 All authors are with the World Bank. We are grateful for comments received from Roy van der Weide, Johannes Hoogeveen, Federico Haslop, Andres Fernando Chamorro Elizondo, Zander Prinsloo, Benjamin Stewart, Emi Suzuki, and the Global Poverty Monitoring Working Group of the World Bank. The authors gracefully acknowledge financial support from the UK government through the Data and Evidence for Tackling Extreme Poverty (DEEP) Research Programme.
# 1 Introduction

Household surveys are needed to measure poverty and design distributional policies, yet in several countries they are not conducted due to low statistical capacity, conflict, or lack of resources. In other cases, household surveys are collected but not shared with researchers and policy makers (Dang et al. 2019, Ekhator-Mobayode and Hoogeveen 2022). Lack of data disproportionally affects poorer countries, meaning that ignoring or not properly accounting for such countries in global analyses biases results.

We address these gaps by developing a method that through a simple regression can predict annual income and consumption (henceforth welfare) distributions with a credible distributional shape for each country. The method uses widely available social and economic indicators at the country level and does not require any household survey data for the country of interest. We explicitly search for a simple model that can be easily taken up in applied work and can work for the most data deprived countries. To estimate such a model, we leverage rich information on welfare distributions from more than 2,000 household surveys available in the World Bank’s Poverty and Inequality Platform (PIP), which covers 168 countries, using data between 1991 and 2020. For each of these surveys, we have distributions of daily per-capita household income or consumption expressed in purchasing-power-parity-adjusted dollars.

We sequentially remove one of the 168 countries from the sample and predict the excluded distribution for this country using the remaining 167 countries and various predictors. As potential predictors, we search among more than 1,000 candidate variables spanning multiple databases and including remote sensing indicators. After repeating this leave-one-out cross-validation for each of the 168 countries with available data, we compare the predicted distributions to the survey-based distributions, favoring models that minimize the prediction error.

We find that a model that uses GDP per capita, under-5 mortality, life expectancy, rural population shares, and regional dummies predicts welfare well, and that adding more information does not lead to any relevant gains. National accounts data stand out as the single best predictor of welfare, even, but to a lesser extent, in data-deprived countries. This suggests that notwithstanding the gaps between welfare from surveys and national accounts (Deaton 2005; Pinkovskiy and Sala-iMartin 2016, Deaton and Schreyer 2022, Prydz et al. 2022) and measurement issues with GDP in autocratic countries (Martinez 2022), GDP provides valuable information on welfare in contexts where household surveys are unavailable. However, about half of the countries are so datadeprived that they not only lack an income or consumption distribution, but also GDP. For these countries, we use World Bank income groups as a proxy, resulting in two tiers of models depending on whether GDP data is available for the country of interest.

These two tiers outperform models based on remote sensing data (e.g., nighttime lights, vegetation), which do not meaningfully lower the out-of-sample error if added to the models. This suggests that, on average, remote sensing data are worse predictors of welfare at the national level than GDP, which is consistent with evidence suggesting that remote sensing data might produce household welfare estimates very different from survey-based ones (Van Der Weide et al. 2024). This suggests that a relatively simple model using readily available data outperforms more complicated models using costly data.

2
We implement our preferred methods for all countries to estimate global poverty, benchmarking the results against poverty estimates published by the World Bank. We find that the models track poverty rates relatively well in general but with notable exceptions. We show that these errors are in part due to poverty estimates not being comparable across countries and within countries over time but surely also due to modeling errors.

On average, our preferred models predict income or consumption off by around 30%. While this is a large error, it is important to assess it against an appropriate benchmark. A random forest on all 1,000+ possible predictors does not lead to any gains in the out-of-sample error, suggesting that much of the remaining error is likely irreducible. Furthermore, at a global scale, a 30% error is small in comparison with the large observed income differences: The median welfare of the richest country in our sample is more than 100 times that of the poorest country, and the 75<sup>th</sup> percentile of medians is 5 times greater than the 25<sup>th</sup> percentile.

A long-standing literature has tried to overcome data gaps and predict distributions when limited information was available. Survey-to-survey imputations can be used when survey data on welfare is unavailable at a desired point in time, but data on correlates of households’ wellbeing is available together with welfare data from a prior household survey (Stifel and Christiansen 2007, Roy and Van Der Weide 2024). Alternatively, national accounts data can be used to extrapolate older welfare vectors forward in time (Mahler et al. 2022; Angrist et al. 2021). Others have estimated full distributions when grouped data or summary statistics are available (Chen 2018; Chotikapanich et al. 2012, Eckernkemper and Gribisch 2021, Jorda and Niño-Zarazúa 2019; Hajargasht et al. 2012). Wealth indices have been used to predict full distributions for individual countries that lack consumption or income data but have a Demographic and Health Survey (Filmer and Prichett 2001, Dang et al. 2019). However, all these methods require at least one survey-based welfare vector, thus making them inapplicable for countries that do not have any survey data.

Remote sensing data and mobile phone data have been used to predict mean welfare, the poverty rate, or another distributional statistic in a country in the absence of survey data (Pinkovskiy and Sala-i-Martin 2016; Blumenstock et al. 2015, Steele et al. 2017; Pokhriyala and Jacques 2017; Lee & Braithwaite 2022; Engstrom et al. 2022). However, these approaches do not predict full distributions. Given the multiple poverty lines and welfare measures used in practice (see for example Jorda et al. 2023, Decerf and Ferrando 2022, Kanbur et al. 2022, Jolliffe & Prydz 2021), using such a model for each relevant welfare metric would jeopardize the simplicity of our approach. Moreover, the remote sensing data needed for these approaches do not stretch back far in time for long-term time trends and are not always publicly available, making these methods difficult to implement for practitioners.

The remainder of the paper is structured as follows. The data and method are described in sections 2 and 3. Sections 4 and 5 present results and robustness checks. Section 6 applies the models to global poverty measurement, and section 7 concludes.

3
# 2 Data

Our primary data source is household survey data on disposable income or consumption available in PIP. We use data from 1,989 surveys covering 168 countries for the period 1991 and 2020. We exclude data before the 1990s as the quality was generally worse then, particularly for low- and middle-income countries. The data are standardized as far as possible but differences exist with regards to the method of data collection, and whether the welfare aggregate is based on income or consumption. We use information on per capita household welfare expressed in 2017 USD PPPs. We use PIP’s public percentile database (version 20230919), utilizing 99 percentiles on the distribution from each income or consumption vector. Concretely, we use the values of income or consumption such that the cumulative density function takes the following values {0.01, 0.02, ... ,0.99} . That is, we retain the 99 poverty lines that result in poverty rates of FF(yy) {1%, 2%, ... ,99%} . The final dataset consists of 196,903 quantile-country-year observations on pairs of daily per-capita welfare and the associated quantile in the distribution.

We combine this survey data with various possible predictors of welfare at the country level. We use data from the World Development Indicators (WDI) of the World Bank, which is one of the largest databases of country-year development indicators spanning a wide range of topics. The WDI contains information on around 1,400 indicators covering topics such as health, agriculture, education, climate change, infrastructure and more. We also use all data from the World Economic Outlook of the International Monetary Fund, which contains dozens of variables on macroeconomic indicators, and all data from the UN’s World Population Prospects, which contains dozens of variables on population, health, and demographics. We compliment GDP data from the sources above with estimates from the Madison Database (Bolt and Van Zanden 2024). We also use country and region classifications by the World Bank and data on political rights, civil liberties, and freedom status from the Freedom House.

In addition, we use remote sensing data available from the Google Earth Engine. We use data on nighttime lights, precipitation, temperature, impervious surface, cropland, the normalized difference water/snow/vegetation index, and the enhanced vegetation index. While spatial coverage of remote sensing variables is not a concern as they cover the earth’s entire surface, temporal coverage is at times limited. Nighttime light data, for example, dates back to 1992. To fit into this exercise, the remote sensing data need to be aggregated to the country-year level. We first aggregate them to annual data by calculating the mean, max, min, and standard deviation of each location (e.g., a pixel) over a year. Afterwards, we aggregate them spatially by taking the mean, max, min, and standard deviation of the annual data for a country. This gives 16 features for each type of variable. Nighttime lights are also converted to a per capita level by dividing the sum of lights by the population size. We weigh each grid equally, and hence the indices reflect, for example, the mean temperature in the territory of a country, not the mean temperature experienced by a person in a country. Given that many of the variables impact welfare through agriculture, it is not clear that population weighting (which would give a dominance to urban areas) would make them more related to welfare distributions. Yet we also add population-grid weighted estimates of temperature and rainfall from Gortan et al. (2024).

4
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We calculate the mean absolute deviation for every survey distribution available for a country, average these losses, and then aggregate over all countries as follows: L L =<sup>1</sup> L , � �L ~~�~~<sup>1</sup> � cc,tt CC cc,TT where is the number of surveys for a country with data and NN cc∈CC NN tt∈TT is the number of countries with surveys. Across countries, the frequency of surveys varies drastically and systematically with cc,TT CC NN NN income. For example, the average low-income country has 4 surveys between 1991 and 2020, compared with 20 surveys in the average high-income country. To ensure that we do not select models that only work well for countries with many surveys, our aggregation formula weighs each country by the inverse of its number of surveys, such that the total weight for each country equals one. We multiply the final loss by 100 such that the loss approximately equals the average error in predicting welfare in percent. Our loss function and use of a linear model to predict leads us to estimate equation (3) using a quantile regression. Quantile regressions estimate the parameters while minimizing the llGG(yy) absolute size of the error, which is consistent with our loss function. As a robustness check, we also use OLS, which minimizes the sum of squared errors, and hence is consistent with a mean squared error loss function (see section 5.1).

# 3.3 Model selection

The selection of our preferred model is not only guided by the loss function, but also by three additional principles, which we define below: simplicity, useability, and coherence.

With respect to _simplicity_ , we prefer models that can be applied easily, which is in part why we use a linear model. One challenge with a linear model is that missing values in the covariates cannot be handled easily. A potential solution is to impute the missing values, but this would make the model intractable. To keep the framework simple, we will only use one covariate with missing values, and otherwise restrict the model to covariates with at most 1% missing values. This results in two tiers of models, one where the covariate with more than 1% missing values is available and one where it is not. We allow for 1% missing values in other covariates because some of the databases we use exclude certain economies for political reasons (notably Taiwan, China; and Kosovo), yet data are often available for these excluded economies from country-specific sources. So in practice, the second tier model can be applied everywhere. To select the primary variable of interest, we will compare the error from regressions of the type shown in equation (4) but replacing GDP per capita sequentially with all covariates in our dataset.

By _useability,_ we mean that the model can be applied and performs relatively well even in the most data deprived contexts. The tier 1 covariate is selected based on a balance of predictive accuracy and non-missingness. By construction, our tier 2 model will only use covariates available for virtually all countries, and can hence be applied everywhere. Even if the model can be applied everywhere, it is possible that the relationship between welfare and covariates is fundamentally different for data deprived countries. Martinez (2022) for example finds that GDP growth is less reliable for authoritarian countries, which also tend to be the ones that do not produce or publish 8
survey data. To ensure that our model works well for data deprived countries, we check if our model selection and performance are robust to using only the countries with at most three poverty estimates, which reflects the 25% most data deprived countries for which we have some data. These countries tend to be more authoritarian and conflict-ridden but also include a couple of wealthy countries which simply do not share much data (Table A.1).

With respect to _coherence_ , we mean that we are willing to tolerate marginal increases in errors if doing so results in a model that is easier to rationalize. This is in part why we are restricting ourselves to predictions consistent with the log-logistic distribution, but it also matters for the covariates we will select. For example, if we find that a model using GDP per capita in 2011 PPPs performs slightly better than a model using GDP per capita in 2017 PPPs, we will favor the latter as the welfare distributions are expressed in 2017 PPPs, and hence makes for a more consistent model.

The use of these three principles in addition to the error of the model means that, at times, value judgments are needed to assess when an increase in the error may be merited by a greater adherence to the three principles. This complicates the model selection somewhat in contrast to a sole reliance on the model error. As a robustness check, we use machine learning to select a model guided exclusively on model performance as a test of how much accuracy we give up by including these three additional principles (section 5.2).

# 4 Results

Our first objective is to select the main variable to use for the tier 1 model. To that end, we run separate quantile regressions following equation (4) using one candidate covariate at a time, replacing ) in the equation. We evaluate the fit in-sample for reasons of efficiency, since evaluating all models out-of-sample is too computationally intensive. Given that all models are llGG(GGl identical and simple, overfitting is unlikely to be an issue. The left panel of Figure 3 plots the error from these regressions against the availability of each indicator from 1991-2020 for the 218 economies considered by the World Bank. We exclude variables with less than 50% availability given that they have too much missingness to be useful for our application.

We are primarily interested in variables for which no other variable has a lower error and lower missingness. When using the full sample (panel a), this concerns national accounts variables and under-five mortality. The national accounts variables on the frontier are GDP, Household Final Consumption Expenditure (HFCE), and Gross National Income (GNI) (the national accounts variables are expressed in logs and per capita terms throughout). We use versions of these variables expressed in 2017 PPP-adjusted USD even though at times non-PPP adjusted versions perform slightly better (see the unlabeled orange dots in Figure 3). These variables have the advantage of being highly correlated with welfare but the drawback of not always being available. For example, GNI per capita is available only for 58% of the country-year observations. Hence, national accounts data can only offer a partial solution to predict the distribution of welfare. To the contrary, under-five mortality is universally available due to modeling done by the UN Population Division.

9
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The lasso and stepwise regression did not include interactions. We next test if adding interactions with the income/consumption dummy, or between the variables and <u>p</u> (i.e. letting the ~~�~~ � variables influence the Gini) could lower the error. As we show in the next section, regional llGG 1−pp dummies are most predictive of the Gini index among all 1,000+ variables. Therefore, we also test whether accuracy improves when we allow for variation in the Gini index by region. We try both Gini dummies for all regions and for the three regions that show notable differences in their Gini indices from the rest of the world. These regions are Latin America & the Caribbean and SubSaharan Africa which are regions with high inequality (Haddad et al. 2024), and Europe & Central Asia, which tends to have lower inequality. Finally, we test if the Gini should be a second-order polynomial of log GDP per capita, as the Kuznets curve would suggest (Kuznets 1955).

The error of both tiers would be reduced by letting the Gini differ by the three regions mentioned above (by 1.4 for tier 1 and 1.2 for tier 2). For tier 1, there is additional evidence in favor of adding a dummy for welfare type (income or consumption) and interacting this with GDP per capita. This means that as GDP grows, it has differential impacts on income and consumption vectors, which is in line with existing evidence (Lakner et al 2022, Mahler et al. 2022, Prydz et al 2022). This reduced the error of tier 1 further to 26.7. On the other hand, for tier 2, there is no similar case for adding a welfare type dummy or interacting the income group classifications with welfare type. Finally, we substitute under-60 mortality for the rural population share in the tier 1 model, which increases the error very marginally (from 26.67 to 26.69). This improves the consistency between the two models, and hence reduces revisions to the predictions if a country moves from one tier to another. In sum, we end up with two almost parallel models, where GDP per capita is proxied by income group in tier 2. The final out-of-sample error of the two tiers are 26.7 and 30.1. The regression outputs from the final models are shown in Table 1 (for the full sample).

|**Table 1: Re**<br>Outcome variable: Logwelfare(lG(y))|**gression**<br>|**output**<br>Tier 1|Ti|er 2|
|---|---|---|---|---|
|Intercept|-1.975***|(0.052)|1.837***|(0.047)|
|Log GDP per capita (2017 PPP)|0.393***|(0.004)|||
|Log under-5 mortality (per 1,000 live births)|-0.185***|(0.003)|-0.307***|(0.004)|
|Life expectancy (years)|0.016***|(0.000)|0.017***|(0.000)|
|Rural population share (0-100)|-0.003***|(0.000)|-0.008***|(0.000)|
|Income group|||||
|Low income|||Base||
|Lower-middle income|||0.229***|(0.006)|
|Upper-middle income|||0.450***|(0.008)|
|High income|||1.102***|(0.011)|
|Welfare type (income =1, consumption = 0)<br>|-3.671***|(0.030)|||
|Welfare type * log GDP per capita<br> <br>|0.392***|(0.003)|||
|lG(p/(1 −p))<br> <br>|0.354***|(0.002)|0.350***|(0.002)|
|<br>lG(p/(1 −p))* I[Europe & Central Asia]<br> <br>|-0.045***|(0.002)|-0.034***|(0.003)|
|<br> <br>lG(p/(1 −p))* I[Latin America & Caribbean]<br>|0.159***|(0.002)|0.166***|(0.003)|
|<br> <br>lG(p/(1 −p))* I[Sub-Saharan Africa]|0.060***|(0.002)|0.069***|(0.003)|
|<br><br>Observations|194,626||194,824||
|Pseudo R<sup>2</sup>|0.7512||0.719||

Note: *=0.05, **=0.01, ***=0.001. Robust standard errors in parentheses.

13
In(y) = — .975 + 0.393 In(GDPpc) — 0.185 In(u5m) — 0.003ruralshare + 0.016lifeexp + (0.354 + 0.060)In ~~—)~~ wo -feef In(y) 1.837 4+ 0.450 — 0.307 In(u5m) + 0.017lifeexp — 0.008ruralshare + 0.350ln ~~(—)~~ «o- (uf
log-logistic, we assume that they are log-normal. Given that the quantile function for the lognormal distribution results in ~~√~~ , we can essentially run the <u>p</u> same regressions as we have run so far, but instead of interacting covariates with , we ~~� �~~ lln(yy) = ln(μμ) + 2σσ<sup>2</sup> ∗eerrll<sup>−1</sup> (2pp−1) interact them with . We find that in all three cases, the error increases (modestly) llGG 1−pp compared to our preferred approach (Figure A.1). eerrll<sup>−1</sup> (2pp−1)

# **5.2 Accuracy using machine learning on all gathered indicators**

The errors of our two models -- 26.7 or 30.1 -- are substantial on an absolute scale, as they imply that welfare is predicted off by around 30% on average. We test whether the error is high because our model ultimately is too simple to perform well, because of the distributional assumption we impose, or because of irreducible error related to the uncertainty involved with constructing welfare aggregates and converting them to a common currency.

First, to estimate the limitations imposed by the simple model, we predict the median and Gini using a conditional inference random forest (Hothorn et al. 2006) using all the 1,000+ covariates we gathered. This helps shed light on whether the limitations of the functional form imposed, or the set of covariates considered causes our relatively large error. When doing so, we get an outof-sample error of 27.9 on the full sample and 36.5 on the data-deprived sample. This is higher than the errors from the tier 1 model (26.7 and 31.1). Though it certainly is possible to improve upon this error using even more covariates or other machine learning methods, this suggests that the main reason for the error is not the simplicity of the model we used. The intuition for this result is clear from the variable importance plots of the random forest: The main predictor of medians is GDP per capita, while the most predictive variable of the Gini is the region (Figure A.2). Both variables are already included in our preferred models.

Second, to assess the potential loss from the distributional assumption, we estimate a hypothetical error if we predicted the median and Gini perfectly and then impose a log-logistic distribution. This results in errors of 5.6 on the full sample and 6.6 on the data-deprived sample. Hence of the final error of our model, around 20% can be ascribed to our distributional assumption, while the remaining 80% are most likely due to irreducible error.

Some additional statistics can also help bring clarity on the size of the error of the two models. Firstly, the R<sup>2</sup> from the regressions of our final models are 0.71 and 0.75, whereas the R<sup>2</sup> of a model without any predictors is 0.15 (i.e. a model which would assign approximately the distribution of the median country to any country). Hence, our models explain most of the variance across and within countries. In addition, it is important to note that countries differ greatly in their welfare levels. The median welfare of the richest country in our sample is more than 100 times the poorest country, and even the 75<sup>th</sup> percentile of medians is 5 times greater than the 25<sup>th</sup> percentile. Hence, an error of around 30% would not lead to a substantial mis-ranking of a particular country, given the large differences in living standards in the world at large.

# **5.3 Accuracy in subsamples**

We next explore how our preferred models perform in various settings (Figure 6). If the model performs relatively poorly in a setting it may either be because the chosen covariates are less related to welfare distributions in this setting or because welfare distributions in general are noisy 15
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some of the differences between the predicted poverty rates can be explained by particularities of how poverty is measured in a country.

Figure 8 shows the predicted and survey-based poverty rates for other populous, or poor and data deprived countries. In most cases, the two are fairly well aligned, though there are exceptions, such as the cases of China and India just discussed as well as the República Bolivariana de Venezuela, where the predicted poverty rates are much lower than the surveybased ones. Figures A.3-A.12 in the annex show similar plots for 218 economies.

PIP currently assigns countries without any poverty estimate (or without national accounts data to extrapolate/interpolate from an old poverty estimate) the regional poverty rate. This concerns about 3% of the global population. In Appendix B we show how PIP’s regional and global poverty rates would change if we used the estimates from our two tiers instead of applying the regional average, as PIP currently does. Global poverty is projected to be revised upwards in 2019 by 11 million at the $2.15 line and 16 million at the $6.85 line. For certain countries the implications are larger, notably Afghanistan, Somalia, and the Democratic People’s Republic of Korea.

# 7 Conclusion

This paper proposes a method to estimate welfare distributions in contexts where little data is available. Data deprivation is often a bigger concern in poorer and more fragile countries where data collection might be limited due to active conflict, lack of resources, or institutional fragility, but where efforts to monitor changes in living conditions are essential. While comprehensive surveys of household income and consumption remain the best way to measure household welfare, we offer a simple alternative to estimate welfare distributions when surveys are not available.

The method consists of leveraging income or consumption distributions from more than 2,000 household surveys available in the World Bank’s Poverty and Inequality Platform (PIP) for 168 countries covering the period between 1991 and 2000. We combine these distributions with more than 1,000 predictors at the country-year level, including remote sensing variables, across various databases. We develop a simple model which predicts distributions for all countries in the world from a regression on country-level data. Guided by variable-selection techniques, we try various versions of such regressions, each time sequentially excluding all surveys available for one of the 168 countries available in our dataset to predict the distribution for the excluded country using the remaining 167 ones. We then calculate the absolute deviation between the true welfare and predicted welfare at 99 points on each distribution. Once we have these deviations for all surveys in the 168 countries, we calculate the mean absolute deviation across all surveys and all countries.

We find that when predicting distributions with GDP per capita (or income groups if GDP/capita is unavailable), under-5-mortality, life expectancy, and rural population shares, no additional feature significantly reduces the error further. Our preferred model predicts log welfare off by around 30% on average. Though this may sound high, we show that a random forest using all 1,000+ predictors is unable to reduce the error, suggesting that much of the remaining error is likely to be noise.

19
We demonstrate how to apply our model to predict poverty rates in a given country, and apply our preferred model to global poverty measurement, comparing it to the World Bank’s poverty estimates. We show that the model in general tracks the official poverty estimates well, but with notable exceptions. Where there are exceptions, these may in part be explained by the deficiencies in the survey methodology of a particular country, and not just because our model comes up short.

# References

- Alkema, Leontine, and Jin Rou New. 2014. "Global Estimation of Child Mortality Using a Bayesian B-spline Bias-Reduction Model." _The Annals of Applied Statistics_ : 2122-2149.

- Angrist, Noam, Pinelopi Koujianou Goldberg, and Dean Jolliffe. 2021. “Why Is Growth in Developing Countries So Hard to Measure?” _Journal of Economic Perspectives_ 35 (3): 215–42.

- Bergstrom, Katy. 2022. "The Role of Income Inequality for Poverty Reduction _." World Bank Economic Review_ 36 (3): 583-604.

-

- Bolt, Jutta, and Jan Luiten Van Zanden. 2024. "Maddison Style Estimates of the Evolution of the World Economy: A New 2023 Update." _Journal of Economic Surveys_ .

- Bresson, Florent. 2009. "On the Estimation of Growth and Inequality Elasticities of Poverty with Grouped Data." _Review of Income and Wealth_ 55(2): 266-302.

- Castaneda Aguilar, R. Andres. 2022. “Pip: Stata Module to Access World Bank’s Global Poverty and Inequality Data (Version 0.3.8).” _STATA_ . https://worldbank.github.io/pip/.

- Chen, Yi-Ting. 2018. “A Unified Approach to Estimating and Testing Income Distributions with Grouped Data.” _Journal of Business & Economic Statistics_ 36(3): 438–55.

- Chotikapanich, Duangkamon, William E. Griffiths, D. S. Prasada Rao, and Vicar Valencia. 2012. “Global Income Distributions and Inequality, 1993 and 2000: Incorporating Country-Level Inequality Modeled with Beta Distributions.” _Review of Economics and Statistics_ 94(1): 52–73.

- Christiaensen, Luc, Peter Lanjouw, Jill Luoto, and David Stifel. 2012. “Small Area EstimationBased Prediction Methods to Track Poverty: Validation and Applications.” _The Journal of Economic Inequality_ 10(2): 267–297.

- Dang, Hai-Anh, Dean Jolliffe, and Calogero Carletto. 2019. “Data Gaps, Data Incomparability, and Data Imputation: A Review of Poverty Measurement Methods for Data-Scarce Environments.” _Journal of Economic Surveys_ 33(3): 757–797.

- Datt, Gaurav, Valerie Kozel, and Martin Ravallion. 2003. “A Model-Based Assessment of India’s Progress in Reducing Poverty in the 1990s.” _Economic and Political Weekly_ , 355–361.

- Datt, Gaurav, and Martin Ravallion. 2002. “Is India’s Economic Growth Leaving the Poor Behind?” _Journal of Economic Perspectives_ 16(3): 89–108.

- Deaton, Angus. 2005. “Measuring Poverty in a Growing World (or Measuring Growth in a Poor World).” _The Review of Economics and Statistics_ 87(1): 1–19.

- Deaton, Angus, and Paul Schreyer. 2022. “GDP, Wellbeing, and Health: Thoughts on the 2017 Round of the International Comparison Program.” _Review of Income and Wealth_ 68(1): 1– 15.

- Decerf, Benoit, and Mery Ferrando. 2022. "Unambiguous Trends Combining Absolute and Relative Income Poverty: New Results and Global Application." _World Bank Economic Review_ 36(3): 605-628.

- Eckernkemper, Tobias, and Bastian Gribisch. 2021. “Classical and Bayesian Inference for Income Distributions Using Grouped Data.” _Oxford Bulletin of Economics and Statistics_ 83(1): 32– 65.

20
Ekhator-Mobayode, Uche E., and Johannes Hoogeveen. 2022. “Microdata Collection and Openness in the Middle East and North Africa.” _Data & Policy_ 4: e31.

- Elbers, Chris, Jean O. Lanjouw, and Peter Lanjouw. 2003. “Micro-Level Estimation of Poverty and Inequality.” _Econometrica_ 71(1): 355–364.

- Engstrom, Ryan, Jonathan Hersh, and David Newhouse. 2022. "Poverty from Space: Using High Resolution Satellite Imagery for Estimating Economic Well-Being." _World Bank Economic Review_ 36(2): 382-412.

- Filmer, Deon, and Lant H. Pritchett. 2001. “Estimating Wealth Effects without Expenditure Data— or Tears: An Application to Educational Enrollments in States of India.” _Demography_ 38 (1): 115–132.

- Gortan, Marco, Lorenzo Testa, Giorgio Fagiolo, and Francesco Lamperti. 2023. "A Unified Repository for Pre-Processed Climate Data Weighted by Gridded Economic Activity." _Scientific Data_ 11: 533.

- Haddad, Cameron Nadim, Daniel Gerszon Mahler, Carolina Diaz-Bonilla, Ruth Hill, Christoph Lakner, and Gabriel Lara Ibarra. 2024. "The World Bank’s New Inequality Indicator: The Number of Countries with High Inequality." Policy Research Working Paper Series 10796.

- Hajargasht, Gholamreza, William E. Griffiths, Joseph Brice, DS Prasada Rao, and Duangkamon Chotikapanich. 2012. "Inference for Income Distributions Using Grouped Data." _Journal of Business & Economic Statistics_ 30(4): 563-575.

- Hothorn, Torsten, Kurt Hornik, and Achim Zeileis. 2006. “Unbiased recursive partitioning: A conditional inference framework,” _Journal of Computational and Graphical Statistics_ 15: 651–674.

- Jolliffe, Dean, and Espen Beer Prydz. 2021. “Societal Poverty: A Relative and Relevant Measure.” World Bank Economic Review 35(1): 180-206.

- Jolliffe, Dean Mitchell r Daniel Gerszon Mahler r Christoph Lakner r Aziz Atamanov r Samuel Kofi Tetteh Baah. 2024. "Assessing the Impact of the 2017 PPPs on the International Poverty Line and Global Poverty." _World Bank Economic Review,_ lhae035.

- Jorda, Vanesa, and Miguel Niño-Zarazúa. 2019. “Global Inequality: How Large Is the Effect of Top Incomes?” _World Development_ 123: 104593.

- Jorda, Vanesa, Miguel Niño-Zarazúa, Laurence Roope, and Finn Tarp. 2023. “Global income polarization: Relative and absolute perspectives.” WIDER Working Paper 146.

- Kanbur, Ravi, Eduardo Ortiz-Juarez, and Andy Sumner. 2022. "The global Inequality Boomerang." WIDER Working Paper 27.

- Kraay, Aart, and Roy Van der Weide. 2022. "Measuring Intragenerational Mobility Using Aggregate Data." _Journal of Economic Growth_ 27(2): 273-314.

- Kraay, Aart r Christoph Lakner r Berk Ozler r Benoit Decerf r Dean Jolliffe r Olivier Sterck r Nishant Yonzan. 2023. “A New Distribution Sensitive Index for Measuring Welfare, Poverty, and Inequality”. Policy Research Working Paper 10470. Washington, D.C.: World Bank Group.

- Kuznets, Simon. 1955. “Economic Growth and Income Inequality.” _American Economic Review_ 45(1): 1-28.

- Lakner, Christoph, Daniel Gerszon Mahler, Mario Negre, and Espen Beer Prydz. 2022. "How Much Does Reducing Inequality Matter for Global Poverty?." _Journal of Economic Inequality_ 20(3): 559-585.

- Lee, Kamwoo, and Jeanine Braithwaite. 2022. "High-Resolution Poverty Maps in Sub-Saharan Africa." _World Development_ 159: 106028.

- Mahler, Daniel Gerszon, R. Andrés Castañeda Aguilar, and David Newhouse. 2022. “Nowcasting Global Poverty.” _World Bank Economic Review_ 36 (4): 835–856.

21
- Mahler, Daniel Gerszon r Nishant Yonzan r Christoph Lakner. 2022. “The Impact of COVID19 on Global Inequality and Poverty.” Policy Research Working Paper 10198; Washington, DC: World Bank Group.

- Martinez, Luis R. 2022. "How Much Should We Trust the Dictator’s GDP Growth Estimates?" _Journal of Political Economy_ 130(10): 2731-2769.

- Nicoletti, Cheti, Franco Peracchi, and Francesca Foliano. 2011. "Estimating Income Poverty in the Presence of Missing Data and Measurement Error." _Journal of Business & Economic Statistics_ 29(1): 61-72.

- Pinkovskiy, Maxim, and Xavier Sala-i-Martin. 2016. “Lights, Camera ... Income! Illuminating the National Accounts-Household Surveys Debate *.” _The Quarterly Journal of Economics_ 131 (2): 579–631.

- Pokhriyal, Neeti, and Damien Christophe Jacques. 2017. "Combining Disparate Data Sources for Improved Poverty Prediction and Mapping." _Proceedings of the National Academy of Sciences_ 114(46): E9783-E9792.

- Prydz, Espen Beer, Dean Jolliffe, and Umar Serajuddin. 2022. “Disparities in Assessments of Living Standards Using National Accounts and Household Surveys.” _Review of Income and Wealth_ 68: S385-S420 _._

-

- Roberts, David R., Volker Bahn, Simone Ciuti, Mark S. Boyce, Jane Elith, Gurutzeta Guillera ‐

- Arroita, and Severin Hauenstein. 2017. "Cross Validation Strategies for Data with Temporal, Spatial, Hierarchical, or Phylogenetic Structure." _Ecography_ 40(8): 913-929.

- Roy, Sutirtha, and Roy Van Der Weide. 2025. “Estimating poverty for India after 2011 using private-sector survey data.” _Journal of Development Economics_ 172, 103386.

- Sherwood, B., & Maidman, A. (2017). rqPen: Penalized quantile regression. R package version, 2.

- Soergel, Bjoern, Elmar Kriegler, Benjamin Leon Bodirsky, Nico Bauer, Marian Leimbach, and Alexander Popp. 2021. "Combining Ambitious Climate Policies with Efforts to Eradicate Poverty." _Nature Communications_ 12(1): 2342.

- Stifel, David, and Luc Christiaensen. 2007. "Tracking Poverty over Time in the Absence of Comparable Consumption Data." _The World Bank Economic Review_ 21(2): 317-341.

- Tarozzi, Alessandro. 2007. Calculating Comparable Statistics from Incomparable Surveys, With An Application to Poverty in India.” _Journal of Business and Economic Statistics_ 25(3), 314-336.

- UN DESA. 2016. “Transforming Our World: The 2030 Agenda for Sustainable Development.”

- United Nations. 2018. “World Urbanization Prospects: The 2018 Revision.” Department of Economic and Social Affairs, Population Division. New York: United Nations.

- United Nations, Department of Economic and Social Affairs, Population Division (2022). World Population Prospects 2022: Methodology of the United Nations population estimates and projections. UN DESA/POP/2022/TR/NO. 4.

- Van Der Weide, Roy, Brian Blankespoor, Chris Elbers, and Peter Lanjouw. 2022. “How Accurate Is a Poverty Map Based on Remote Sensing Data? An Application to Malawi.” _Journal of Development Economics_ 171, 103352.

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<!-- Start of picture text --> Botswana Brazil British Virgin Islands Brunei Darussalam Bulgaria<br>100<br>50 “N<br>NS SteNC f~ ;<br>ot Te fg a — _Menania<br>Burkina Faso Burundi Cabo Verde Cambodia Cameroon<br>1009 SSS | >> —<br>—. . < TM~ \ — ~ — TV > _<br>50 ~ No. IY N .<br>~~ Ny \ 7 TN<br>N° ~N<br>~~ s ~~<br>0 — —<br>Canada Cayman Islands Central African Republic Chad Channel Islands<br>100 SS SSe SFCSr SSSS.<br>a ~N<br>—~<br>7 | +“SN SS<br>Chile China Colombia Comoros Congo, Dem. Rep.<br>100 SS] i<br>~ -s-<br>\ . ° ° 4 — ~~<br>504 \ <> “ NL<br>NonenN \ ‘ \NN SOSNL a ~~<br>o| SPS se TT Sete”<br>Congo, Rep. Costa Rica Croatia Cuba Curagao<br>100<br>NL -<br>—— |<br>* KR NN wa.TM~ —_—<br>—_ _— — —+_> ss — — — ”<br>0 — —_— =: ——_———— — i —_—ee ae ieee ia =<br>2000 2010 2020 2000 2010 2020 2000 2010 2020 2000 2010 2020 2000 2010 2020<br>—-— $2.15 predictions —-— $6.85 predictions $24.35 predictions<br>—— $2.15 from PIP —e— $6.85 from PIP $24.35 from PIP<br><!-- End of picture text -->
<!-- Start of picture text --> Cyprus Czech Republic Céte d'Ivoire Denmark Djibouti<br>100<br>50<br>~ ~~ * .<br>e ~ _—<br>Of mmo ree -co=<t=ane—Socrconoocoocoocs ee<br>Dominica Dominican Republic Ecuador Egypt, Arab Rep. El Salvador<br>100<br>.<br>e _<br>XN ° . — ° N TM~<br>~ LT ~ 4 x es ~<br>> So Ne<br>0 _—_ Sh Se © eo A esseasess ccs a . ON a<br>Equatorial Guinea Eritrea Estonia Eswatini Ethiopia<br>100 — \ —~ A __ ~~ a 8 _ —a ne -<br>> iel to<br>N \ S ~N<br>eM \ \ a, ‘<br>NN | Nw oN, a<br>0 ~~ >~N Deca ~~<br>Faeroe Islands Fiji Finland France French Polynesia<br>; |<br>50 N~N ~ ,<br>O4 — = = = = =! — — = .— © | cr —« ccccccccccccccccee | == ccccccccccccccccsccesscee | —— = == == == =<br>Gabon Gambia, The Georgia Germany Ghana<br>100 a<br>504 ~~ ~— ~ ~ . | ae* \ ~<br>. ~ S ~ ><br>Tel 7 — «__ _ew<br>0 es a Veen —~<br>2000 2010 2020 2000 2010 2020 2000 2010 2020 2000 2010 2020 2000 2010 2020<br>—-— $2.15 predictions —-— $6.85 predictions $24.35 predictions<br>—— $2.15 from PIP —e— $6.85 from PIP $24.35 from PIP<br><!-- End of picture text -->
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<!-- Start of picture text --> Kazakhstan Kenya Kiribati Korea, Dem. Rep. Korea, Rep.<br>100<br>Sy<br>. a . ~<br>~<br>5047 \nw ‘“\ an _ \<br>\<br>\—“ “TSM~ TM JS —— ~ = JTMN \<br>0 AL A oe el en<br>Kosovo Kuwait Kyrgyz Republic Lao PDR Latvia<br>100 =<br>y, ~rr —_—__,<br>I~ \ ~sSews,we TM~s Sy<br>~.. TM~<br>50 = “<br>\ LN<br>|<br>0 _-—_ eS ttececcre i | “~ ‘~rcasam | /~. — iNaeea<br>Lebanon Lesotho Liberia Libya Liechtenstein<br>100 3S Se a oo<br>a =-<br>| | ‘|<br>a — / N\<br>sx (50 ~ \ NN / SN<br>\a<br>— -<br>—<br>o4.--- oO - — ee ee =-~>ytor =<br>Lithuania Luxembourg Macao SAR, China Madagascar Malawi<br>100 tSsSSS_ +. SS<br>50 NA \<br>~<br>\ ~ — TM~S.<br>Pon<br>0 _ — oe. ASAI ESTES REO —[— —<br>Malaysia Maldives Mali Malta Marshall Islands<br>100 ==<br>°<br>. SH<br>\ . ~—. ~S .<br>50 N N<br>S .<br>\N Yt ~~<br>~ NA ~ Y y) ~-- ~~ H<br>2000 2010 2020 2000 2010 2020 2000 2010 2020 2000 2010 2020 2000 2010 2020<br>—-— $2.15 predictions —-— $6.85 predictions $24.35 predictions<br>—— $2.15 from PIP —e— $6.85 from PIP $24.35 from PIP<br><!-- End of picture text -->
<!-- Start of picture text --> Mauritania Mauritius Mexico Micronesia, Fed. Sts. Moldova<br>100<br>50 — / \<br>= LN =<<br>~ ~~ ~~ v<br>0 TTS | eee Se eeereer<br>Monaco Mongolia Montenegro Morocco Mozambique<br>100 _<br>\ nw ><br>50 \ N<br>. \ oN ~<br>ah ye |I \ YN Ne PO ~<br>10 liteestlitestiieetiicmentitomtite S eee eee te<br>Myanmar Namibia Nauru Nepal Netherlands<br>100} == = SS<br>TM~ —_— .TM<br>N ~ |= -<br>eS 50 \ \ \ IN7 |[ \ ~~~ . A<br>Na_~ —_ oN | SN<br>New Caledonia New Zealand Nicaragua Niger Nigeria<br>100 — al 0el oe<br>TM~ . . =~ ~tm. °°<br>—NS sw, ~<br>50 NL a\ LT .<br>= \ vy loae NN S<br>| ~~<br>0 >>> -~ — ——.<br>North Macedonia Northern Mariana Islands Norway Oman Pakistan<br>505 7 \<br>N—<br>.<br>— ~S ~ ~~<br>ane zzSen.<br>of ——— hee || eee | St<br>2000 2010 2020 2000 2010 2020 2000 2010 2020 2000 2010 2020 2000 2010 2020<br>—-— $2.15 predictions —-— $6.85 predictions $24.35 predictions<br>—— $2.15 from PIP —e— $6.85 from PIP $24.35 from PIP<br><!-- End of picture text -->
<!-- Start of picture text --> Palau Panama Papua New Guinea Paraguay Peru<br>100<br>~e— |<br>~~<br>—e<br>” ‘<br>~Inn Pree ° ° i— XN S ~ ar,<br>ae tee, ~|in<br>Philippines Poland Portugal Puerto Rico Qatar<br>100<br>50 os<br>Romania Russian Federation Rwanda Samoa San Marino<br>‘00 4 SSS<br>7 TM ~ _ ~~<br>eS 50 \ \ Se—_.<br>sN<br>.<br>\ran res — S _—__<br>| A et trees | 2 *eatnecccnscnnennscnnnnss es ie<br>Saudi Arabia Senegal Serbia Seychelles Sierra Leone<br>100 i a a<br>50 . . . ee \ ie NX NAL<br>—~ om [JS<br>~L ~<br>lS 7] SN oa<br>Singapore Sint Maarten (Dutch part) Slovak Republic Slovenia Solomon Islands<br>100<br>a ee ee bn<br>2000 2010 2020 2000 2010 2020 2000 2010 2020 2000 2010 2020 2000 2010 2020<br>—-— $2.15 predictions —-— $6.85 predictions $24.35 predictions<br>—— $2.15 from PIP —e— $6.85 from PIP $24.35 from PIP<br><!-- End of picture text -->
<!-- Start of picture text --> Somalia South Africa South Sudan Spain Sri Lanka<br>10-== === == LS<br>‘\ . ° a ~\ ee °<br>7 _ —_—N V e ~.<br>50 .N a —~ ON nN _ NoTM~ ~ aNNA<br>. ° . \Q<br>0 es ities sssseessttzzanna | — >.<br>St. Kitts and Nevis St. Lucia St. Martin (French§battincent and the Grenadines Sudan<br>100<br>~<br>50 TM~<br>. SP ; \ 7 an<br>— — — \<br>of. —7---- ee (el tie<br>Suriname Sweden Switzerland Syrian Arab RepubliSao Tomé and Principe<br>100<br>inte~~<br>se 50f — SN | . ~<br>raw _ __<br>. ~ Ly oN Le<br>0-4 7 = | mee ccetcccccsccszccces | 2 35 secsnnsicsase =. — 77 ~~ Se<br>Taiwan, China Tajikistan Tanzania Thailand Timor-Leste<br>e ~— TM—~ a ~—_<br>NO Lv . \<br>50 f ~\ — TM~ \ YY 4\<br>N — N e<br>/ Awe > ~ N\ Iw<br>~N —_~~ “Wrote As<br>0 A St eeencerernees<br>Togo Tonga Trinidad and Tobago Tunisia Turkmenistan<br>1005 — — —SS<br>~\<br>—N<br>~ ° NQ<br>° ° \ NN _—<br>500 rs — —TM. —_—as_ —~Ss° \—_——_— — | >N +, “~~. —_—_—ae—<br>2000 2010 2020 2000 2010 2020 2000 2010 2020 2000 2010 2020 2000 2010 2020<br>—-— $2.15 predictions —-— $6.85 predictions $24.35 predictions<br>—— $2.15 from PIP —e— $6.85 from PIP $24.35 from PIP<br><!-- End of picture text -->
<!-- Start of picture text --> Turks and Caicos Islands Tuvalu Turkiye Uganda<br>100 SSS<br>a~<br>~<br>°<br>| oS | ;<br>50<br>7 oe<br>NL <7<br>— TM~ TMs —_~ * ~wS ~<br>Ukraine United Arab Emirates United Kingdom United States<br>: | |<br>50 /~ .<br>/ ~<br>0 eo —Serevecereccerecere SO are ae ial a AR |rereee ey,<br>Uruguay Uzbekistan Vanuatu Venezuela, RB<br>100 “_<br>~ —<br>TM~ > — —<br>aN<br>° —<br>S50 d ~ aN /<br>NEN ~—~~-—NX /<br>— — — _ ——— — —<br>Vietnam Virgin Islands (U.S.) West Bank and Gaza Yemen, Rep.<br>100<br>~N SL .<br>~ YN<br>50 ~— NA<br>~~ TMN _ ~~ —* . ~ peo<br>0 ee pe<br>Zambia Zimbabwe<br>1004 oo== =eee —_——_—_ = ~~<br>504" —=o — =" “aA (\<br>N f<br>0 NS | ><br>2000 2010 2020 2000 2010 2020<br>—-— $2.15 predictions —-— $6.85 predictions $24.35 predictions<br>—— $2.15 from PIP —e— $6.85 from PIP $24.35 from PIP<br><!-- End of picture text -->
# Appendix B: Application to the World Bank’s global poverty and inequality measures

The method we developed lends itself to being used in the World Bank’s global poverty measures for the countries that do not have any survey data. For the purpose of calculating regional and global poverty headcounts, countries without a household survey at any point in time, or countries without national accounts data needed for year-to-year extrapolations, are currently assigned the population-weighted regional average poverty rate. This affects 55 economies (Table B.1).<sup>5</sup> A few countries, such as Afghanistan, Saudi Arabia, the República Bolivariana de Venezuela, and the Democratic People’s Republic of Korea, make up the largest part of the population without data, adding up to more than 200 million people across all the missing economies (Table B.2).

**Table B.1: Economies without household survey data at any point in time in PIP**

||Cuba|||
|---|---|---|---|
|Afghanistan|Curaçao|Kosovo|San Marino|
|American Samoa|Dominica|Kuwait|Saudi Arabia|
|Andorra|Equatorial Guinea|Libya|Singapore|
|Antigua and Barbuda|Eritrea|Liechtenstein|Sint Maarten (Dutch part)|
|Aruba|Faeroe Islands|Macao SAR, China|Somalia|
|Bahamas, The|French Polynesia|Monaco|South Sudan|
|Bahrain|Gibraltar|Nauru|St. Kitts and Nevis|
|Barbados|Greenland|New Caledonia|St. Martin (French part)|
|Bermuda|Grenada|New Zealand|St. Vincent and the Grenadines|
|British Virgin Islands|Guam|Northern Mariana Islands|Timor-Leste|
|Brunei Darussalam|Hong Kong SAR, China|Oman|Turks and Caicos Islands|
|Cambodia|Isle of Man|Palau|Venezuela, RB|
|Cayman Islands|Korea, Dem. People’s|Puerto Rico|Virgin Islands (U.S.)|
|Channel Islands|Rep.|Qatar||

**Table B.2: Missing economies ranked by population in 2019**

|Economy|Population 2019(in millions)|
|---|---|
|Afghanistan|38|
|Saudi Arabia|36|
|Venezuela, RB|29|
|Korea, Dem. People’s||
|Rep.|26|
|Cambodia|16|
|Somalia|16|
|Cuba|11|
|South Sudan|10|
|Hong Kong SAR,||
|China|8|
|Libya|7|
|Other Economies|40|
|Total Missing|205|

5 Table B.1 includes economies that are missing in all years (e.g., the Democratic People’s Republic of Korea), but also economies that are missing only for some years (e.g., the República Bolivariana de Venezuela). The latter occurs when the national accounts data needed for the extrapolations is unavailable in some years.

34
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model is held constant in these comparisons: If we had focused exclusively on predicting poverty at the $2.15 line, it is likely that other covariates would have been chosen, which could have led to a model predicting $2.15 poverty rates directly performing better than shown above.

# **B.3 Consistency with PIP’s extrapolation rule**

PIP currently extrapolates old welfare vectors forward in time by assuming that a 1% growth in GDP per capita or HFCE per capita leads to a 1% growth in welfare across the distribution when income is used, and 0.7% when consumption is used. The coefficients from the tier 1 regression (Table 1) suggest that, all else equal, when GDP per capita grows 1%, the predicted median grows by 0.393% for consumption vectors and 0.785% (0.393+0.392) for income vectors. Yet this ignores that growth in GDP is likely to also impact welfare indirectly through lowering under-5 mortality, rural population shares, and by increasing life expectancy (the other three variables). Regressing changes in these other variables on growth in GDP per capita suggests that a 1% growth in GDP per capita is associated with a 0.82% decline in under-5 mortality, a 0.15 pct. point decline in the rural population share, and a 0.06 increase in life expectancy. Taking these factors into account, our estimate suggests that a 1% growth in GDP per capita is expected to increase consumption vectors by 0.69% and income vectors by 1.08%, which is very close to the extrapolation rule.

# **B.4 Implications for global poverty and inequality measurement**

Finally, we implement our preferred methods to predict poverty rates at the international poverty line ($2.15/day) and the upper-middle-income poverty line ($6.85/day) for countries that are missing from PIP. Specifically, we replace missing headcounts for 1,721 country-year observations with predictions from our Tier 1 model when GDP per capita is available (1,092 country-year observations), and from our Tier 2 model in the remainder of the cases (629 observations). Implementing our proposed method increases the global poverty rate in 2019 by about 0.14 percentage points at the $2.15 line and 0.21 percentage points at the $6.85 line, equivalent to an additional 11 million or 16 million poor people globally (Figure B.3). There is a similarly small, estimated increase in global inequality, with the global Gini coefficient estimated at 61.9 instead of 61.8 in 2019. For both global poverty and global inequality, the trend from 19912019 looks strikingly similar with or without our two tiers. This is because countries without data make up only 3% of the global population.

The differences are slightly larger at the regional level, with the extreme poverty rate in East Asia & Pacific increasing by 7%, and the rate of Latin America & the Caribbean and South Asia increasing by 4% (Figure B.4). The increase in the poverty rate for these regions is driven by populous countries without data for which the two tiers suggest higher poverty rates than the regional average. In Afghanistan, the extreme poverty rate is 20 percentage points higher in 2019 (equivalent to 7 million additional poor), while the figures are also notable for Somalia (increase by 14 pct. points, 2 million additional poor), the República Bolivariana de Venezuela (5 pct. points, 1.5 million poor), Cambodia (7 pct. points, 1.1 million poor) and the Democratic People’s Republic of Korea (3 pct. points, 0.7 million poor). These findings suggest that poverty rates are underestimated in data deprived countries which tend to be poorer than others in their regions. Country examples of the poverty rates from the current method and our proposal are shown in Figure B.5.

37
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<!-- Start of picture text --> Afghanistan Cambodia Cuba Hong Kong<br>100 ee ~<br>~/\—-~4 ae<br>\_<br>50 . N NOt \.<br>~n. . a<br>se -- 4<br><2 >+ |TT<br>0 a ee<br>x Libya North Korea Saudi Arabia Somalia<br>100 =—— _—___arr rr<br>-<br>y ~~. \<br>N b-~-~—__we ~<br>~~. -sJO~~<br>50 Ne ~ ~ i<br>0o,---->>>>> -- 8 OO<br>2000 2010 2020 2000 2010 2020 2000 2010 2020 2000 2010 2020<br>—— $2.15 predictions —-— $6.85 predictions $24.35 predictions<br>— $2.15 from PIP — $6.85 from PIP $24.35 from PIP<br><!-- End of picture text -->