posts: 44002

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id	title	slug	type	status	content	archieml	archieml_update_statistics	published_at	updated_at	gdocSuccessorId	authors	excerpt	created_at_in_wordpress	updated_at_in_wordpress	featured_image	formattingOptions	markdown	wpApiSnapshot
44002	Data appendix – The fight against global poverty: 200 years of progress and still a very long way to go	history-of-poverty-data-appendix	post	publish	<!-- wp:html --> <div class="blog-info"> <p>This is an online data appendix explaining the data and methods used to estimate the historical poverty trends presented in Roser and Hasell (2021).<br> For related data and research, see our entry on <strong><a href="https://ourworldindata.org/extreme-poverty" target="_blank" rel="noopener">Extreme Poverty</a></strong>.</p> </div> <!-- /wp:html --> <!-- wp:paragraph --> <p>This is an appendix providing further detail on the data and methods used in our historical reconstructions of global poverty from national accounts data, as presented in Roser and Hasell (2021).</p> <!-- /wp:paragraph --> <!-- wp:paragraph --> <p>The paper will be available online at the <a href="https://www.mdpi.com/books/pdfview/edition/1404">publisher's website</a>.</p> <!-- /wp:paragraph --> <!-- wp:paragraph --> <p>Note that:</p> <!-- /wp:paragraph --> <!-- wp:list --> <ul><li>All dollar figures below are expressed in international-$ in 2011 prices (adjusted to account for price differences across countries and for inflation).</li><li>You can download the data of each interactive chart shown below using the download tab found at the bottom of each chart.</li></ul> <!-- /wp:list --> <!-- wp:heading {"level":3} --> <h3>1) Baseline estimates</h3> <!-- /wp:heading --> <!-- wp:paragraph --> <p>First we present the baseline poverty estimates presented in the paper.</p> <!-- /wp:paragraph --> <!-- wp:heading {"level":4} --> <h4>The number and share of people living at different income thresholds.</h4> <!-- /wp:heading --> <!-- wp:paragraph --> <p>This is an interactive version of the charts included as figure 11 in the main paper.</p> <!-- /wp:paragraph --> <!-- wp:columns {"className":"is-style-side-by-side"} --> <div class="wp-block-columns is-style-side-by-side"><!-- wp:column --> <div class="wp-block-column"><!-- wp:html --> <iframe src="https://ourworldindata.org/grapher/historical-national-accounts-estimates-of-the-distribution-of-people-living-at-different-income-thresholds-globally?country=~OWID_WRL" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe> <!-- /wp:html --></div> <!-- /wp:column --> <!-- wp:column --> <div class="wp-block-column"><!-- wp:html --> <iframe src="https://ourworldindata.org/grapher/historical-national-accounts-estimates-of-the-distribution-of-people-living-at-different-income-thresholds-globally?stackMode=relative&country=~OWID_WRL" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe> <!-- /wp:html --></div> <!-- /wp:column --></div> <!-- /wp:columns --> <!-- wp:heading {"level":4} --> <h4>The share living below $5 a day, by region</h4> <!-- /wp:heading --> <!-- wp:paragraph --> <p>Here we provide interactive versions of figures 12 and 13 of the main paper.</p> <!-- /wp:paragraph --> <!-- wp:columns {"className":"is-style-side-by-side"} --> <div class="wp-block-columns is-style-side-by-side"><!-- wp:column --> <div class="wp-block-column"><!-- wp:html --> <iframe src="https://ourworldindata.org/grapher/regional_pov_rate" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe> <!-- /wp:html --></div> <!-- /wp:column --> <!-- wp:column --> <div class="wp-block-column"><!-- wp:html --> <iframe src="https://ourworldindata.org/grapher/historical-share-of-population-living-on-less-than-5-per-day-roser-hasell" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe> <!-- /wp:html --></div> <!-- /wp:column --></div> <!-- /wp:columns --> <!-- wp:heading {"level":4} --> <h4>A single long-run series of extreme poverty combining national accounts and recent survey based estimates</h4> <!-- /wp:heading --> <!-- wp:paragraph --> <p>This is an interactive version of figure 14 of the main paper.</p> <!-- /wp:paragraph --> <!-- wp:paragraph --> <p>It joins recent World Bank estimates of the share of people globally living below $1.90 a day from 1980, with our own historical national accounts estimates using a poverty line of $5.20. For a discussion of these two approaches to estimating poverty and how they relate to one another see the main paper.</p> <!-- /wp:paragraph --> <!-- wp:html --> <iframe src="https://ourworldindata.org/grapher/reconstruction-of-historical-global-extreme-poverty-rates-1820-2017-roser-and-hasell-2021-and-world-bank2020?stackMode=relative" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe> <!-- /wp:html --> <!-- wp:heading {"level":3} --> <h3>2) Data sources</h3> <!-- /wp:heading --> <!-- wp:paragraph --> <p>As explained in the paper, the estimates above are based on three inputs: </p> <!-- /wp:paragraph --> <!-- wp:list --> <ul><li>data on inequality, as measured by Gini coefficient,</li><li>data on average incomes, as measured by GDP per capita</li><li>population data</li></ul> <!-- /wp:list --> <!-- wp:paragraph --> <p>Here we discuss the sources used for each of these inputs.</p> <!-- /wp:paragraph --> <!-- wp:heading {"level":4} --> <h4>Inequality data</h4> <!-- /wp:heading --> <!-- wp:paragraph --> <p>Our baseline estimates are based on a combination of two datasets:</p> <!-- /wp:paragraph --> <!-- wp:list --> <ul><li>The historical inequality dataset gathered and published in van Zanden and others (2014){ref}Zanden, Jan Luiten van, Joerg Baten, Peter Foldvari, and Bas van Leeuwen. 2014. “The Changing Shape of Global Inequality 1820–2000; Exploring a New Dataset.” <em>Review of Income and Wealth</em> 60 (2): 279–97.{/ref} and, made available online by the authors at <a href="https://clio-infra.eu/Indicators/IncomeInequality.html">clio-infra</a>.</li><li>From 1960, an interpolated dataset of income Ginis produced by the <a href="http://gcip.info/">Global Consumption and Income Project (GCIP)</a>.</li></ul> <!-- /wp:list --> <!-- wp:paragraph --> <p>Alternative estimates (presented below) combine the historical data from van Zanden and others (2014) with two other datasets for more recent decades respectively:</p> <!-- /wp:paragraph --> <!-- wp:list --> <ul><li><a href="http://gcip.info">GCIP</a>’s dataset of consumption Ginis</li><li>the World Bank's <a href="http://iresearch.worldbank.org/PovcalNet/home.aspx">Povcal dataset</a></li></ul> <!-- /wp:list --> <!-- wp:heading {"level":4} --> <h4>GDP per capita and population data</h4> <!-- /wp:heading --> <!-- wp:paragraph --> <p>All population data and almost all data on GDP per capita is derived purely from the 2020 release of the <a href="https://www.rug.nl/ggdc/historicaldevelopment/maddison/releases/maddison-project-database-2020?lang=en">Maddison Project Database</a>.</p> <!-- /wp:paragraph --> <!-- wp:paragraph --> <p>For Sub-Saharan African countries, estimates for GDP per capita for most countries prior to 1950 were obtained by applying the growth rates estimated by Prados de la Escosura (2012){ref}Prados de la Escosura, Leandro. 2012. “OUTPUT PER HEAD IN PRE-INDEPENDENCE AFRICA: QUANTITATIVE CONJECTURES.” <em>Economic History of Developing Regions</em> 27 (2): 1–36.</p> <!-- /wp:paragraph --> <!-- wp:paragraph --> <p>A working paper version is available online at Core Econ <a href="https://core.ac.uk/download/pdf/29403639.pdf">here</a>.{/ref} to extend the Maddison estimates backwards (see next section on extrapolation).</p> <!-- /wp:paragraph --> <!-- wp:heading {"level":3} --> <h3>3) Imputation of missing data points</h3> <!-- /wp:heading --> <!-- wp:paragraph --> <p>The inequality, GDP per capita and population datasets listed above do not provide complete coverage. In order to produce global poverty estimates for a set of benchmark years, estimates for these three variables had to first be interpolated or extrapolated where missing for all countries for each benchmark year.</p> <!-- /wp:paragraph --> <!-- wp:paragraph --> <p>The process was as follows.</p> <!-- /wp:paragraph --> <!-- wp:paragraph --> <p>For GDP per capita and population data:</p> <!-- /wp:paragraph --> <!-- wp:list {"ordered":true} --> <ol><li>Where no observation for a given benchmark year was available, but an earlier and later observation was provided in the dataset, a datapoint was interpolated assuming a constant annual rate of growth between the available data points.</li><li>Where no observation prior to the benchmark year was available, a data point was extrapolated by applying an assumed growth rate. The growth rate applied was calculated as follows:<ol><li>If the country was formerly part of either the USSR or Yugoslavia, growth rates observed in the aggregate bloc (available within the Maddison dataset) were applied, where available.</li><li>For other countries, or for periods where data for the aggregate blocs of USSR or Yugoslavia were not available or applicable, the growth rate applied was the average rate observed within the region (according Maddison region definitions).</li><li>For Sub-Saharan African countries, the growth rates estimated by Prados de la Escosura (2012) were applied as mentioned above.</li></ol></li></ol> <!-- /wp:list --> <!-- wp:paragraph --> <p>For the Gini coefficient, missing values were replaced with the average observed across either the bloc (former Yugoslavia or USSR countries) or the region (according Maddison region definitions) in the given benchmark year.</p> <!-- /wp:paragraph --> <!-- wp:paragraph --> <p>For the purposes of replication, the fully interpolated dataset is shown in the two charts below. Both charts show the same data points: GDP per capita along the horizontal axis, Gini coefficient along the vertical axis and population as bubble size. The colour indicates the source and treatment used to arrive at the GDP per capita data points and the Gini data points respectively.</p> <!-- /wp:paragraph --> <!-- wp:paragraph --> <p>It should be noted that the objective of the interpolation was to provide a complete dataset of country-benchmark year observations that fall within plausible bounds, in order to derive global poverty estimates. To understand trends in particular countries, we refer you to the original data sources, listed above.</p> <!-- /wp:paragraph --> <!-- wp:columns {"className":"is-style-side-by-side"} --> <div class="wp-block-columns is-style-side-by-side"><!-- wp:column --> <div class="wp-block-column"><!-- wp:html --> <iframe src="https://ourworldindata.org/grapher/use-of-interpolation-and-extrapolation-on-maddison-gdp-per-capita-data" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe> <!-- /wp:html --></div> <!-- /wp:column --> <!-- wp:column --> <div class="wp-block-column"><!-- wp:html --> <iframe src="https://ourworldindata.org/grapher/use-of-interpolation-and-extrapolation-on-gini-data?time=1820" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe> <!-- /wp:html --></div> <!-- /wp:column --></div> <!-- /wp:columns --> <!-- wp:heading {"level":3} --> <h3>4) Deriving poverty estimates from a fitted parametric distribution</h3> <!-- /wp:heading --> <!-- wp:paragraph --> <p>Poverty estimates for each country and benchmark year were derived by fitting a lognormal income distribution.</p> <!-- /wp:paragraph --> <!-- wp:paragraph --> <p>A lognormal distribution is defined by two parameters, [latex]\mu[/latex] and [latex]\sigma[/latex]:</p> <!-- /wp:paragraph --> <!-- wp:paragraph --> <p> These are the expected value (or mean) and standard deviation of the variable's natural logarithm. These can be obtained from average incomes (GDP per capita) and the Gini coefficient as follows:</p> <!-- /wp:paragraph --> <!-- wp:html --> <ol><li><p>[latex]\sigma[/latex] is obtained from the Gini coefficient given the following relationship (see for instance Jorda, Sarabia, Jäntti (2018)):{ref}Jorda, Sarabia, Jäntti (2018) ‘Estimation of income inequality from grouped data’, available at arxiv.org <a href="https://arxiv.org/pdf/1808.09831.pdf">here</a>.{/ref}<br><br> [latex] \[G = 2\Phi\left(\frac{\sigma}{\sqrt{2}}\right) -1 \] [/latex]<br><br> where [latex]G[/latex] is the Gini coefficient, [latex]\Phi[/latex] the cumulative standard normal distribution, and [latex]\Phi^{-1}[/latex] its inverse.</p> <p>Rearranging, we find <br><br> [latex] \[G = 2\Phi\left(\frac{\sigma}{\sqrt{2}}\right) -1 \] [/latex] </p> </li><li>Assuming incomes, [latex]X[/latex], are distributed lognormally, the average income is given by: <br><br> [latex] \[ \bar{X} = e^{\mu + \frac{1}{2}\sigma^2} \] [/latex] <br><br> Rearranging we find <br><br> [latex] \[ \mu = \ln{\bar{X}}-\frac{1}{2}\sigma^2 \] [/latex] <br><br> In our approach, the average income is given by GDP per capita. </li><li>Poverty rates are then calculated, for a given poverty line, [latex]p[/latex], using the cumulative lognormal distribution defined by these two parameters: <br><br> [latex] \[ Poverty(p) = P(X\leq p) = \Phi\left(\frac{(\ln{p})-\mu}{\sigma}\right) \] [/latex] <br><br> This yields the poverty estimates for individual countries, shown in the chart. (You can change the country in the visualization or download the data for all countries). As discussed above, the data for many countries relies on extensive interpolation or extrapolation and should not be relied on to understand trends in particular countries without consulting the underlying data sources. </li><li>World and regional poverty rates are then calculated as the population-weighted average rates across countries. </li></ol> <!-- /wp:html --> <!-- wp:html --> <iframe src="https://ourworldindata.org/grapher/reconstruction-of-historical-poverty-trends-by-country?country=~GBR" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe> <!-- /wp:html --> <!-- wp:heading {"level":3} --> <h3>4) Alternative specifications and robustness checks</h3> <!-- /wp:heading --> <!-- wp:heading {"level":4} --> <h4>Alternative selection of inequality data</h4> <!-- /wp:heading --> <!-- wp:paragraph --> <p>Here we show global poverty estimates for four poverty lines, constructed in the way described above, using different data sources for the Gini coefficient for more recent decades.</p> <!-- /wp:paragraph --> <!-- wp:paragraph --> <p>The blue lines show again our baseline estimates which use GCIP data for income inequality. The red lines recalculate the estimates using the GCIP data for consumption inequality instead. The green lines show poverty estimates using instead data taken from the World Bank’s Povcal database, which is a mix of consumption and income inequality figures. In all three cases the historical estimates from van Zanden are used for earlier periods (in the case of the Povcal data iteration, data points from van Zanden are also used in more recent decades to increase the coverage prior to imputation).</p> <!-- /wp:paragraph --> <!-- wp:paragraph --> <p>The different inequality data sources yield very similar trends.</p> <!-- /wp:paragraph --> <!-- wp:image {"id":44062,"sizeSlug":"large","linkDestination":"none"} --> <figure class="wp-block-image size-large"><img src="https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-412x550.png" alt="" class="wp-image-44062"/></figure> <!-- /wp:image --> <!-- wp:paragraph --> <p></p> <!-- /wp:paragraph --> <!-- wp:heading {"level":4} --> <h4>Comparison with higher and lower inequality scenarios</h4> <!-- /wp:heading --> <!-- wp:paragraph --> <p>In this comparison chart, the green lines now plot global poverty rates where the estimates of the Gini coefficients used in our baseline figures have been replaced by much <strong>higher</strong> levels: the maximum of either the original value increased by one third or the highest value observed across the original dataset. The red lines plot global poverty rates where the Gini coefficients have been replaced by much <strong>lower</strong> levels: the minimum of either the original value reduced by one third or the lowest value observed across the original dataset.<br>As we see from the chart, and as discussed in the main paper, different assumptions concerning the level of inequality have relatively little impact on the long-run poverty trends given the large growth seen in average incomes over this period. Where the <em>average</em> income falls close to or below the poverty line, reducing inequality has a negligible effect on the poverty rate (perversely, the poverty rate may rise if it results in even fewer ‘rich’ people with incomes high enough to fall above the poverty line). This demonstrates that the major trends are not sensitive to uncertainty in the historical distributional data we have used.</p> <!-- /wp:paragraph --> <!-- wp:image {"id":44064,"sizeSlug":"large","linkDestination":"none"} --> <figure class="wp-block-image size-large"><img src="https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-409x550.png" alt="" class="wp-image-44064"/></figure> <!-- /wp:image --> <!-- wp:heading {"level":4} --> <h4>Comparison with higher and lower GDP per capita scenarios</h4> <!-- /wp:heading --> <!-- wp:paragraph --> <p>Here we show a similar check on the sensitivity of our global poverty estimates to different assumptions concerning the level of GDP per capita.</p> <!-- /wp:paragraph --> <!-- wp:paragraph --> <p>The green lines plot global poverty rates where the estimates of GDP per capita have been replaced by much <strong>higher</strong> levels: the original value increased by one third. The red lines plot global poverty rates where the estimates of GDP per capita have been replaced by much <strong>lower</strong> levels: the original value reduced by one third.</p> <!-- /wp:paragraph --> <!-- wp:paragraph --> <p>The fall in poverty shown in these estimates is driven by economic growth – with average income per person globally increasing by roughly a factor of ten over this period. As such, the overall trends are robust to a wide degree of uncertainty concerning the level of income in any given year.</p> <!-- /wp:paragraph --> <!-- wp:image {"id":44065,"sizeSlug":"large","linkDestination":"none"} --> <figure class="wp-block-image size-large"><img src="https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-413x550.png" alt="" class="wp-image-44065"/></figure> <!-- /wp:image --> <!-- wp:heading {"level":3} --> <h3>5) Code availability</h3> <!-- /wp:heading --> <!-- wp:paragraph --> <p>R was used to interpolate the data missing from the original sources and estimate global and regional poverty rates. All code is available to download <a href="https://drive.google.com/drive/folders/1wXlRLWnPegVoCTQDP_jLoRHGidXxPLOP?usp=sharing">here</a>.</p> <!-- /wp:paragraph -->	{ "id": "wp-44002", "slug": "history-of-poverty-data-appendix", "content": { "toc": [], "body": [ { "type": "text", "value": [ { "text": "This is an online data appendix explaining the data and methods used to estimate the historical poverty trends presented in Roser and Hasell (2021).", "spanType": "span-simple-text" }, { "spanType": "span-newline" }, { "text": " For related data and research, see our entry on ", "spanType": "span-simple-text" }, { "children": [ { "url": "https://ourworldindata.org/extreme-poverty", "children": [ { "text": "Extreme Poverty", "spanType": "span-simple-text" } ], "spanType": "span-link" } ], "spanType": "span-bold" }, { "text": ".", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "This is an appendix providing further detail on the data and methods used in our historical reconstructions of global poverty from national accounts data, as presented in Roser and Hasell (2021).", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "The paper will be available online at the ", "spanType": "span-simple-text" }, { "url": "https://www.mdpi.com/books/pdfview/edition/1404", "children": [ { "text": "publisher's website", "spanType": "span-simple-text" } ], "spanType": "span-link" }, { "text": ".", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "Note that:", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "list", "items": [ { "type": "text", "value": [ { "text": "All dollar figures below are expressed in international-$ in 2011 prices (adjusted to account for price differences across countries and for inflation).", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "You can download the data of each interactive chart shown below using the download tab found at the bottom of each chart.", "spanType": "span-simple-text" } ], "parseErrors": [] } ], "parseErrors": [] }, { "text": [ { "text": "1) Baseline estimates", "spanType": "span-simple-text" } ], "type": "heading", "level": 2, "parseErrors": [] }, { "type": "text", "value": [ { "text": "First we present the baseline poverty estimates presented in the paper.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "text": [ { "text": "The number and share of people living at different income thresholds.", "spanType": "span-simple-text" } ], "type": "heading", "level": 3, "parseErrors": [] }, { "type": "text", "value": [ { "text": "This is an interactive version of the charts included as figure 11 in the main paper.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "left": [ { "url": "https://ourworldindata.org/grapher/historical-national-accounts-estimates-of-the-distribution-of-people-living-at-different-income-thresholds-globally?country=~OWID_WRL", "type": "chart", "parseErrors": [] } ], "type": "sticky-right", "right": [ { "url": "https://ourworldindata.org/grapher/historical-national-accounts-estimates-of-the-distribution-of-people-living-at-different-income-thresholds-globally?stackMode=relative&country=~OWID_WRL", "type": "chart", "parseErrors": [] } ], "parseErrors": [] }, { "text": [ { "text": "The share living below $5 a day, by region", "spanType": "span-simple-text" } ], "type": "heading", "level": 3, "parseErrors": [] }, { "type": "text", "value": [ { "text": "Here we provide interactive versions of figures 12 and 13 of the main paper.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "left": [ { "url": "https://ourworldindata.org/grapher/regional_pov_rate", "type": "chart", "parseErrors": [] } ], "type": "sticky-right", "right": [ { "url": "https://ourworldindata.org/grapher/historical-share-of-population-living-on-less-than-5-per-day-roser-hasell", "type": "chart", "parseErrors": [] } ], "parseErrors": [] }, { "text": [ { "text": "A single long-run series of extreme poverty combining national accounts and recent survey based estimates", "spanType": "span-simple-text" } ], "type": "heading", "level": 3, "parseErrors": [] }, { "type": "text", "value": [ { "text": "This is an interactive version of figure 14 of the main paper.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "It joins recent World Bank estimates of the share of people globally living below $1.90 a day from 1980, with our own historical national accounts estimates using a poverty line of $5.20. For a discussion of these two approaches to estimating poverty and how they relate to one another see the main paper.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "url": "https://ourworldindata.org/grapher/reconstruction-of-historical-global-extreme-poverty-rates-1820-2017-roser-and-hasell-2021-and-world-bank2020?stackMode=relative", "type": "chart", "parseErrors": [] }, { "text": [ { "text": "2) Data sources", "spanType": "span-simple-text" } ], "type": "heading", "level": 2, "parseErrors": [] }, { "type": "text", "value": [ { "text": "As explained in the paper, the estimates above are based on three inputs:\u00a0", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "list", "items": [ { "type": "text", "value": [ { "text": "data on inequality, as measured by Gini coefficient,", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "data on average incomes, as measured by GDP per capita", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "population data", "spanType": "span-simple-text" } ], "parseErrors": [] } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "Here we discuss the sources used for each of these inputs.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "text": [ { "text": "Inequality data", "spanType": "span-simple-text" } ], "type": "heading", "level": 3, "parseErrors": [] }, { "type": "text", "value": [ { "text": "Our baseline estimates are based on a combination of two datasets:", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "list", "items": [ { "type": "text", "value": [ { "text": "The historical inequality dataset gathered and published in van Zanden and others (2014){ref}Zanden, Jan Luiten van, Joerg Baten, Peter Foldvari, and Bas van Leeuwen. 2014. \u201cThe Changing Shape of Global Inequality 1820\u20132000; Exploring a New Dataset.\u201d ", "spanType": "span-simple-text" }, { "children": [ { "text": "Review of Income and Wealth", "spanType": "span-simple-text" } ], "spanType": "span-italic" }, { "text": " 60 (2): 279\u201397.{/ref} and, made available online by the authors at ", "spanType": "span-simple-text" }, { "url": "https://clio-infra.eu/Indicators/IncomeInequality.html", "children": [ { "text": "clio-infra", "spanType": "span-simple-text" } ], "spanType": "span-link" }, { "text": ".", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "From 1960, an interpolated dataset of income Ginis produced by the ", "spanType": "span-simple-text" }, { "url": "http://gcip.info/", "children": [ { "text": "Global Consumption and Income Project (GCIP)", "spanType": "span-simple-text" } ], "spanType": "span-link" }, { "text": ".", "spanType": "span-simple-text" } ], "parseErrors": [] } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "Alternative estimates (presented below) combine the historical data from van Zanden and others (2014) with two other datasets for more recent decades respectively:", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "list", "items": [ { "type": "text", "value": [ { "url": "http://gcip.info", "children": [ { "text": "GCIP", "spanType": "span-simple-text" } ], "spanType": "span-link" }, { "text": "\u2019s dataset of consumption Ginis", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "the World Bank's ", "spanType": "span-simple-text" }, { "url": "http://iresearch.worldbank.org/PovcalNet/home.aspx", "children": [ { "text": "Povcal dataset", "spanType": "span-simple-text" } ], "spanType": "span-link" } ], "parseErrors": [] } ], "parseErrors": [] }, { "text": [ { "text": "GDP per capita and population data", "spanType": "span-simple-text" } ], "type": "heading", "level": 3, "parseErrors": [] }, { "type": "text", "value": [ { "text": "All population data and almost all data on GDP per capita is derived purely from the 2020 release of the ", "spanType": "span-simple-text" }, { "url": "https://www.rug.nl/ggdc/historicaldevelopment/maddison/releases/maddison-project-database-2020?lang=en", "children": [ { "text": "Maddison Project Database", "spanType": "span-simple-text" } ], "spanType": "span-link" }, { "text": ".", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "For Sub-Saharan African countries, estimates for GDP per capita for most countries prior to 1950 were obtained by applying the growth rates estimated by Prados de la Escosura (2012){ref}Prados de la Escosura, Leandro. 2012. \u201cOUTPUT PER HEAD IN PRE-INDEPENDENCE AFRICA: QUANTITATIVE CONJECTURES.\u201d ", "spanType": "span-simple-text" }, { "children": [ { "text": "Economic History of Developing Regions", "spanType": "span-simple-text" } ], "spanType": "span-italic" }, { "text": " 27 (2): 1\u201336.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "A working paper version is available online at Core Econ ", "spanType": "span-simple-text" }, { "url": "https://core.ac.uk/download/pdf/29403639.pdf", "children": [ { "text": "here", "spanType": "span-simple-text" } ], "spanType": "span-link" }, { "text": ".{/ref} to extend the Maddison estimates backwards (see next section on extrapolation).", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "text": [ { "text": "3) Imputation of missing data points", "spanType": "span-simple-text" } ], "type": "heading", "level": 2, "parseErrors": [] }, { "type": "text", "value": [ { "text": "The inequality, GDP per capita and population datasets listed above do not provide complete coverage. In order to produce global poverty estimates for a set of benchmark years, estimates for these three variables had to first be interpolated or extrapolated where missing for all countries for each benchmark year.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "The process was as follows.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "For GDP per capita and population data:", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "numbered-list", "items": [ { "type": "text", "value": [ { "text": "Where no observation for a given benchmark year was available, but an earlier and later observation was provided in the dataset, a datapoint was interpolated assuming a constant annual rate of growth between the available data points.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "Where no observation prior to the benchmark year was available, a data point was extrapolated by applying an assumed growth rate. The growth rate applied was calculated as follows:", "spanType": "span-simple-text" } ], "parseErrors": [] } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "For the Gini coefficient, missing values were replaced with the average observed across either the bloc (former Yugoslavia or USSR countries) or the region (according Maddison region definitions) in the given benchmark year.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "For the purposes of replication, the fully interpolated dataset is shown in the two charts below. Both charts show the same data points: GDP per capita along the horizontal axis, Gini coefficient along the vertical axis and population as bubble size. The colour indicates the source and treatment used to arrive at the GDP per capita data points and the Gini data points respectively.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "It should be noted that the objective of the interpolation was to provide a complete dataset of country-benchmark year observations that fall within plausible bounds, in order to derive global poverty estimates. To understand trends in particular countries, we refer you to the original data sources, listed above.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "left": [ { "url": "https://ourworldindata.org/grapher/use-of-interpolation-and-extrapolation-on-maddison-gdp-per-capita-data", "type": "chart", "parseErrors": [] } ], "type": "sticky-right", "right": [ { "url": "https://ourworldindata.org/grapher/use-of-interpolation-and-extrapolation-on-gini-data?time=1820", "type": "chart", "parseErrors": [] } ], "parseErrors": [] }, { "text": [ { "text": "4) Deriving poverty estimates from a fitted parametric distribution", "spanType": "span-simple-text" } ], "type": "heading", "level": 2, "parseErrors": [] }, { "type": "text", "value": [ { "text": "Poverty estimates for each country and benchmark year were derived by fitting a lognormal income distribution.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "A lognormal distribution is defined by two parameters, [latex]\\mu[/latex] and [latex]\\sigma[/latex]:", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": " These are the expected value (or mean) and standard deviation of the variable's natural logarithm. These can be obtained from average incomes (GDP per capita) and the Gini coefficient as follows:", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "numbered-list", "items": [ { "type": "text", "value": [ { "text": "[latex]\\sigma[/latex] is obtained from the Gini coefficient given the following relationship (see for instance Jorda, Sarabia, J\u00e4ntti (2018)):{ref}Jorda, Sarabia, J\u00e4ntti (2018) \u2018Estimation of income inequality from grouped data\u2019, available at arxiv.org ", "spanType": "span-simple-text" }, { "url": "https://arxiv.org/pdf/1808.09831.pdf", "children": [ { "text": "here", "spanType": "span-simple-text" } ], "spanType": "span-link" }, { "text": ".{/ref}", "spanType": "span-simple-text" }, { "spanType": "span-newline" }, { "spanType": "span-newline" }, { "text": "\n[latex]\n\\[G = 2\\Phi\\left(\\frac{\\sigma}{\\sqrt{2}}\\right) -1 \\]\n[/latex]", "spanType": "span-simple-text" }, { "spanType": "span-newline" }, { "spanType": "span-newline" }, { "text": "\nwhere [latex]G[/latex] is the Gini coefficient, [latex]\\Phi[/latex] the cumulative standard normal distribution, and [latex]\\Phi^{-1}[/latex] its inverse.", "spanType": "span-simple-text" }, { "text": "Rearranging, we find ", "spanType": "span-simple-text" }, { "spanType": "span-newline" }, { "spanType": "span-newline" }, { "text": "\n[latex]\n\\[G = 2\\Phi\\left(\\frac{\\sigma}{\\sqrt{2}}\\right) -1 \\]\n[/latex] ", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "Assuming incomes, [latex]X[/latex], are distributed lognormally, the average income is given by: ", "spanType": "span-simple-text" }, { "spanType": "span-newline" }, { "spanType": "span-newline" }, { "text": "\n[latex]\n\\[ \\bar{X} = e^{\\mu + \\frac{1}{2}\\sigma^2} \\]\n[/latex] ", "spanType": "span-simple-text" }, { "spanType": "span-newline" }, { "spanType": "span-newline" }, { "text": "\nRearranging we find ", "spanType": "span-simple-text" }, { "spanType": "span-newline" }, { "spanType": "span-newline" }, { "text": "\n[latex]\n\\[ \\mu = \\ln{\\bar{X}}-\\frac{1}{2}\\sigma^2 \\]\n[/latex] ", "spanType": "span-simple-text" }, { "spanType": "span-newline" }, { "spanType": "span-newline" }, { "text": "\nIn our approach, the average income is given by GDP per capita. \n", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "Poverty rates are then calculated, for a given poverty line, [latex]p[/latex], using the cumulative lognormal distribution defined by these two parameters: ", "spanType": "span-simple-text" }, { "spanType": "span-newline" }, { "spanType": "span-newline" }, { "text": "\n[latex]\n\\[ Poverty(p) = P(X\\leq p) = \\Phi\\left(\\frac{(\\ln{p})-\\mu}{\\sigma}\\right) \\]\n[/latex] ", "spanType": "span-simple-text" }, { "spanType": "span-newline" }, { "spanType": "span-newline" }, { "text": "\nThis yields the poverty estimates for individual countries, shown in the chart. (You can change the country in the visualization or download the data for all countries). As discussed above, the data for many countries relies on extensive interpolation or extrapolation and should not be relied on to understand trends in particular countries without consulting the underlying data sources.\n", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "World and regional poverty rates are then calculated as the population-weighted average rates across countries.\n", "spanType": "span-simple-text" } ], "parseErrors": [] } ], "parseErrors": [] }, { "url": "https://ourworldindata.org/grapher/reconstruction-of-historical-poverty-trends-by-country?country=~GBR", "type": "chart", "parseErrors": [] }, { "text": [ { "text": "4) Alternative specifications and robustness checks", "spanType": "span-simple-text" } ], "type": "heading", "level": 2, "parseErrors": [] }, { "text": [ { "text": "Alternative selection of inequality data", "spanType": "span-simple-text" } ], "type": "heading", "level": 3, "parseErrors": [] }, { "type": "text", "value": [ { "text": "Here we show global poverty estimates for four poverty lines, constructed in the way described above, using different data sources for the Gini coefficient for more recent decades.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "The blue lines show again our baseline estimates which use GCIP data for income inequality. The red lines recalculate the estimates using the GCIP data for consumption inequality instead. The green lines show poverty estimates using instead data taken from the World Bank\u2019s Povcal database, which is a mix of consumption and income inequality figures. In all three cases the historical estimates from van Zanden are used for earlier periods (in the case of the Povcal data iteration, data points from van Zanden are also used in more recent decades to increase the coverage prior to imputation).", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "The different inequality data sources yield very similar trends.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "alt": "", "size": "wide", "type": "image", "filename": "Robustness-checks-01.png", "parseErrors": [] }, { "text": [ { "text": "Comparison with higher and lower inequality scenarios", "spanType": "span-simple-text" } ], "type": "heading", "level": 3, "parseErrors": [] }, { "type": "text", "value": [ { "text": "In this comparison chart, the green lines now plot global poverty rates where the estimates of the Gini coefficients used in our baseline figures have been replaced by much ", "spanType": "span-simple-text" }, { "children": [ { "text": "higher", "spanType": "span-simple-text" } ], "spanType": "span-bold" }, { "text": " levels: the maximum of either the original value increased by one third or the highest value observed across the original dataset. The red lines plot global poverty rates where the Gini coefficients have been replaced by much ", "spanType": "span-simple-text" }, { "children": [ { "text": "lower", "spanType": "span-simple-text" } ], "spanType": "span-bold" }, { "text": " levels: the minimum of either the original value reduced by one third or the lowest value observed across the original dataset.", "spanType": "span-simple-text" }, { "spanType": "span-newline" }, { "text": "As we see from the chart, and as discussed in the main paper, different assumptions concerning the level of inequality have relatively little impact on the long-run poverty trends given the large growth seen in average incomes over this period. Where the ", "spanType": "span-simple-text" }, { "children": [ { "text": "average", "spanType": "span-simple-text" } ], "spanType": "span-italic" }, { "text": " income falls close to or below the poverty line, reducing inequality has a negligible effect on the poverty rate (perversely, the poverty rate may rise if it results in even fewer \u2018rich\u2019 people with incomes high enough to fall above the poverty line). This demonstrates that the major trends are not sensitive to uncertainty in the historical distributional data we have used.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "alt": "", "size": "wide", "type": "image", "filename": "Robustness-checks-02.png", "parseErrors": [] }, { "text": [ { "text": "Comparison with higher and lower GDP per capita scenarios", "spanType": "span-simple-text" } ], "type": "heading", "level": 3, "parseErrors": [] }, { "type": "text", "value": [ { "text": "Here we show a similar check on the sensitivity of our global poverty estimates to different assumptions concerning the level of GDP per capita.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "The green lines plot global poverty rates where the estimates of GDP per capita have been replaced by much ", "spanType": "span-simple-text" }, { "children": [ { "text": "higher", "spanType": "span-simple-text" } ], "spanType": "span-bold" }, { "text": " levels: the original value increased by one third. The red lines plot global poverty rates where the estimates of GDP per capita have been replaced by much ", "spanType": "span-simple-text" }, { "children": [ { "text": "lower", "spanType": "span-simple-text" } ], "spanType": "span-bold" }, { "text": " levels: the original value reduced by one third.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "type": "text", "value": [ { "text": "The fall in poverty shown in these estimates is driven by economic growth \u2013 with average income per person globally increasing by roughly a factor of ten over this period. As such, the overall trends are robust to a wide degree of uncertainty concerning the level of income in any given year.", "spanType": "span-simple-text" } ], "parseErrors": [] }, { "alt": "", "size": "wide", "type": "image", "filename": "Robustness-checks-03.png", "parseErrors": [] }, { "text": [ { "text": "5) Code availability", "spanType": "span-simple-text" } ], "type": "heading", "level": 2, "parseErrors": [] }, { "type": "text", "value": [ { "text": "R was used to interpolate the data missing from the original sources and estimate global and regional poverty rates. All code is available to download ", "spanType": "span-simple-text" }, { "url": "https://drive.google.com/drive/folders/1wXlRLWnPegVoCTQDP_jLoRHGidXxPLOP?usp=sharing", "children": [ { "text": "here", "spanType": "span-simple-text" } ], "spanType": "span-link" }, { "text": ".", "spanType": "span-simple-text" } ], "parseErrors": [] } ], "type": "article", "title": "Data appendix \u2013 The fight against global poverty: 200 years of progress and still a very long way to go", "authors": [ "Joe Hasell" ], "excerpt": "An online data appendix explaining the data and methods used to estimate the historical poverty trends presented in Roser and Hasell (2021)", "dateline": "July 7, 2019", "subtitle": "An online data appendix explaining the data and methods used to estimate the historical poverty trends presented in Roser and Hasell (2021)", "sidebar-toc": false, "featured-image": "reconstruction-of-historical-global-extreme-poverty-rates-1820-2017-roser-and-hasell-2021-and-world-bank2020.png" }, "createdAt": "2021-07-06T10:21:27.000Z", "published": false, "updatedAt": "2021-07-07T18:08:35.000Z", "revisionId": null, "publishedAt": "2019-07-07T13:23:00.000Z", "relatedCharts": [], "publicationContext": "listed" }	{ "errors": [ { "name": "unexpected wp component tag", "details": "Found unhandled wp:comment tag list" }, { "name": "unexpected wp component tag", "details": "Found unhandled wp:comment tag list" }, { "name": "unexpected wp component tag", "details": "Found unhandled wp:comment tag list" }, { "name": "unexpected wp component tag", "details": "Found unhandled wp:comment tag list" }, { "name": "unexpected elements in list item", "details": "Found 1 elements" }, { "name": "unexpected wp component tag", "details": "Found unhandled wp:comment tag list" }, { "name": "unexpected wp component tag", "details": "Found unhandled wp:comment tag image" }, { "name": "unexpected wp component tag", "details": "Found unhandled wp:comment tag image" }, { "name": "unexpected wp component tag", "details": "Found unhandled wp:comment tag image" } ], "numBlocks": 61, "numErrors": 9, "wpTagCounts": { "html": 10, "list": 5, "image": 3, "column": 6, "columns": 3, "heading": 14, "paragraph": 33 }, "htmlTagCounts": { "p": 36, "h3": 6, "h4": 8, "ol": 3, "ul": 4, "div": 10, "figure": 3, "iframe": 8 } }	2019-07-07 13:23:00	2024-06-19 11:10:00	1NJRWwn6xcH_O8vMG4ZKqI_5i7V6mhpZu6ctyG-hZvPo	[ "Joe Hasell" ]	An online data appendix explaining the data and methods used to estimate the historical poverty trends presented in Roser and Hasell (2021)	2021-07-06 10:21:27	2021-07-07 18:08:35	https://ourworldindata.org/wp-content/uploads/2021/07/reconstruction-of-historical-global-extreme-poverty-rates-1820-2017-roser-and-hasell-2021-and-world-bank2020.png	{}	This is an online data appendix explaining the data and methods used to estimate the historical poverty trends presented in Roser and Hasell (2021). For related data and research, see our entry on [Extreme Poverty](https://ourworldindata.org/extreme-poverty). This is an appendix providing further detail on the data and methods used in our historical reconstructions of global poverty from national accounts data, as presented in Roser and Hasell (2021). The paper will be available online at the [publisher's website](https://www.mdpi.com/books/pdfview/edition/1404). Note that: * All dollar figures below are expressed in international-$ in 2011 prices (adjusted to account for price differences across countries and for inflation). * You can download the data of each interactive chart shown below using the download tab found at the bottom of each chart. ## 1) Baseline estimates First we present the baseline poverty estimates presented in the paper. ### The number and share of people living at different income thresholds. This is an interactive version of the charts included as figure 11 in the main paper. <Chart url="https://ourworldindata.org/grapher/historical-national-accounts-estimates-of-the-distribution-of-people-living-at-different-income-thresholds-globally?country=~OWID_WRL"/> <Chart url="https://ourworldindata.org/grapher/historical-national-accounts-estimates-of-the-distribution-of-people-living-at-different-income-thresholds-globally?stackMode=relative&country=~OWID_WRL"/> ### The share living below $5 a day, by region Here we provide interactive versions of figures 12 and 13 of the main paper. <Chart url="https://ourworldindata.org/grapher/regional_pov_rate"/> <Chart url="https://ourworldindata.org/grapher/historical-share-of-population-living-on-less-than-5-per-day-roser-hasell"/> ### A single long-run series of extreme poverty combining national accounts and recent survey based estimates This is an interactive version of figure 14 of the main paper. It joins recent World Bank estimates of the share of people globally living below $1.90 a day from 1980, with our own historical national accounts estimates using a poverty line of $5.20. For a discussion of these two approaches to estimating poverty and how they relate to one another see the main paper. <Chart url="https://ourworldindata.org/grapher/reconstruction-of-historical-global-extreme-poverty-rates-1820-2017-roser-and-hasell-2021-and-world-bank2020?stackMode=relative"/> ## 2) Data sources As explained in the paper, the estimates above are based on three inputs: * data on inequality, as measured by Gini coefficient, * data on average incomes, as measured by GDP per capita * population data Here we discuss the sources used for each of these inputs. ### Inequality data Our baseline estimates are based on a combination of two datasets: * The historical inequality dataset gathered and published in van Zanden and others (2014){ref}Zanden, Jan Luiten van, Joerg Baten, Peter Foldvari, and Bas van Leeuwen. 2014. “The Changing Shape of Global Inequality 1820–2000; Exploring a New Dataset.” _Review of Income and Wealth_ 60 (2): 279–97.{/ref} and, made available online by the authors at [clio-infra](https://clio-infra.eu/Indicators/IncomeInequality.html). * From 1960, an interpolated dataset of income Ginis produced by the [Global Consumption and Income Project (GCIP)](http://gcip.info/). Alternative estimates (presented below) combine the historical data from van Zanden and others (2014) with two other datasets for more recent decades respectively: * [GCIP](http://gcip.info)’s dataset of consumption Ginis * the World Bank's [Povcal dataset](http://iresearch.worldbank.org/PovcalNet/home.aspx) ### GDP per capita and population data All population data and almost all data on GDP per capita is derived purely from the 2020 release of the [Maddison Project Database](https://www.rug.nl/ggdc/historicaldevelopment/maddison/releases/maddison-project-database-2020?lang=en). For Sub-Saharan African countries, estimates for GDP per capita for most countries prior to 1950 were obtained by applying the growth rates estimated by Prados de la Escosura (2012){ref}Prados de la Escosura, Leandro. 2012. “OUTPUT PER HEAD IN PRE-INDEPENDENCE AFRICA: QUANTITATIVE CONJECTURES.” _Economic History of Developing Regions_ 27 (2): 1–36. A working paper version is available online at Core Econ [here](https://core.ac.uk/download/pdf/29403639.pdf).{/ref} to extend the Maddison estimates backwards (see next section on extrapolation). ## 3) Imputation of missing data points The inequality, GDP per capita and population datasets listed above do not provide complete coverage. In order to produce global poverty estimates for a set of benchmark years, estimates for these three variables had to first be interpolated or extrapolated where missing for all countries for each benchmark year. The process was as follows. For GDP per capita and population data: 0. Where no observation for a given benchmark year was available, but an earlier and later observation was provided in the dataset, a datapoint was interpolated assuming a constant annual rate of growth between the available data points. 1. Where no observation prior to the benchmark year was available, a data point was extrapolated by applying an assumed growth rate. The growth rate applied was calculated as follows: For the Gini coefficient, missing values were replaced with the average observed across either the bloc (former Yugoslavia or USSR countries) or the region (according Maddison region definitions) in the given benchmark year. For the purposes of replication, the fully interpolated dataset is shown in the two charts below. Both charts show the same data points: GDP per capita along the horizontal axis, Gini coefficient along the vertical axis and population as bubble size. The colour indicates the source and treatment used to arrive at the GDP per capita data points and the Gini data points respectively. It should be noted that the objective of the interpolation was to provide a complete dataset of country-benchmark year observations that fall within plausible bounds, in order to derive global poverty estimates. To understand trends in particular countries, we refer you to the original data sources, listed above. <Chart url="https://ourworldindata.org/grapher/use-of-interpolation-and-extrapolation-on-maddison-gdp-per-capita-data"/> <Chart url="https://ourworldindata.org/grapher/use-of-interpolation-and-extrapolation-on-gini-data?time=1820"/> ## 4) Deriving poverty estimates from a fitted parametric distribution Poverty estimates for each country and benchmark year were derived by fitting a lognormal income distribution. A lognormal distribution is defined by two parameters, [latex]\mu[/latex] and [latex]\sigma[/latex]: These are the expected value (or mean) and standard deviation of the variable's natural logarithm. These can be obtained from average incomes (GDP per capita) and the Gini coefficient as follows: 0. [latex]\sigma[/latex] is obtained from the Gini coefficient given the following relationship (see for instance Jorda, Sarabia, Jäntti (2018)):{ref}Jorda, Sarabia, Jäntti (2018) ‘Estimation of income inequality from grouped data’, available at arxiv.org [here](https://arxiv.org/pdf/1808.09831.pdf).{/ref} [latex] \[G = 2\Phi\left(\frac{\sigma}{\sqrt{2}}\right) -1 \] [/latex] where [latex]G[/latex] is the Gini coefficient, [latex]\Phi[/latex] the cumulative standard normal distribution, and [latex]\Phi^{-1}[/latex] its inverse.Rearranging, we find [latex] \[G = 2\Phi\left(\frac{\sigma}{\sqrt{2}}\right) -1 \] [/latex] 1. Assuming incomes, [latex]X[/latex], are distributed lognormally, the average income is given by: [latex] \[ \bar{X} = e^{\mu + \frac{1}{2}\sigma^2} \] [/latex] Rearranging we find [latex] \[ \mu = \ln{\bar{X}}-\frac{1}{2}\sigma^2 \] [/latex] In our approach, the average income is given by GDP per capita. 2. Poverty rates are then calculated, for a given poverty line, [latex]p[/latex], using the cumulative lognormal distribution defined by these two parameters: [latex] \[ Poverty(p) = P(X\leq p) = \Phi\left(\frac{(\ln{p})-\mu}{\sigma}\right) \] [/latex] This yields the poverty estimates for individual countries, shown in the chart. (You can change the country in the visualization or download the data for all countries). As discussed above, the data for many countries relies on extensive interpolation or extrapolation and should not be relied on to understand trends in particular countries without consulting the underlying data sources. 3. World and regional poverty rates are then calculated as the population-weighted average rates across countries. <Chart url="https://ourworldindata.org/grapher/reconstruction-of-historical-poverty-trends-by-country?country=~GBR"/> ## 4) Alternative specifications and robustness checks ### Alternative selection of inequality data Here we show global poverty estimates for four poverty lines, constructed in the way described above, using different data sources for the Gini coefficient for more recent decades. The blue lines show again our baseline estimates which use GCIP data for income inequality. The red lines recalculate the estimates using the GCIP data for consumption inequality instead. The green lines show poverty estimates using instead data taken from the World Bank’s Povcal database, which is a mix of consumption and income inequality figures. In all three cases the historical estimates from van Zanden are used for earlier periods (in the case of the Povcal data iteration, data points from van Zanden are also used in more recent decades to increase the coverage prior to imputation). The different inequality data sources yield very similar trends. <Image filename="Robustness-checks-01.png" alt=""/> ### Comparison with higher and lower inequality scenarios In this comparison chart, the green lines now plot global poverty rates where the estimates of the Gini coefficients used in our baseline figures have been replaced by much higher levels: the maximum of either the original value increased by one third or the highest value observed across the original dataset. The red lines plot global poverty rates where the Gini coefficients have been replaced by much lower levels: the minimum of either the original value reduced by one third or the lowest value observed across the original dataset. As we see from the chart, and as discussed in the main paper, different assumptions concerning the level of inequality have relatively little impact on the long-run poverty trends given the large growth seen in average incomes over this period. Where the _average_ income falls close to or below the poverty line, reducing inequality has a negligible effect on the poverty rate (perversely, the poverty rate may rise if it results in even fewer ‘rich’ people with incomes high enough to fall above the poverty line). This demonstrates that the major trends are not sensitive to uncertainty in the historical distributional data we have used. <Image filename="Robustness-checks-02.png" alt=""/> ### Comparison with higher and lower GDP per capita scenarios Here we show a similar check on the sensitivity of our global poverty estimates to different assumptions concerning the level of GDP per capita. The green lines plot global poverty rates where the estimates of GDP per capita have been replaced by much higher levels: the original value increased by one third. The red lines plot global poverty rates where the estimates of GDP per capita have been replaced by much lower levels: the original value reduced by one third. The fall in poverty shown in these estimates is driven by economic growth – with average income per person globally increasing by roughly a factor of ten over this period. As such, the overall trends are robust to a wide degree of uncertainty concerning the level of income in any given year. <Image filename="Robustness-checks-03.png" alt=""/> ## 5) Code availability R was used to interpolate the data missing from the original sources and estimate global and regional poverty rates. All code is available to download [here](https://drive.google.com/drive/folders/1wXlRLWnPegVoCTQDP_jLoRHGidXxPLOP?usp=sharing).	{ "id": 44002, "date": "2019-07-07T14:23:00", "guid": { "rendered": "https://owid.cloud/?p=44002" }, "link": "https://owid.cloud/history-of-poverty-data-appendix", "meta": { "owid_publication_context_meta_field": { "latest": true, "homepage": true, "immediate_newsletter": true } }, "slug": "history-of-poverty-data-appendix", "tags": [], "type": "post", "title": { "rendered": "Data appendix \u2013 The fight against global poverty: 200 years of progress and still a very long way to go" }, "_links": { "self": [ { "href": "https://owid.cloud/wp-json/wp/v2/posts/44002" } ], "about": [ { "href": "https://owid.cloud/wp-json/wp/v2/types/post" } ], "author": [ { "href": "https://owid.cloud/wp-json/wp/v2/users/14", "embeddable": true } ], "curies": [ { "href": "https://api.w.org/{rel}", "name": "wp", "templated": true } ], "replies": [ { "href": "https://owid.cloud/wp-json/wp/v2/comments?post=44002", "embeddable": true } ], "wp:term": [ { "href": "https://owid.cloud/wp-json/wp/v2/categories?post=44002", "taxonomy": "category", "embeddable": true }, { "href": "https://owid.cloud/wp-json/wp/v2/tags?post=44002", "taxonomy": "post_tag", "embeddable": true } ], "collection": [ { "href": "https://owid.cloud/wp-json/wp/v2/posts" } ], "wp:attachment": [ { "href": "https://owid.cloud/wp-json/wp/v2/media?parent=44002" } ], "version-history": [ { "href": "https://owid.cloud/wp-json/wp/v2/posts/44002/revisions", "count": 55 } ], "wp:featuredmedia": [ { "href": "https://owid.cloud/wp-json/wp/v2/media/44082", "embeddable": true } ], "predecessor-version": [ { "id": 44084, "href": "https://owid.cloud/wp-json/wp/v2/posts/44002/revisions/44084" } ] }, "author": 14, "format": "standard", "status": "publish", "sticky": false, "content": { "rendered": "<div class=\"blog-info\">\n <p>\n This is an online data appendix explaining the data and methods used to\n estimate the historical poverty trends presented in Roser and Hasell (2021).\n <br />\n For related data and research, see our entry on\n <strong>\n <a\n href=\"https://ourworldindata.org/extreme-poverty\"\n target=\"_blank\"\n rel=\"noopener\">\n Extreme Poverty\n </a> </strong\n >.\n </p>\n</div>\n\n<p>\n This is an appendix providing further detail on the data and methods used in\n our historical reconstructions of global poverty from national accounts data,\n as presented in Roser and Hasell (2021).\n</p>\n\n<p>\n The paper will be available online at the\n <a href=\"https://www.mdpi.com/books/pdfview/edition/1404\">\n publisher’s website </a\n >.\n</p>\n\n<p>Note that:</p>\n\n<ul>\n <li>\n All dollar figures below are expressed in international-$ in 2011 prices\n (adjusted to account for price differences across countries and for\n inflation).\n </li>\n <li>\n You can download the data of each interactive chart shown below using the\n download tab found at the bottom of each chart.\n </li>\n</ul>\n\n<h3>1) Baseline estimates</h3>\n\n<p>First we present the baseline poverty estimates presented in the paper.</p>\n\n<h4>The number and share of people living at different income thresholds.</h4>\n\n<p>\n This is an interactive version of the charts included as figure 11 in the main\n paper.\n</p>\n\n<div class=\"wp-block-columns is-style-side-by-side\">\n <div class=\"wp-block-column\">\n <iframe\n src=\"https://ourworldindata.org/grapher/historical-national-accounts-estimates-of-the-distribution-of-people-living-at-different-income-thresholds-globally?country=~OWID_WRL\"\n loading=\"lazy\"\n style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n </div>\n\n <div class=\"wp-block-column\">\n <iframe\n src=\"https://ourworldindata.org/grapher/historical-national-accounts-estimates-of-the-distribution-of-people-living-at-different-income-thresholds-globally?stackMode=relative&country=~OWID_WRL\"\n loading=\"lazy\"\n style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n </div>\n</div>\n\n<h4>The share living below $5 a day, by region</h4>\n\n<p>\n Here we provide interactive versions of figures 12 and 13 of the main paper.\n</p>\n\n<div class=\"wp-block-columns is-style-side-by-side\">\n <div class=\"wp-block-column\">\n <iframe\n src=\"https://ourworldindata.org/grapher/regional_pov_rate\"\n loading=\"lazy\"\n style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n </div>\n\n <div class=\"wp-block-column\">\n <iframe\n src=\"https://ourworldindata.org/grapher/historical-share-of-population-living-on-less-than-5-per-day-roser-hasell\"\n loading=\"lazy\"\n style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n </div>\n</div>\n\n<h4>\n A single long-run series of extreme poverty combining national accounts and\n recent survey based estimates\n</h4>\n\n<p>This is an interactive version of figure 14 of the main paper.</p>\n\n<p>\n It joins recent World Bank estimates of the share of people globally living\n below $1.90 a day from 1980, with our own historical national accounts\n estimates using a poverty line of $5.20. For a discussion of these two\n approaches to estimating poverty and how they relate to one another see the\n main paper.\n</p>\n\n<iframe\n src=\"https://ourworldindata.org/grapher/reconstruction-of-historical-global-extreme-poverty-rates-1820-2017-roser-and-hasell-2021-and-world-bank2020?stackMode=relative\"\n loading=\"lazy\"\n style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n\n<h3>2) Data sources</h3>\n\n<p>\n As explained in the paper, the estimates above are based on three\n inputs: \n</p>\n\n<ul>\n <li>data on inequality, as measured by Gini coefficient,</li>\n <li>data on average incomes, as measured by GDP per capita</li>\n <li>population data</li>\n</ul>\n\n<p>Here we discuss the sources used for each of these inputs.</p>\n\n<h4>Inequality data</h4>\n\n<p>Our baseline estimates are based on a combination of two datasets:</p>\n\n<ul>\n <li>\n The historical inequality dataset gathered and published in van Zanden and\n others (2014){ref}Zanden, Jan Luiten van, Joerg Baten, Peter Foldvari, and\n Bas van Leeuwen. 2014. \u201cThe Changing Shape of Global Inequality 1820\u20132000;\n Exploring a New Dataset.\u201d\n <em>Review of Income and Wealth</em>\n 60 (2): 279\u201397.{/ref} and, made available online by the authors at\n <a href=\"https://clio-infra.eu/Indicators/IncomeInequality.html\">\n clio-infra </a\n >.\n </li>\n <li>\n From 1960, an interpolated dataset of income Ginis produced by the\n <a href=\"http://gcip.info/\">Global Consumption and Income Project (GCIP)</a\n >.\n </li>\n</ul>\n\n<p>\n Alternative estimates (presented below) combine the historical data from van\n Zanden and others (2014) with two other datasets for more recent decades\n respectively:\n</p>\n\n<ul>\n <li>\n <a href=\"http://gcip.info\">GCIP</a>\n \u2019s dataset of consumption Ginis\n </li>\n <li>\n the World Bank’s\n <a href=\"http://iresearch.worldbank.org/PovcalNet/home.aspx\">\n Povcal dataset\n </a>\n </li>\n</ul>\n\n<h4>GDP per capita and population data</h4>\n\n<p>\n All population data and almost all data on GDP per capita is derived purely\n from the 2020 release of the\n <a\n href=\"https://www.rug.nl/ggdc/historicaldevelopment/maddison/releases/maddison-project-database-2020?lang=en\">\n Maddison Project Database </a\n >.\n</p>\n\n<p>\n For Sub-Saharan African countries, estimates for GDP per capita for most\n countries prior to 1950 were obtained by applying the growth rates estimated\n by Prados de la Escosura (2012){ref}Prados de la Escosura, Leandro. 2012.\n \u201cOUTPUT PER HEAD IN PRE-INDEPENDENCE AFRICA: QUANTITATIVE CONJECTURES.\u201d\n <em>Economic History of Developing Regions</em>\n 27 (2): 1\u201336.\n</p>\n\n<p>\n A working paper version is available online at Core Econ\n <a href=\"https://core.ac.uk/download/pdf/29403639.pdf\">here</a>.{/ref} to\n extend the Maddison estimates backwards (see next section on extrapolation).\n</p>\n\n<h3>3) Imputation of missing data points</h3>\n\n<p>\n The inequality, GDP per capita and population datasets listed above do not\n provide complete coverage. In order to produce global poverty estimates for a\n set of benchmark years, estimates for these three variables had to first be\n interpolated or extrapolated where missing for all countries for each\n benchmark year.\n</p>\n\n<p>The process was as follows.</p>\n\n<p>For GDP per capita and population data:</p>\n\n<ol>\n <li>\n Where no observation for a given benchmark year was available, but an\n earlier and later observation was provided in the dataset, a datapoint was\n interpolated assuming a constant annual rate of growth between the available\n data points.\n </li>\n <li>\n Where no observation prior to the benchmark year was available, a data point\n was extrapolated by applying an assumed growth rate. The growth rate applied\n was calculated as follows:\n <ol>\n <li>\n If the country was formerly part of either the USSR or Yugoslavia,\n growth rates observed in the aggregate bloc (available within the\n Maddison dataset) were applied, where available.\n </li>\n <li>\n For other countries, or for periods where data for the aggregate blocs\n of USSR or Yugoslavia were not available or applicable, the growth rate\n applied was the average rate observed within the region (according\n Maddison region definitions).\n </li>\n <li>\n For Sub-Saharan African countries, the growth rates estimated by Prados\n de la Escosura (2012) were applied as mentioned above.\n </li>\n </ol>\n </li>\n</ol>\n\n<p>\n For the Gini coefficient, missing values were replaced with the average\n observed across either the bloc (former Yugoslavia or USSR countries) or the\n region (according Maddison region definitions) in the given benchmark year.\n</p>\n\n<p>\n For the purposes of replication, the fully interpolated dataset is shown in\n the two charts below. Both charts show the same data points: GDP per capita\n along the horizontal axis, Gini coefficient along the vertical axis and\n population as bubble size. The colour indicates the source and treatment used\n to arrive at the GDP per capita data points and the Gini data points\n respectively.\n</p>\n\n<p>\n It should be noted that the objective of the interpolation was to provide a\n complete dataset of country-benchmark year observations that fall within\n plausible bounds, in order to derive global poverty estimates. To understand\n trends in particular countries, we refer you to the original data sources,\n listed above.\n</p>\n\n<div class=\"wp-block-columns is-style-side-by-side\">\n <div class=\"wp-block-column\">\n <iframe\n src=\"https://ourworldindata.org/grapher/use-of-interpolation-and-extrapolation-on-maddison-gdp-per-capita-data\"\n loading=\"lazy\"\n style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n </div>\n\n <div class=\"wp-block-column\">\n <iframe\n src=\"https://ourworldindata.org/grapher/use-of-interpolation-and-extrapolation-on-gini-data?time=1820\"\n loading=\"lazy\"\n style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n </div>\n</div>\n\n<h3>4) Deriving poverty estimates from a fitted parametric distribution</h3>\n\n<p>\n Poverty estimates for each country and benchmark year were derived by fitting\n a lognormal income distribution.\n</p>\n\n<p>\n A lognormal distribution is defined by two parameters,\n <!-- latex: \\mu -->\n <math><mi>μ</mi></math>\n and\n <!-- latex: \\sigma -->\n <math><mi>σ</mi></math>\n :\n</p>\n\n<p>\n These are the expected value (or mean) and standard deviation of the\n variable’s natural logarithm. These can be obtained from average incomes\n (GDP per capita) and the Gini coefficient as follows:\n</p>\n\n<ol>\n <li>\n <p>\n <!-- latex: \\sigma -->\n <math><mi>σ</mi></math>\n is obtained from the Gini coefficient given the following relationship\n (see for instance Jorda, Sarabia, J\u00e4ntti (2018)):{ref}Jorda, Sarabia,\n J\u00e4ntti (2018) \u2018Estimation of income inequality from grouped data\u2019,\n available at arxiv.org\n <a href=\"https://arxiv.org/pdf/1808.09831.pdf\">here</a>.{/ref}\n <br />\n <br />\n <!-- latex: \\[G = 2\\Phi\\left(\\frac{\\sigma}{\\sqrt{2}}\\right) -1 \\] -->\n <math display=\"block\" style=\"display: inline-block\">\n <mrow>\n <mi>G</mi>\n <mo>=</mo>\n <mn>2</mn>\n <mrow>\n <mi mathvariant=\"normal\">\u03a6</mi>\n </mrow>\n <mrow>\n <mo fence=\"true\" form=\"prefix\">(</mo>\n <mfrac>\n <mi>\u03c3</mi>\n <msqrt>\n <mn>2</mn>\n </msqrt>\n </mfrac>\n <mo fence=\"true\" form=\"postfix\">)</mo>\n </mrow>\n <mo>\u2212</mo>\n <mn>1</mn>\n </mrow>\n </math>\n <br />\n <br />\n where\n <!-- latex: G -->\n <math><mi>G</mi></math>\n is the Gini coefficient,\n <!-- latex: \\Phi -->\n <math><mi>Φ</mi></math>\n the cumulative standard normal distribution, and\n <!-- latex: \\Phi^{-1} -->\n <math>\n <msup>\n <mrow>\n <mi mathvariant=\"normal\">\u03a6</mi>\n </mrow>\n <mrow>\n <mo lspace=\"0em\" rspace=\"0em\">\u2212</mo>\n <mn>1</mn>\n </mrow>\n </msup>\n </math>\n its inverse.\n </p>\n <p>\n Rearranging, we find\n <br />\n <br />\n <!-- latex: \\[G = 2\\Phi\\left(\\frac{\\sigma}{\\sqrt{2}}\\right) -1 \\] -->\n <math display=\"block\" style=\"display: inline-block\">\n <mrow>\n <mi>G</mi>\n <mo>=</mo>\n <mn>2</mn>\n <mrow>\n <mi mathvariant=\"normal\">\u03a6</mi>\n </mrow>\n <mrow>\n <mo fence=\"true\" form=\"prefix\">(</mo>\n <mfrac>\n <mi>\u03c3</mi>\n <msqrt>\n <mn>2</mn>\n </msqrt>\n </mfrac>\n <mo fence=\"true\" form=\"postfix\">)</mo>\n </mrow>\n <mo>\u2212</mo>\n <mn>1</mn>\n </mrow>\n </math>\n </p>\n </li>\n <li>\n Assuming incomes,\n <!-- latex: X -->\n <math><mi>X</mi></math\n >, are distributed lognormally, the average income is given by:\n <br />\n <br />\n <!-- latex: \\[ \\bar{X} = e^{\\mu + \\frac{1}{2}\\sigma^2} \\] -->\n <math display=\"block\" style=\"display: inline-block\">\n <mrow>\n <mover>\n <mi>X</mi>\n <mo stretchy=\"false\" style=\"math-style: normal; math-depth: 0\"\n >–</mo\n >\n </mover>\n <mo>=</mo>\n <msup>\n <mi>e</mi>\n <mrow>\n <mi>\u03bc</mi>\n <mo>+</mo>\n <mfrac>\n <mn>1</mn>\n <mn>2</mn>\n </mfrac>\n <msup>\n <mi>\u03c3</mi>\n <mn>2</mn>\n </msup>\n </mrow>\n </msup>\n </mrow>\n </math>\n <br />\n <br />\n Rearranging we find\n <br />\n <br />\n <!-- latex: \\[ \\mu = \\ln{\\bar{X}}-\\frac{1}{2}\\sigma^2 \\] -->\n <math display=\"block\" style=\"display: inline-block\">\n <mrow>\n <mi>\u03bc</mi>\n <mo>=</mo>\n <mrow>\n <mi>ln</mi>\n <mo>\u2061</mo>\n <mspace width=\"0.1667em\"></mspace>\n </mrow>\n <mover>\n <mi>X</mi>\n <mo stretchy=\"false\" style=\"math-style: normal; math-depth: 0\"\n >–</mo\n >\n </mover>\n <mo>\u2212</mo>\n <mfrac>\n <mn>1</mn>\n <mn>2</mn>\n </mfrac>\n <msup>\n <mi>\u03c3</mi>\n <mn>2</mn>\n </msup>\n </mrow>\n </math>\n <br />\n <br />\n In our approach, the average income is given by GDP per capita.\n </li>\n <li>\n Poverty rates are then calculated, for a given poverty line,\n <!-- latex: p -->\n <math><mi>p</mi></math\n >, using the cumulative lognormal distribution defined by these two\n parameters:\n <br />\n <br />\n <!-- latex: \\[ Poverty(p) = P(X\\leq p) = \\Phi\\left(\\frac{(\\ln{p})-\\mu}{\\sigma}\\right) \\] -->\n <math display=\"block\" style=\"display: inline-block\">\n <mrow>\n <mi>Poverty</mi>\n <mo form=\"prefix\" stretchy=\"false\">(</mo>\n <mi>p</mi>\n <mo form=\"postfix\" stretchy=\"false\">)</mo>\n <mo>=</mo>\n <mi>P</mi>\n <mo form=\"prefix\" stretchy=\"false\">(</mo>\n <mi>X</mi>\n <mo>\u2264</mo>\n <mi>p</mi>\n <mo form=\"postfix\" stretchy=\"false\">)</mo>\n <mo>=</mo>\n <mrow>\n <mi mathvariant=\"normal\">\u03a6</mi>\n </mrow>\n <mrow>\n <mo fence=\"true\" form=\"prefix\">(</mo>\n <mfrac>\n <mrow>\n <mo form=\"prefix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\"\n >(</mo\n >\n <mrow>\n <mi>ln</mi>\n <mo>\u2061</mo>\n <mspace width=\"0.1667em\"></mspace>\n </mrow>\n <mi>p</mi>\n <mo form=\"postfix\" stretchy=\"false\">)</mo>\n <mo>\u2212</mo>\n <mi>\u03bc</mi>\n </mrow>\n <mi>\u03c3</mi>\n </mfrac>\n <mo fence=\"true\" form=\"postfix\">)</mo>\n </mrow>\n </mrow>\n </math>\n <br />\n <br />\n This yields the poverty estimates for individual countries, shown in the\n chart. (You can change the country in the visualization or download the data\n for all countries). As discussed above, the data for many countries relies\n on extensive interpolation or extrapolation and should not be relied on to\n understand trends in particular countries without consulting the underlying\n data sources.\n </li>\n <li>\n World and regional poverty rates are then calculated as the\n population-weighted average rates across countries.\n </li>\n</ol>\n\n<iframe\n src=\"https://ourworldindata.org/grapher/reconstruction-of-historical-poverty-trends-by-country?country=~GBR\"\n loading=\"lazy\"\n style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n\n<h3>4) Alternative specifications and robustness checks</h3>\n\n<h4>Alternative selection of inequality data</h4>\n\n<p>\n Here we show global poverty estimates for four poverty lines, constructed in\n the way described above, using different data sources for the Gini coefficient\n for more recent decades.\n</p>\n\n<p>\n The blue lines show again our baseline estimates which use GCIP data for\n income inequality. The red lines recalculate the estimates using the GCIP data\n for consumption inequality instead. The green lines show poverty estimates\n using instead data taken from the World Bank\u2019s Povcal database, which is a mix\n of consumption and income inequality figures. In all three cases the\n historical estimates from van Zanden are used for earlier periods (in the case\n of the Povcal data iteration, data points from van Zanden are also used in\n more recent decades to increase the coverage prior to imputation).\n</p>\n\n<p>The different inequality data sources yield very similar trends.</p>\n\n<figure class=\"wp-block-image size-large\">\n <img\n loading=\"lazy\"\n width=\"412\"\n height=\"550\"\n src=\"https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-412x550.png\"\n alt=\"\"\n class=\"wp-image-44062\"\n srcset=\"\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-412x550.png 412w,\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-300x400.png 300w,\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-112x150.png 112w,\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-768x1025.png 768w,\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-1150x1536.png 1150w,\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-1534x2048.png 1534w\n \"\n sizes=\"(max-width: 412px) 100vw, 412px\" />\n</figure>\n\n<p></p>\n\n<h4>Comparison with higher and lower inequality scenarios</h4>\n\n<p>\n In this comparison chart, the green lines now plot global poverty rates where\n the estimates of the Gini coefficients used in our baseline figures have been\n replaced by much\n <strong>higher</strong>\n levels: the maximum of either the original value increased by one third or the\n highest value observed across the original dataset. The red lines plot global\n poverty rates where the Gini coefficients have been replaced by much\n <strong>lower</strong>\n levels: the minimum of either the original value reduced by one third or the\n lowest value observed across the original dataset.\n <br />\n As we see from the chart, and as discussed in the main paper, different\n assumptions concerning the level of inequality have relatively little impact\n on the long-run poverty trends given the large growth seen in average incomes\n over this period. Where the\n <em>average</em>\n income falls close to or below the poverty line, reducing inequality has a\n negligible effect on the poverty rate (perversely, the poverty rate may rise\n if it results in even fewer \u2018rich\u2019 people with incomes high enough to fall\n above the poverty line). This demonstrates that the major trends are not\n sensitive to uncertainty in the historical distributional data we have used.\n</p>\n\n<figure class=\"wp-block-image size-large\">\n <img\n loading=\"lazy\"\n width=\"409\"\n height=\"550\"\n src=\"https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-409x550.png\"\n alt=\"\"\n class=\"wp-image-44064\"\n srcset=\"\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-409x550.png 409w,\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-297x400.png 297w,\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-112x150.png 112w,\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-768x1033.png 768w,\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-1142x1536.png 1142w,\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-1523x2048.png 1523w\n \"\n sizes=\"(max-width: 409px) 100vw, 409px\" />\n</figure>\n\n<h4>Comparison with higher and lower GDP per capita scenarios</h4>\n\n<p>\n Here we show a similar check on the sensitivity of our global poverty\n estimates to different assumptions concerning the level of GDP per capita.\n</p>\n\n<p>\n The green lines plot global poverty rates where the estimates of GDP per\n capita have been replaced by much\n <strong>higher</strong>\n levels: the original value increased by one third. The red lines plot global\n poverty rates where the estimates of GDP per capita have been replaced by much\n <strong>lower</strong>\n levels: the original value reduced by one third.\n</p>\n\n<p>\n The fall in poverty shown in these estimates is driven by economic growth \u2013\n with average income per person globally increasing by roughly a factor of ten\n over this period. As such, the overall trends are robust to a wide degree of\n uncertainty concerning the level of income in any given year.\n</p>\n\n<figure class=\"wp-block-image size-large\">\n <img\n loading=\"lazy\"\n width=\"413\"\n height=\"550\"\n src=\"https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-413x550.png\"\n alt=\"\"\n class=\"wp-image-44065\"\n srcset=\"\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-413x550.png 413w,\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-300x400.png 300w,\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-113x150.png 113w,\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-768x1024.png 768w,\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-1153x1536.png 1153w,\n https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-1537x2048.png 1537w\n \"\n sizes=\"(max-width: 413px) 100vw, 413px\" />\n</figure>\n\n<h3>5) Code availability</h3>\n\n<p>\n R was used to interpolate the data missing from the original sources and\n estimate global and regional poverty rates. All code is available to download\n <a\n href=\"https://drive.google.com/drive/folders/1wXlRLWnPegVoCTQDP_jLoRHGidXxPLOP?usp=sharing\">\n here </a\n >.\n</p>\n", "protected": false }, "excerpt": { "rendered": "An online data appendix explaining the data and methods used to estimate the historical poverty trends presented in Roser and Hasell (2021)", "protected": false }, "date_gmt": "2019-07-07T13:23:00", "modified": "2021-07-07T19:08:35", "template": "", "categories": [ 1 ], "ping_status": "closed", "authors_name": [ "Joe Hasell" ], "modified_gmt": "2021-07-07T18:08:35", "comment_status": "closed", "featured_media": 44082, "featured_media_paths": { "thumbnail": "/app/uploads/2021/07/reconstruction-of-historical-global-extreme-poverty-rates-1820-2017-roser-and-hasell-2021-and-world-bank2020-150x106.png", "medium_large": "/app/uploads/2021/07/reconstruction-of-historical-global-extreme-poverty-rates-1820-2017-roser-and-hasell-2021-and-world-bank2020-768x542.png" } }

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Data appendix – The fight against global poverty: 200 years of progress and still a very long way to go

history-of-poverty-data-appendix

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<div class="blog-info"> <p>This is an online data appendix explaining the data and methods used to estimate the historical poverty trends presented in Roser and Hasell (2021).<br> For related data and research, see our entry on <strong><a href="https://ourworldindata.org/extreme-poverty" target="_blank" rel="noopener">Extreme Poverty</a></strong>.</p> </div>   <p>This is an appendix providing further detail on the data and methods used in our historical reconstructions of global poverty from national accounts data, as presented in Roser and Hasell (2021).</p>   <p>The paper will be available online at the <a href="https://www.mdpi.com/books/pdfview/edition/1404">publisher's website</a>.</p>   <p>Note that:</p>   <ul><li>All dollar figures below are expressed in international-$ in 2011 prices (adjusted to account for price differences across countries and for inflation).</li><li>You can download the data of each interactive chart shown below using the download tab found at the bottom of each chart.</li></ul>   <h3>1) Baseline estimates</h3>   <p>First we present the baseline poverty estimates presented in the paper.</p>   <h4>The number and share of people living at different income thresholds.</h4>   <p>This is an interactive version of the charts included as figure 11 in the main paper.</p>   <div class="wp-block-columns is-style-side-by-side"> <div class="wp-block-column"> <iframe src="https://ourworldindata.org/grapher/historical-national-accounts-estimates-of-the-distribution-of-people-living-at-different-income-thresholds-globally?country=~OWID_WRL" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe> </div>   <div class="wp-block-column"> <iframe src="https://ourworldindata.org/grapher/historical-national-accounts-estimates-of-the-distribution-of-people-living-at-different-income-thresholds-globally?stackMode=relative&country=~OWID_WRL" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe> </div> </div>   <h4>The share living below $5 a day, by region</h4>   <p>Here we provide interactive versions of figures 12 and 13 of the main paper.</p>   <div class="wp-block-columns is-style-side-by-side"> <div class="wp-block-column"> <iframe src="https://ourworldindata.org/grapher/regional_pov_rate" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe> </div>   <div class="wp-block-column"> <iframe src="https://ourworldindata.org/grapher/historical-share-of-population-living-on-less-than-5-per-day-roser-hasell" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe> </div> </div>   <h4>A single long-run series of extreme poverty combining national accounts and recent survey based estimates</h4>   <p>This is an interactive version of figure 14 of the main paper.</p>   <p>It joins recent World Bank estimates of the share of people globally living below $1.90 a day from 1980, with our own historical national accounts estimates using a poverty line of $5.20. For a discussion of these two approaches to estimating poverty and how they relate to one another see the main paper.</p>   <iframe src="https://ourworldindata.org/grapher/reconstruction-of-historical-global-extreme-poverty-rates-1820-2017-roser-and-hasell-2021-and-world-bank2020?stackMode=relative" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe>   <h3>2) Data sources</h3>   <p>As explained in the paper, the estimates above are based on three inputs: </p>   <ul><li>data on inequality, as measured by Gini coefficient,</li><li>data on average incomes, as measured by GDP per capita</li><li>population data</li></ul>   <p>Here we discuss the sources used for each of these inputs.</p>   <h4>Inequality data</h4>   <p>Our baseline estimates are based on a combination of two datasets:</p>   <ul><li>The historical inequality dataset gathered and published in van Zanden and others (2014){ref}Zanden, Jan Luiten van, Joerg Baten, Peter Foldvari, and Bas van Leeuwen. 2014. “The Changing Shape of Global Inequality 1820–2000; Exploring a New Dataset.” <em>Review of Income and Wealth</em> 60 (2): 279–97.{/ref} and, made available online by the authors at <a href="https://clio-infra.eu/Indicators/IncomeInequality.html">clio-infra</a>.</li><li>From 1960, an interpolated dataset of income Ginis produced by the <a href="http://gcip.info/">Global Consumption and Income Project (GCIP)</a>.</li></ul>   <p>Alternative estimates (presented below) combine the historical data from van Zanden and others (2014) with two other datasets for more recent decades respectively:</p>   <ul><li><a href="http://gcip.info">GCIP</a>’s dataset of consumption Ginis</li><li>the World Bank's <a href="http://iresearch.worldbank.org/PovcalNet/home.aspx">Povcal dataset</a></li></ul>   <h4>GDP per capita and population data</h4>   <p>All population data and almost all data on GDP per capita is derived purely from the 2020 release of the <a href="https://www.rug.nl/ggdc/historicaldevelopment/maddison/releases/maddison-project-database-2020?lang=en">Maddison Project Database</a>.</p>   <p>For Sub-Saharan African countries, estimates for GDP per capita for most countries prior to 1950 were obtained by applying the growth rates estimated by Prados de la Escosura (2012){ref}Prados de la Escosura, Leandro. 2012. “OUTPUT PER HEAD IN PRE-INDEPENDENCE AFRICA: QUANTITATIVE CONJECTURES.” <em>Economic History of Developing Regions</em> 27 (2): 1–36.</p>   <p>A working paper version is available online at Core Econ <a href="https://core.ac.uk/download/pdf/29403639.pdf">here</a>.{/ref} to extend the Maddison estimates backwards (see next section on extrapolation).</p>   <h3>3) Imputation of missing data points</h3>   <p>The inequality, GDP per capita and population datasets listed above do not provide complete coverage. In order to produce global poverty estimates for a set of benchmark years, estimates for these three variables had to first be interpolated or extrapolated where missing for all countries for each benchmark year.</p>   <p>The process was as follows.</p>   <p>For GDP per capita and population data:</p>   <ol><li>Where no observation for a given benchmark year was available, but an earlier and later observation was provided in the dataset, a datapoint was interpolated assuming a constant annual rate of growth between the available data points.</li><li>Where no observation prior to the benchmark year was available, a data point was extrapolated by applying an assumed growth rate. The growth rate applied was calculated as follows:<ol><li>If the country was formerly part of either the USSR or Yugoslavia, growth rates observed in the aggregate bloc (available within the Maddison dataset) were applied, where available.</li><li>For other countries, or for periods where data for the aggregate blocs of USSR or Yugoslavia were not available or applicable, the growth rate applied was the average rate observed within the region (according Maddison region definitions).</li><li>For Sub-Saharan African countries, the growth rates estimated by Prados de la Escosura (2012) were applied as mentioned above.</li></ol></li></ol>   <p>For the Gini coefficient, missing values were replaced with the average observed across either the bloc (former Yugoslavia or USSR countries) or the region (according Maddison region definitions) in the given benchmark year.</p>   <p>For the purposes of replication, the fully interpolated dataset is shown in the two charts below. Both charts show the same data points: GDP per capita along the horizontal axis, Gini coefficient along the vertical axis and population as bubble size. The colour indicates the source and treatment used to arrive at the GDP per capita data points and the Gini data points respectively.</p>   <p>It should be noted that the objective of the interpolation was to provide a complete dataset of country-benchmark year observations that fall within plausible bounds, in order to derive global poverty estimates. To understand trends in particular countries, we refer you to the original data sources, listed above.</p>   <div class="wp-block-columns is-style-side-by-side"> <div class="wp-block-column"> <iframe src="https://ourworldindata.org/grapher/use-of-interpolation-and-extrapolation-on-maddison-gdp-per-capita-data" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe> </div>   <div class="wp-block-column"> <iframe src="https://ourworldindata.org/grapher/use-of-interpolation-and-extrapolation-on-gini-data?time=1820" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe> </div> </div>   <h3>4) Deriving poverty estimates from a fitted parametric distribution</h3>   <p>Poverty estimates for each country and benchmark year were derived by fitting a lognormal income distribution.</p>   <p>A lognormal distribution is defined by two parameters, [latex]\mu[/latex] and [latex]\sigma[/latex]:</p>   <p> These are the expected value (or mean) and standard deviation of the variable's natural logarithm. These can be obtained from average incomes (GDP per capita) and the Gini coefficient as follows:</p>   <ol><li><p>[latex]\sigma[/latex] is obtained from the Gini coefficient given the following relationship (see for instance Jorda, Sarabia, Jäntti (2018)):{ref}Jorda, Sarabia, Jäntti (2018) ‘Estimation of income inequality from grouped data’, available at arxiv.org <a href="https://arxiv.org/pdf/1808.09831.pdf">here</a>.{/ref}<br><br> [latex] \[G = 2\Phi\left(\frac{\sigma}{\sqrt{2}}\right) -1 \] [/latex]<br><br> where [latex]G[/latex] is the Gini coefficient, [latex]\Phi[/latex] the cumulative standard normal distribution, and [latex]\Phi^{-1}[/latex] its inverse.</p> <p>Rearranging, we find <br><br> [latex] \[G = 2\Phi\left(\frac{\sigma}{\sqrt{2}}\right) -1 \] [/latex] </p> </li><li>Assuming incomes, [latex]X[/latex], are distributed lognormally, the average income is given by: <br><br> [latex] \[ \bar{X} = e^{\mu + \frac{1}{2}\sigma^2} \] [/latex] <br><br> Rearranging we find <br><br> [latex] \[ \mu = \ln{\bar{X}}-\frac{1}{2}\sigma^2 \] [/latex] <br><br> In our approach, the average income is given by GDP per capita. </li><li>Poverty rates are then calculated, for a given poverty line, [latex]p[/latex], using the cumulative lognormal distribution defined by these two parameters: <br><br> [latex] \[ Poverty(p) = P(X\leq p) = \Phi\left(\frac{(\ln{p})-\mu}{\sigma}\right) \] [/latex] <br><br> This yields the poverty estimates for individual countries, shown in the chart. (You can change the country in the visualization or download the data for all countries). As discussed above, the data for many countries relies on extensive interpolation or extrapolation and should not be relied on to understand trends in particular countries without consulting the underlying data sources. </li><li>World and regional poverty rates are then calculated as the population-weighted average rates across countries. </li></ol>   <iframe src="https://ourworldindata.org/grapher/reconstruction-of-historical-poverty-trends-by-country?country=~GBR" loading="lazy" style="width: 100%; height: 600px; border: 0px none;"></iframe>   <h3>4) Alternative specifications and robustness checks</h3>   <h4>Alternative selection of inequality data</h4>   <p>Here we show global poverty estimates for four poverty lines, constructed in the way described above, using different data sources for the Gini coefficient for more recent decades.</p>   <p>The blue lines show again our baseline estimates which use GCIP data for income inequality. The red lines recalculate the estimates using the GCIP data for consumption inequality instead. The green lines show poverty estimates using instead data taken from the World Bank’s Povcal database, which is a mix of consumption and income inequality figures. In all three cases the historical estimates from van Zanden are used for earlier periods (in the case of the Povcal data iteration, data points from van Zanden are also used in more recent decades to increase the coverage prior to imputation).</p>   <p>The different inequality data sources yield very similar trends.</p>   <figure class="wp-block-image size-large"><img src="https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-412x550.png" alt="" class="wp-image-44062"/></figure>   <p></p>   <h4>Comparison with higher and lower inequality scenarios</h4>   <p>In this comparison chart, the green lines now plot global poverty rates where the estimates of the Gini coefficients used in our baseline figures have been replaced by much <strong>higher</strong> levels: the maximum of either the original value increased by one third or the highest value observed across the original dataset. The red lines plot global poverty rates where the Gini coefficients have been replaced by much <strong>lower</strong> levels: the minimum of either the original value reduced by one third or the lowest value observed across the original dataset.<br>As we see from the chart, and as discussed in the main paper, different assumptions concerning the level of inequality have relatively little impact on the long-run poverty trends given the large growth seen in average incomes over this period. Where the <em>average</em> income falls close to or below the poverty line, reducing inequality has a negligible effect on the poverty rate (perversely, the poverty rate may rise if it results in even fewer ‘rich’ people with incomes high enough to fall above the poverty line). This demonstrates that the major trends are not sensitive to uncertainty in the historical distributional data we have used.</p>   <figure class="wp-block-image size-large"><img src="https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-409x550.png" alt="" class="wp-image-44064"/></figure>   <h4>Comparison with higher and lower GDP per capita scenarios</h4>   <p>Here we show a similar check on the sensitivity of our global poverty estimates to different assumptions concerning the level of GDP per capita.</p>   <p>The green lines plot global poverty rates where the estimates of GDP per capita have been replaced by much <strong>higher</strong> levels: the original value increased by one third. The red lines plot global poverty rates where the estimates of GDP per capita have been replaced by much <strong>lower</strong> levels: the original value reduced by one third.</p>   <p>The fall in poverty shown in these estimates is driven by economic growth – with average income per person globally increasing by roughly a factor of ten over this period. As such, the overall trends are robust to a wide degree of uncertainty concerning the level of income in any given year.</p>   <figure class="wp-block-image size-large"><img src="https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-413x550.png" alt="" class="wp-image-44065"/></figure>   <h3>5) Code availability</h3>   <p>R was used to interpolate the data missing from the original sources and estimate global and regional poverty rates. All code is available to download <a href="https://drive.google.com/drive/folders/1wXlRLWnPegVoCTQDP_jLoRHGidXxPLOP?usp=sharing">here</a>.</p>

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                        "text": "This is an online data appendix explaining the data and methods used to estimate the historical poverty trends presented in Roser and Hasell (2021).",
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                        "text": " For related data and research, see our entry on ",
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                                "url": "https://ourworldindata.org/extreme-poverty",
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                                        "text": "Extreme Poverty",
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                        "text": "This is an appendix providing further detail on the data and methods used in our historical reconstructions of global poverty from national accounts data, as presented in Roser and Hasell (2021).",
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                        "text": "The paper will be available online at the ",
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                                "text": "publisher's website",
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                        "text": ".",
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                        "text": "Note that:",
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                                "text": "All dollar figures below are expressed in international-$ in 2011 prices (adjusted to account for price differences across countries and for inflation).",
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                                "text": "You can download the data of each interactive chart shown below using the download tab found at the bottom of each chart.",
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                        "text": "1) Baseline estimates",
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                        "text": "First we present the baseline poverty estimates presented in the paper.",
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                "text": [
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                        "text": "The number and share of people living at different income thresholds.",
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                        "text": "This is an interactive version of the charts included as figure 11 in the main paper.",
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                        "url": "https://ourworldindata.org/grapher/historical-national-accounts-estimates-of-the-distribution-of-people-living-at-different-income-thresholds-globally?country=~OWID_WRL",
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                        "text": "The share living below $5 a day, by region",
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                        "text": "Here we provide interactive versions of figures 12 and 13 of the main paper.",
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                        "text": "A single long-run series of extreme poverty combining national accounts and recent survey based estimates",
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                        "text": "This is an interactive version of figure 14 of the main paper.",
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                        "text": "It joins recent World Bank estimates of the share of people globally living below $1.90 a day from 1980, with our own historical national accounts estimates using a poverty line of $5.20. For a discussion of these two approaches to estimating poverty and how they relate to one another see the main paper.",
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                        "text": "2) Data sources",
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                        "text": "As explained in the paper, the estimates above are based on three inputs:\u00a0",
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                                "text": "data on inequality, as measured by Gini coefficient,",
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                        "text": "Inequality data",
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                        "text": "Our baseline estimates are based on a combination of two datasets:",
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                                "text": "The historical inequality dataset gathered and published in van Zanden and others (2014){ref}Zanden, Jan Luiten van, Joerg Baten, Peter Foldvari, and Bas van Leeuwen. 2014. \u201cThe Changing Shape of Global Inequality 1820\u20132000; Exploring a New Dataset.\u201d ",
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                                "children": [
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                                        "text": "Review of Income and Wealth",
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                                "text": " 60 (2): 279\u201397.{/ref} and, made available online by the authors at ",
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                                "url": "https://clio-infra.eu/Indicators/IncomeInequality.html",
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                                        "text": "clio-infra",
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                                "text": ".",
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                                "text": "From 1960, an interpolated dataset of income Ginis produced by the ",
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                                "url": "http://gcip.info/",
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                                        "text": "Global Consumption and Income Project (GCIP)",
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                                "text": ".",
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                        "text": "Alternative estimates (presented below) combine the historical data from van Zanden and others (2014) with two other datasets for more recent decades respectively:",
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                                        "text": "GCIP",
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                                "text": "\u2019s dataset of consumption Ginis",
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                                "text": "the World Bank's ",
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                                "url": "http://iresearch.worldbank.org/PovcalNet/home.aspx",
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                                        "text": "Povcal dataset",
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                        "text": "GDP per capita and population data",
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                        "text": "All population data and almost all data on GDP per capita is derived purely from the 2020 release of the ",
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                        "url": "https://www.rug.nl/ggdc/historicaldevelopment/maddison/releases/maddison-project-database-2020?lang=en",
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                                "text": "Maddison Project Database",
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                        "text": ".",
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                        "text": "For Sub-Saharan African countries, estimates for GDP per capita for most countries prior to 1950 were obtained by applying the growth rates estimated by Prados de la Escosura (2012){ref}Prados de la Escosura, Leandro. 2012. \u201cOUTPUT PER HEAD IN PRE-INDEPENDENCE AFRICA: QUANTITATIVE CONJECTURES.\u201d ",
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                                "text": "Economic History of Developing Regions",
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                        "text": " 27 (2): 1\u201336.",
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                        "text": "A working paper version is available online at Core Econ ",
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                        "url": "https://core.ac.uk/download/pdf/29403639.pdf",
                        "children": [
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                                "text": "here",
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                        "text": ".{/ref} to extend the Maddison estimates backwards (see next section on extrapolation).",
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                "text": [
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                        "text": "3) Imputation of missing data points",
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                        "text": "The inequality, GDP per capita and population datasets listed above do not provide complete coverage. In order to produce global poverty estimates for a set of benchmark years, estimates for these three variables had to first be interpolated or extrapolated where missing for all countries for each benchmark year.",
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                        "text": "The process was as follows.",
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                        "text": "For GDP per capita and population data:",
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                                "text": "Where no observation for a given benchmark year was available, but an earlier and later observation was provided in the dataset, a datapoint was interpolated assuming a constant annual rate of growth between the available data points.",
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                            {
                                "text": "Where no observation prior to the benchmark year was available, a data point was extrapolated by applying an assumed growth rate. The growth rate applied was calculated as follows:",
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                        "text": "For the Gini coefficient, missing values were replaced with the average observed across either the bloc (former Yugoslavia or USSR countries) or the region (according Maddison region definitions) in the given benchmark year.",
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                        "text": "For the purposes of replication, the fully interpolated dataset is shown in the two charts below. Both charts show the same data points: GDP per capita along the horizontal axis, Gini coefficient along the vertical axis and population as bubble size. The colour indicates the source and treatment used to arrive at the GDP per capita data points and the Gini data points respectively.",
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                        "text": "It should be noted that the objective of the interpolation was to provide a complete dataset of country-benchmark year observations that fall within plausible bounds, in order to derive global poverty estimates. To understand trends in particular countries, we refer you to the original data sources, listed above.",
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                "text": [
                    {
                        "text": "4) Deriving poverty estimates from a fitted parametric distribution",
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                        "text": "Poverty estimates for each country and benchmark year were derived by fitting a lognormal income distribution.",
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                "type": "text",
                "value": [
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                        "text": "A lognormal distribution is defined by two parameters, [latex]\\mu[/latex] and [latex]\\sigma[/latex]:",
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                        "text": " These are the expected value (or mean) and standard deviation of the variable's natural logarithm. These can be obtained from average incomes (GDP per capita) and the Gini coefficient as follows:",
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                                "text": "[latex]\\sigma[/latex] is obtained from the Gini coefficient given the following relationship (see for instance Jorda, Sarabia, J\u00e4ntti (2018)):{ref}Jorda, Sarabia, J\u00e4ntti (2018) \u2018Estimation of income inequality from grouped data\u2019, available at arxiv.org ",
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                            {
                                "url": "https://arxiv.org/pdf/1808.09831.pdf",
                                "children": [
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                                        "text": "here",
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                                "text": ".{/ref}",
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                                "spanType": "span-newline"
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                                "spanType": "span-newline"
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                                "text": "\n[latex]\n\\[G = 2\\Phi\\left(\\frac{\\sigma}{\\sqrt{2}}\\right) -1 \\]\n[/latex]",
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                            {
                                "spanType": "span-newline"
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                            {
                                "spanType": "span-newline"
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                                "text": "\nwhere [latex]G[/latex] is the Gini coefficient, [latex]\\Phi[/latex] the cumulative standard normal distribution, and [latex]\\Phi^{-1}[/latex] its inverse.",
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                            {
                                "text": "Rearranging, we find ",
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                                "spanType": "span-newline"
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                                "text": "\n[latex]\n\\[G = 2\\Phi\\left(\\frac{\\sigma}{\\sqrt{2}}\\right) -1 \\]\n[/latex] ",
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                        "text": "The blue lines show again our baseline estimates which use GCIP data for income inequality. The red lines recalculate the estimates using the GCIP data for consumption inequality instead. The green lines show poverty estimates using instead data taken from the World Bank\u2019s Povcal database, which is a mix of consumption and income inequality figures. In all three cases the historical estimates from van Zanden are used for earlier periods (in the case of the Povcal data iteration, data points from van Zanden are also used in more recent decades to increase the coverage prior to imputation).",
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2019-07-07 13:23:00

2024-06-19 11:10:00

1NJRWwn6xcH_O8vMG4ZKqI_5i7V6mhpZu6ctyG-hZvPo

[
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An online data appendix explaining the data and methods used to estimate the historical poverty trends presented in Roser and Hasell (2021)

2021-07-06 10:21:27

2021-07-07 18:08:35

https://ourworldindata.org/wp-content/uploads/2021/07/reconstruction-of-historical-global-extreme-poverty-rates-1820-2017-roser-and-hasell-2021-and-world-bank2020.png

{}

This is an online data appendix explaining the data and methods used to estimate the historical poverty trends presented in Roser and Hasell (2021). For related data and research, see our entry on **[Extreme Poverty](https://ourworldindata.org/extreme-poverty)**. This is an appendix providing further detail on the data and methods used in our historical reconstructions of global poverty from national accounts data, as presented in Roser and Hasell (2021). The paper will be available online at the [publisher's website](https://www.mdpi.com/books/pdfview/edition/1404). Note that: * All dollar figures below are expressed in international-$ in 2011 prices (adjusted to account for price differences across countries and for inflation). * You can download the data of each interactive chart shown below using the download tab found at the bottom of each chart. ## 1) Baseline estimates First we present the baseline poverty estimates presented in the paper. ### The number and share of people living at different income thresholds. This is an interactive version of the charts included as figure 11 in the main paper. <Chart url="https://ourworldindata.org/grapher/historical-national-accounts-estimates-of-the-distribution-of-people-living-at-different-income-thresholds-globally?country=~OWID_WRL"/> <Chart url="https://ourworldindata.org/grapher/historical-national-accounts-estimates-of-the-distribution-of-people-living-at-different-income-thresholds-globally?stackMode=relative&country=~OWID_WRL"/> ### The share living below $5 a day, by region Here we provide interactive versions of figures 12 and 13 of the main paper. <Chart url="https://ourworldindata.org/grapher/regional_pov_rate"/> <Chart url="https://ourworldindata.org/grapher/historical-share-of-population-living-on-less-than-5-per-day-roser-hasell"/> ### A single long-run series of extreme poverty combining national accounts and recent survey based estimates This is an interactive version of figure 14 of the main paper. It joins recent World Bank estimates of the share of people globally living below $1.90 a day from 1980, with our own historical national accounts estimates using a poverty line of $5.20. For a discussion of these two approaches to estimating poverty and how they relate to one another see the main paper. <Chart url="https://ourworldindata.org/grapher/reconstruction-of-historical-global-extreme-poverty-rates-1820-2017-roser-and-hasell-2021-and-world-bank2020?stackMode=relative"/> ## 2) Data sources As explained in the paper, the estimates above are based on three inputs: * data on inequality, as measured by Gini coefficient, * data on average incomes, as measured by GDP per capita * population data Here we discuss the sources used for each of these inputs. ### Inequality data Our baseline estimates are based on a combination of two datasets: * The historical inequality dataset gathered and published in van Zanden and others (2014){ref}Zanden, Jan Luiten van, Joerg Baten, Peter Foldvari, and Bas van Leeuwen. 2014. “The Changing Shape of Global Inequality 1820–2000; Exploring a New Dataset.” _Review of Income and Wealth_ 60 (2): 279–97.{/ref} and, made available online by the authors at [clio-infra](https://clio-infra.eu/Indicators/IncomeInequality.html). * From 1960, an interpolated dataset of income Ginis produced by the [Global Consumption and Income Project (GCIP)](http://gcip.info/). Alternative estimates (presented below) combine the historical data from van Zanden and others (2014) with two other datasets for more recent decades respectively: * [GCIP](http://gcip.info)’s dataset of consumption Ginis * the World Bank's [Povcal dataset](http://iresearch.worldbank.org/PovcalNet/home.aspx) ### GDP per capita and population data All population data and almost all data on GDP per capita is derived purely from the 2020 release of the [Maddison Project Database](https://www.rug.nl/ggdc/historicaldevelopment/maddison/releases/maddison-project-database-2020?lang=en). For Sub-Saharan African countries, estimates for GDP per capita for most countries prior to 1950 were obtained by applying the growth rates estimated by Prados de la Escosura (2012){ref}Prados de la Escosura, Leandro. 2012. “OUTPUT PER HEAD IN PRE-INDEPENDENCE AFRICA: QUANTITATIVE CONJECTURES.” _Economic History of Developing Regions_ 27 (2): 1–36. A working paper version is available online at Core Econ [here](https://core.ac.uk/download/pdf/29403639.pdf).{/ref} to extend the Maddison estimates backwards (see next section on extrapolation). ## 3) Imputation of missing data points The inequality, GDP per capita and population datasets listed above do not provide complete coverage. In order to produce global poverty estimates for a set of benchmark years, estimates for these three variables had to first be interpolated or extrapolated where missing for all countries for each benchmark year. The process was as follows. For GDP per capita and population data: 0. Where no observation for a given benchmark year was available, but an earlier and later observation was provided in the dataset, a datapoint was interpolated assuming a constant annual rate of growth between the available data points. 1. Where no observation prior to the benchmark year was available, a data point was extrapolated by applying an assumed growth rate. The growth rate applied was calculated as follows: For the Gini coefficient, missing values were replaced with the average observed across either the bloc (former Yugoslavia or USSR countries) or the region (according Maddison region definitions) in the given benchmark year. For the purposes of replication, the fully interpolated dataset is shown in the two charts below. Both charts show the same data points: GDP per capita along the horizontal axis, Gini coefficient along the vertical axis and population as bubble size. The colour indicates the source and treatment used to arrive at the GDP per capita data points and the Gini data points respectively. It should be noted that the objective of the interpolation was to provide a complete dataset of country-benchmark year observations that fall within plausible bounds, in order to derive global poverty estimates. To understand trends in particular countries, we refer you to the original data sources, listed above. <Chart url="https://ourworldindata.org/grapher/use-of-interpolation-and-extrapolation-on-maddison-gdp-per-capita-data"/> <Chart url="https://ourworldindata.org/grapher/use-of-interpolation-and-extrapolation-on-gini-data?time=1820"/> ## 4) Deriving poverty estimates from a fitted parametric distribution Poverty estimates for each country and benchmark year were derived by fitting a lognormal income distribution. A lognormal distribution is defined by two parameters, [latex]\mu[/latex] and [latex]\sigma[/latex]: These are the expected value (or mean) and standard deviation of the variable's natural logarithm. These can be obtained from average incomes (GDP per capita) and the Gini coefficient as follows: 0. [latex]\sigma[/latex] is obtained from the Gini coefficient given the following relationship (see for instance Jorda, Sarabia, Jäntti (2018)):{ref}Jorda, Sarabia, Jäntti (2018) ‘Estimation of income inequality from grouped data’, available at arxiv.org [here](https://arxiv.org/pdf/1808.09831.pdf).{/ref} [latex] \[G = 2\Phi\left(\frac{\sigma}{\sqrt{2}}\right) -1 \] [/latex] where [latex]G[/latex] is the Gini coefficient, [latex]\Phi[/latex] the cumulative standard normal distribution, and [latex]\Phi^{-1}[/latex] its inverse.Rearranging, we find [latex] \[G = 2\Phi\left(\frac{\sigma}{\sqrt{2}}\right) -1 \] [/latex] 1. Assuming incomes, [latex]X[/latex], are distributed lognormally, the average income is given by: [latex] \[ \bar{X} = e^{\mu + \frac{1}{2}\sigma^2} \] [/latex] Rearranging we find [latex] \[ \mu = \ln{\bar{X}}-\frac{1}{2}\sigma^2 \] [/latex] In our approach, the average income is given by GDP per capita. 2. Poverty rates are then calculated, for a given poverty line, [latex]p[/latex], using the cumulative lognormal distribution defined by these two parameters: [latex] \[ Poverty(p) = P(X\leq p) = \Phi\left(\frac{(\ln{p})-\mu}{\sigma}\right) \] [/latex] This yields the poverty estimates for individual countries, shown in the chart. (You can change the country in the visualization or download the data for all countries). As discussed above, the data for many countries relies on extensive interpolation or extrapolation and should not be relied on to understand trends in particular countries without consulting the underlying data sources. 3. World and regional poverty rates are then calculated as the population-weighted average rates across countries. <Chart url="https://ourworldindata.org/grapher/reconstruction-of-historical-poverty-trends-by-country?country=~GBR"/> ## 4) Alternative specifications and robustness checks ### Alternative selection of inequality data Here we show global poverty estimates for four poverty lines, constructed in the way described above, using different data sources for the Gini coefficient for more recent decades. The blue lines show again our baseline estimates which use GCIP data for income inequality. The red lines recalculate the estimates using the GCIP data for consumption inequality instead. The green lines show poverty estimates using instead data taken from the World Bank’s Povcal database, which is a mix of consumption and income inequality figures. In all three cases the historical estimates from van Zanden are used for earlier periods (in the case of the Povcal data iteration, data points from van Zanden are also used in more recent decades to increase the coverage prior to imputation). The different inequality data sources yield very similar trends. <Image filename="Robustness-checks-01.png" alt=""/> ### Comparison with higher and lower inequality scenarios In this comparison chart, the green lines now plot global poverty rates where the estimates of the Gini coefficients used in our baseline figures have been replaced by much **higher** levels: the maximum of either the original value increased by one third or the highest value observed across the original dataset. The red lines plot global poverty rates where the Gini coefficients have been replaced by much **lower** levels: the minimum of either the original value reduced by one third or the lowest value observed across the original dataset. As we see from the chart, and as discussed in the main paper, different assumptions concerning the level of inequality have relatively little impact on the long-run poverty trends given the large growth seen in average incomes over this period. Where the _average_ income falls close to or below the poverty line, reducing inequality has a negligible effect on the poverty rate (perversely, the poverty rate may rise if it results in even fewer ‘rich’ people with incomes high enough to fall above the poverty line). This demonstrates that the major trends are not sensitive to uncertainty in the historical distributional data we have used. <Image filename="Robustness-checks-02.png" alt=""/> ### Comparison with higher and lower GDP per capita scenarios Here we show a similar check on the sensitivity of our global poverty estimates to different assumptions concerning the level of GDP per capita. The green lines plot global poverty rates where the estimates of GDP per capita have been replaced by much **higher** levels: the original value increased by one third. The red lines plot global poverty rates where the estimates of GDP per capita have been replaced by much **lower** levels: the original value reduced by one third. The fall in poverty shown in these estimates is driven by economic growth – with average income per person globally increasing by roughly a factor of ten over this period. As such, the overall trends are robust to a wide degree of uncertainty concerning the level of income in any given year. <Image filename="Robustness-checks-03.png" alt=""/> ## 5) Code availability R was used to interpolate the data missing from the original sources and estimate global and regional poverty rates. All code is available to download [here](https://drive.google.com/drive/folders/1wXlRLWnPegVoCTQDP_jLoRHGidXxPLOP?usp=sharing).

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        "rendered": "<div class=\"blog-info\">\n  <p>\n    This is an online data appendix explaining the data and methods used to\n    estimate the historical poverty trends presented in Roser and Hasell (2021).\n    <br />\n    For related data and research, see our entry on\n    <strong>\n      <a\n        href=\"https://ourworldindata.org/extreme-poverty\"\n        target=\"_blank\"\n        rel=\"noopener\">\n        Extreme Poverty\n      </a> </strong\n    >.\n  </p>\n</div>\n\n<p>\n  This is an appendix providing further detail on the data and methods used in\n  our historical reconstructions of global poverty from national accounts data,\n  as presented in Roser and Hasell (2021).\n</p>\n\n<p>\n  The paper will be available online at the\n  <a href=\"https://www.mdpi.com/books/pdfview/edition/1404\">\n    publisher&#8217;s website </a\n  >.\n</p>\n\n<p>Note that:</p>\n\n<ul>\n  <li>\n    All dollar figures below are expressed in international-$ in 2011 prices\n    (adjusted to account for price differences across countries and for\n    inflation).\n  </li>\n  <li>\n    You can download the data of each interactive chart shown below using the\n    download tab found at the bottom of each chart.\n  </li>\n</ul>\n\n<h3>1) Baseline estimates</h3>\n\n<p>First we present the baseline poverty estimates presented in the paper.</p>\n\n<h4>The number and share of people living at different income thresholds.</h4>\n\n<p>\n  This is an interactive version of the charts included as figure 11 in the main\n  paper.\n</p>\n\n<div class=\"wp-block-columns is-style-side-by-side\">\n  <div class=\"wp-block-column\">\n    <iframe\n      src=\"https://ourworldindata.org/grapher/historical-national-accounts-estimates-of-the-distribution-of-people-living-at-different-income-thresholds-globally?country=~OWID_WRL\"\n      loading=\"lazy\"\n      style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n  </div>\n\n  <div class=\"wp-block-column\">\n    <iframe\n      src=\"https://ourworldindata.org/grapher/historical-national-accounts-estimates-of-the-distribution-of-people-living-at-different-income-thresholds-globally?stackMode=relative&amp;country=~OWID_WRL\"\n      loading=\"lazy\"\n      style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n  </div>\n</div>\n\n<h4>The share living below $5 a day, by region</h4>\n\n<p>\n  Here we provide interactive versions of figures 12 and 13 of the main paper.\n</p>\n\n<div class=\"wp-block-columns is-style-side-by-side\">\n  <div class=\"wp-block-column\">\n    <iframe\n      src=\"https://ourworldindata.org/grapher/regional_pov_rate\"\n      loading=\"lazy\"\n      style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n  </div>\n\n  <div class=\"wp-block-column\">\n    <iframe\n      src=\"https://ourworldindata.org/grapher/historical-share-of-population-living-on-less-than-5-per-day-roser-hasell\"\n      loading=\"lazy\"\n      style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n  </div>\n</div>\n\n<h4>\n  A single long-run series of extreme poverty combining national accounts and\n  recent survey based estimates\n</h4>\n\n<p>This is an interactive version of figure 14 of the main paper.</p>\n\n<p>\n  It joins recent World Bank estimates of the share of people globally living\n  below $1.90 a day from 1980, with our own historical national accounts\n  estimates using a poverty line of $5.20. For a discussion of these two\n  approaches to estimating poverty and how they relate to one another see the\n  main paper.\n</p>\n\n<iframe\n  src=\"https://ourworldindata.org/grapher/reconstruction-of-historical-global-extreme-poverty-rates-1820-2017-roser-and-hasell-2021-and-world-bank2020?stackMode=relative\"\n  loading=\"lazy\"\n  style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n\n<h3>2) Data sources</h3>\n\n<p>\n  As explained in the paper, the estimates above are based on three\n  inputs:&nbsp;\n</p>\n\n<ul>\n  <li>data on inequality, as measured by Gini coefficient,</li>\n  <li>data on average incomes, as measured by GDP per capita</li>\n  <li>population data</li>\n</ul>\n\n<p>Here we discuss the sources used for each of these inputs.</p>\n\n<h4>Inequality data</h4>\n\n<p>Our baseline estimates are based on a combination of two datasets:</p>\n\n<ul>\n  <li>\n    The historical inequality dataset gathered and published in van Zanden and\n    others (2014){ref}Zanden, Jan Luiten van, Joerg Baten, Peter Foldvari, and\n    Bas van Leeuwen. 2014. \u201cThe Changing Shape of Global Inequality 1820\u20132000;\n    Exploring a New Dataset.\u201d\n    <em>Review of Income and Wealth</em>\n    60 (2): 279\u201397.{/ref} and, made available online by the authors at\n    <a href=\"https://clio-infra.eu/Indicators/IncomeInequality.html\">\n      clio-infra </a\n    >.\n  </li>\n  <li>\n    From 1960, an interpolated dataset of income Ginis produced by the\n    <a href=\"http://gcip.info/\">Global Consumption and Income Project (GCIP)</a\n    >.\n  </li>\n</ul>\n\n<p>\n  Alternative estimates (presented below) combine the historical data from van\n  Zanden and others (2014) with two other datasets for more recent decades\n  respectively:\n</p>\n\n<ul>\n  <li>\n    <a href=\"http://gcip.info\">GCIP</a>\n    \u2019s dataset of consumption Ginis\n  </li>\n  <li>\n    the World Bank&#8217;s\n    <a href=\"http://iresearch.worldbank.org/PovcalNet/home.aspx\">\n      Povcal dataset\n    </a>\n  </li>\n</ul>\n\n<h4>GDP per capita and population data</h4>\n\n<p>\n  All population data and almost all data on GDP per capita is derived purely\n  from the 2020 release of the\n  <a\n    href=\"https://www.rug.nl/ggdc/historicaldevelopment/maddison/releases/maddison-project-database-2020?lang=en\">\n    Maddison Project Database </a\n  >.\n</p>\n\n<p>\n  For Sub-Saharan African countries, estimates for GDP per capita for most\n  countries prior to 1950 were obtained by applying the growth rates estimated\n  by Prados de la Escosura (2012){ref}Prados de la Escosura, Leandro. 2012.\n  \u201cOUTPUT PER HEAD IN PRE-INDEPENDENCE AFRICA: QUANTITATIVE CONJECTURES.\u201d\n  <em>Economic History of Developing Regions</em>\n  27 (2): 1\u201336.\n</p>\n\n<p>\n  A working paper version is available online at Core Econ\n  <a href=\"https://core.ac.uk/download/pdf/29403639.pdf\">here</a>.{/ref} to\n  extend the Maddison estimates backwards (see next section on extrapolation).\n</p>\n\n<h3>3) Imputation of missing data points</h3>\n\n<p>\n  The inequality, GDP per capita and population datasets listed above do not\n  provide complete coverage. In order to produce global poverty estimates for a\n  set of benchmark years, estimates for these three variables had to first be\n  interpolated or extrapolated where missing for all countries for each\n  benchmark year.\n</p>\n\n<p>The process was as follows.</p>\n\n<p>For GDP per capita and population data:</p>\n\n<ol>\n  <li>\n    Where no observation for a given benchmark year was available, but an\n    earlier and later observation was provided in the dataset, a datapoint was\n    interpolated assuming a constant annual rate of growth between the available\n    data points.\n  </li>\n  <li>\n    Where no observation prior to the benchmark year was available, a data point\n    was extrapolated by applying an assumed growth rate. The growth rate applied\n    was calculated as follows:\n    <ol>\n      <li>\n        If the country was formerly part of either the USSR or Yugoslavia,\n        growth rates observed in the aggregate bloc (available within the\n        Maddison dataset) were applied, where available.\n      </li>\n      <li>\n        For other countries, or for periods where data for the aggregate blocs\n        of USSR or Yugoslavia were not available or applicable, the growth rate\n        applied was the average rate observed within the region (according\n        Maddison region definitions).\n      </li>\n      <li>\n        For Sub-Saharan African countries, the growth rates estimated by Prados\n        de la Escosura (2012) were applied as mentioned above.\n      </li>\n    </ol>\n  </li>\n</ol>\n\n<p>\n  For the Gini coefficient, missing values were replaced with the average\n  observed across either the bloc (former Yugoslavia or USSR countries) or the\n  region (according Maddison region definitions) in the given benchmark year.\n</p>\n\n<p>\n  For the purposes of replication, the fully interpolated dataset is shown in\n  the two charts below. Both charts show the same data points: GDP per capita\n  along the horizontal axis, Gini coefficient along the vertical axis and\n  population as bubble size. The colour indicates the source and treatment used\n  to arrive at the GDP per capita data points and the Gini data points\n  respectively.\n</p>\n\n<p>\n  It should be noted that the objective of the interpolation was to provide a\n  complete dataset of country-benchmark year observations that fall within\n  plausible bounds, in order to derive global poverty estimates. To understand\n  trends in particular countries, we refer you to the original data sources,\n  listed above.\n</p>\n\n<div class=\"wp-block-columns is-style-side-by-side\">\n  <div class=\"wp-block-column\">\n    <iframe\n      src=\"https://ourworldindata.org/grapher/use-of-interpolation-and-extrapolation-on-maddison-gdp-per-capita-data\"\n      loading=\"lazy\"\n      style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n  </div>\n\n  <div class=\"wp-block-column\">\n    <iframe\n      src=\"https://ourworldindata.org/grapher/use-of-interpolation-and-extrapolation-on-gini-data?time=1820\"\n      loading=\"lazy\"\n      style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n  </div>\n</div>\n\n<h3>4) Deriving poverty estimates from a fitted parametric distribution</h3>\n\n<p>\n  Poverty estimates for each country and benchmark year were derived by fitting\n  a lognormal income distribution.\n</p>\n\n<p>\n  A lognormal distribution is defined by two parameters,\n  <!-- latex: \\mu -->\n  <math><mi>&mu;</mi></math>\n  and\n  <!-- latex: \\sigma -->\n  <math><mi>&sigma;</mi></math>\n  :\n</p>\n\n<p>\n  These are the expected value (or mean) and standard deviation of the\n  variable&#8217;s natural logarithm. These can be obtained from average incomes\n  (GDP per capita) and the Gini coefficient as follows:\n</p>\n\n<ol>\n  <li>\n    <p>\n      <!-- latex: \\sigma -->\n      <math><mi>&sigma;</mi></math>\n      is obtained from the Gini coefficient given the following relationship\n      (see for instance Jorda, Sarabia, J\u00e4ntti (2018)):{ref}Jorda, Sarabia,\n      J\u00e4ntti (2018) \u2018Estimation of income inequality from grouped data\u2019,\n      available at arxiv.org\n      <a href=\"https://arxiv.org/pdf/1808.09831.pdf\">here</a>.{/ref}\n      <br />\n      <br />\n      <!-- latex: \\[G = 2\\Phi\\left(\\frac{\\sigma}{\\sqrt{2}}\\right) -1 \\] -->\n      <math display=\"block\" style=\"display: inline-block\">\n        <mrow>\n          <mi>G</mi>\n          <mo>=</mo>\n          <mn>2</mn>\n          <mrow>\n            <mi mathvariant=\"normal\">\u03a6</mi>\n          </mrow>\n          <mrow>\n            <mo fence=\"true\" form=\"prefix\">(</mo>\n            <mfrac>\n              <mi>\u03c3</mi>\n              <msqrt>\n                <mn>2</mn>\n              </msqrt>\n            </mfrac>\n            <mo fence=\"true\" form=\"postfix\">)</mo>\n          </mrow>\n          <mo>\u2212</mo>\n          <mn>1</mn>\n        </mrow>\n      </math>\n      <br />\n      <br />\n      where\n      <!-- latex: G -->\n      <math><mi>G</mi></math>\n      is the Gini coefficient,\n      <!-- latex: \\Phi -->\n      <math><mi>&Phi;</mi></math>\n      the cumulative standard normal distribution, and\n      <!-- latex: \\Phi^{-1} -->\n      <math>\n        <msup>\n          <mrow>\n            <mi mathvariant=\"normal\">\u03a6</mi>\n          </mrow>\n          <mrow>\n            <mo lspace=\"0em\" rspace=\"0em\">\u2212</mo>\n            <mn>1</mn>\n          </mrow>\n        </msup>\n      </math>\n      its inverse.\n    </p>\n    <p>\n      Rearranging, we find\n      <br />\n      <br />\n      <!-- latex: \\[G = 2\\Phi\\left(\\frac{\\sigma}{\\sqrt{2}}\\right) -1 \\] -->\n      <math display=\"block\" style=\"display: inline-block\">\n        <mrow>\n          <mi>G</mi>\n          <mo>=</mo>\n          <mn>2</mn>\n          <mrow>\n            <mi mathvariant=\"normal\">\u03a6</mi>\n          </mrow>\n          <mrow>\n            <mo fence=\"true\" form=\"prefix\">(</mo>\n            <mfrac>\n              <mi>\u03c3</mi>\n              <msqrt>\n                <mn>2</mn>\n              </msqrt>\n            </mfrac>\n            <mo fence=\"true\" form=\"postfix\">)</mo>\n          </mrow>\n          <mo>\u2212</mo>\n          <mn>1</mn>\n        </mrow>\n      </math>\n    </p>\n  </li>\n  <li>\n    Assuming incomes,\n    <!-- latex: X -->\n    <math><mi>X</mi></math\n    >, are distributed lognormally, the average income is given by:\n    <br />\n    <br />\n    <!-- latex: \\[ \\bar{X} = e^{\\mu + \\frac{1}{2}\\sigma^2} \\] -->\n    <math display=\"block\" style=\"display: inline-block\">\n      <mrow>\n        <mover>\n          <mi>X</mi>\n          <mo stretchy=\"false\" style=\"math-style: normal; math-depth: 0\"\n            >&ndash;</mo\n          >\n        </mover>\n        <mo>=</mo>\n        <msup>\n          <mi>e</mi>\n          <mrow>\n            <mi>\u03bc</mi>\n            <mo>+</mo>\n            <mfrac>\n              <mn>1</mn>\n              <mn>2</mn>\n            </mfrac>\n            <msup>\n              <mi>\u03c3</mi>\n              <mn>2</mn>\n            </msup>\n          </mrow>\n        </msup>\n      </mrow>\n    </math>\n    <br />\n    <br />\n    Rearranging we find\n    <br />\n    <br />\n    <!-- latex: \\[ \\mu = \\ln{\\bar{X}}-\\frac{1}{2}\\sigma^2 \\] -->\n    <math display=\"block\" style=\"display: inline-block\">\n      <mrow>\n        <mi>\u03bc</mi>\n        <mo>=</mo>\n        <mrow>\n          <mi>ln</mi>\n          <mo>\u2061</mo>\n          <mspace width=\"0.1667em\"></mspace>\n        </mrow>\n        <mover>\n          <mi>X</mi>\n          <mo stretchy=\"false\" style=\"math-style: normal; math-depth: 0\"\n            >&ndash;</mo\n          >\n        </mover>\n        <mo>\u2212</mo>\n        <mfrac>\n          <mn>1</mn>\n          <mn>2</mn>\n        </mfrac>\n        <msup>\n          <mi>\u03c3</mi>\n          <mn>2</mn>\n        </msup>\n      </mrow>\n    </math>\n    <br />\n    <br />\n    In our approach, the average income is given by GDP per capita.\n  </li>\n  <li>\n    Poverty rates are then calculated, for a given poverty line,\n    <!-- latex: p -->\n    <math><mi>p</mi></math\n    >, using the cumulative lognormal distribution defined by these two\n    parameters:\n    <br />\n    <br />\n    <!-- latex: \\[ Poverty(p) = P(X\\leq p) = \\Phi\\left(\\frac{(\\ln{p})-\\mu}{\\sigma}\\right) \\] -->\n    <math display=\"block\" style=\"display: inline-block\">\n      <mrow>\n        <mi>Poverty</mi>\n        <mo form=\"prefix\" stretchy=\"false\">(</mo>\n        <mi>p</mi>\n        <mo form=\"postfix\" stretchy=\"false\">)</mo>\n        <mo>=</mo>\n        <mi>P</mi>\n        <mo form=\"prefix\" stretchy=\"false\">(</mo>\n        <mi>X</mi>\n        <mo>\u2264</mo>\n        <mi>p</mi>\n        <mo form=\"postfix\" stretchy=\"false\">)</mo>\n        <mo>=</mo>\n        <mrow>\n          <mi mathvariant=\"normal\">\u03a6</mi>\n        </mrow>\n        <mrow>\n          <mo fence=\"true\" form=\"prefix\">(</mo>\n          <mfrac>\n            <mrow>\n              <mo form=\"prefix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\"\n                >(</mo\n              >\n              <mrow>\n                <mi>ln</mi>\n                <mo>\u2061</mo>\n                <mspace width=\"0.1667em\"></mspace>\n              </mrow>\n              <mi>p</mi>\n              <mo form=\"postfix\" stretchy=\"false\">)</mo>\n              <mo>\u2212</mo>\n              <mi>\u03bc</mi>\n            </mrow>\n            <mi>\u03c3</mi>\n          </mfrac>\n          <mo fence=\"true\" form=\"postfix\">)</mo>\n        </mrow>\n      </mrow>\n    </math>\n    <br />\n    <br />\n    This yields the poverty estimates for individual countries, shown in the\n    chart. (You can change the country in the visualization or download the data\n    for all countries). As discussed above, the data for many countries relies\n    on extensive interpolation or extrapolation and should not be relied on to\n    understand trends in particular countries without consulting the underlying\n    data sources.\n  </li>\n  <li>\n    World and regional poverty rates are then calculated as the\n    population-weighted average rates across countries.\n  </li>\n</ol>\n\n<iframe\n  src=\"https://ourworldindata.org/grapher/reconstruction-of-historical-poverty-trends-by-country?country=~GBR\"\n  loading=\"lazy\"\n  style=\"width: 100%; height: 600px; border: 0px none\"></iframe>\n\n<h3>4) Alternative specifications and robustness checks</h3>\n\n<h4>Alternative selection of inequality data</h4>\n\n<p>\n  Here we show global poverty estimates for four poverty lines, constructed in\n  the way described above, using different data sources for the Gini coefficient\n  for more recent decades.\n</p>\n\n<p>\n  The blue lines show again our baseline estimates which use GCIP data for\n  income inequality. The red lines recalculate the estimates using the GCIP data\n  for consumption inequality instead. The green lines show poverty estimates\n  using instead data taken from the World Bank\u2019s Povcal database, which is a mix\n  of consumption and income inequality figures. In all three cases the\n  historical estimates from van Zanden are used for earlier periods (in the case\n  of the Povcal data iteration, data points from van Zanden are also used in\n  more recent decades to increase the coverage prior to imputation).\n</p>\n\n<p>The different inequality data sources yield very similar trends.</p>\n\n<figure class=\"wp-block-image size-large\">\n  <img\n    loading=\"lazy\"\n    width=\"412\"\n    height=\"550\"\n    src=\"https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-412x550.png\"\n    alt=\"\"\n    class=\"wp-image-44062\"\n    srcset=\"\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-412x550.png    412w,\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-300x400.png    300w,\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-112x150.png    112w,\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-768x1025.png   768w,\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-1150x1536.png 1150w,\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-01-1534x2048.png 1534w\n    \"\n    sizes=\"(max-width: 412px) 100vw, 412px\" />\n</figure>\n\n<p></p>\n\n<h4>Comparison with higher and lower inequality scenarios</h4>\n\n<p>\n  In this comparison chart, the green lines now plot global poverty rates where\n  the estimates of the Gini coefficients used in our baseline figures have been\n  replaced by much\n  <strong>higher</strong>\n  levels: the maximum of either the original value increased by one third or the\n  highest value observed across the original dataset. The red lines plot global\n  poverty rates where the Gini coefficients have been replaced by much\n  <strong>lower</strong>\n  levels: the minimum of either the original value reduced by one third or the\n  lowest value observed across the original dataset.\n  <br />\n  As we see from the chart, and as discussed in the main paper, different\n  assumptions concerning the level of inequality have relatively little impact\n  on the long-run poverty trends given the large growth seen in average incomes\n  over this period. Where the\n  <em>average</em>\n  income falls close to or below the poverty line, reducing inequality has a\n  negligible effect on the poverty rate (perversely, the poverty rate may rise\n  if it results in even fewer \u2018rich\u2019 people with incomes high enough to fall\n  above the poverty line). This demonstrates that the major trends are not\n  sensitive to uncertainty in the historical distributional data we have used.\n</p>\n\n<figure class=\"wp-block-image size-large\">\n  <img\n    loading=\"lazy\"\n    width=\"409\"\n    height=\"550\"\n    src=\"https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-409x550.png\"\n    alt=\"\"\n    class=\"wp-image-44064\"\n    srcset=\"\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-409x550.png    409w,\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-297x400.png    297w,\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-112x150.png    112w,\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-768x1033.png   768w,\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-1142x1536.png 1142w,\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-02-1523x2048.png 1523w\n    \"\n    sizes=\"(max-width: 409px) 100vw, 409px\" />\n</figure>\n\n<h4>Comparison with higher and lower GDP per capita scenarios</h4>\n\n<p>\n  Here we show a similar check on the sensitivity of our global poverty\n  estimates to different assumptions concerning the level of GDP per capita.\n</p>\n\n<p>\n  The green lines plot global poverty rates where the estimates of GDP per\n  capita have been replaced by much\n  <strong>higher</strong>\n  levels: the original value increased by one third. The red lines plot global\n  poverty rates where the estimates of GDP per capita have been replaced by much\n  <strong>lower</strong>\n  levels: the original value reduced by one third.\n</p>\n\n<p>\n  The fall in poverty shown in these estimates is driven by economic growth \u2013\n  with average income per person globally increasing by roughly a factor of ten\n  over this period. As such, the overall trends are robust to a wide degree of\n  uncertainty concerning the level of income in any given year.\n</p>\n\n<figure class=\"wp-block-image size-large\">\n  <img\n    loading=\"lazy\"\n    width=\"413\"\n    height=\"550\"\n    src=\"https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-413x550.png\"\n    alt=\"\"\n    class=\"wp-image-44065\"\n    srcset=\"\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-413x550.png    413w,\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-300x400.png    300w,\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-113x150.png    113w,\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-768x1024.png   768w,\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-1153x1536.png 1153w,\n      https://owid.cloud/app/uploads/2021/07/Robustness-checks-03-1537x2048.png 1537w\n    \"\n    sizes=\"(max-width: 413px) 100vw, 413px\" />\n</figure>\n\n<h3>5) Code availability</h3>\n\n<p>\n  R was used to interpolate the data missing from the original sources and\n  estimate global and regional poverty rates. All code is available to download\n  <a\n    href=\"https://drive.google.com/drive/folders/1wXlRLWnPegVoCTQDP_jLoRHGidXxPLOP?usp=sharing\">\n    here </a\n  >.\n</p>\n",
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    "excerpt": {
        "rendered": "An online data appendix explaining the data and methods used to estimate the historical poverty trends presented in Roser and Hasell (2021)",
        "protected": false
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    "date_gmt": "2019-07-07T13:23:00",
    "modified": "2021-07-07T19:08:35",
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    "categories": [
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    "ping_status": "closed",
    "authors_name": [
        "Joe Hasell"
    ],
    "modified_gmt": "2021-07-07T18:08:35",
    "comment_status": "closed",
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