# Introduction

Open a newspaper and chances are you will find some statistic referring to how the world is fairing: “Global growth is projected to recover”, “the number of refugees worldwide is set to increase for the third straight year”, “global CO2 emissions are reaching an all-time high.” The demand for global statistics is perhaps best embodied in the Sustainable Development Goals (SDGs), whose 231 indicators for the most part can be and are aggregated to the global level.

In reality, there is rarely complete global data behind such statistics. Due to lack of resources, capacity, and political will, some countries do not produce information on the indicators of interest (Dang et al. 2021; Serajuddin et al. 2015). When creating global statistics, estimates for these countries are either imputed or simply ignored. This inevitably creates a trade-off between the _availability_ of global statistics, and the _accuracy_ of these statistics. If global statistics are only published when data are universally or nearuniversally available, there will be many important topics that cannot be illuminated. If global statistics are published even when the data coverage is weak, the accuracy of the statistics may be doubtful in the sense that they are likely to deviate from the figure had all data been available.

In this paper, we quantify this trade-off between data accuracy and data availability using the World Bank’s World Development Indicators. We select 165 indicators spanning a wide range of topics where, for a given year, data are available for at least 99% of the world’s population. We randomly remove data from these indicators and calculate the expected difference in the global statistic as a function of the share of the world’s population without data. We show that if the fraction of the world’s population on which one lacks data is _x_ , then one should expect to be 0.37* _x_ standard deviations away from the true mean, and as much as _x_ standard deviations from the mean at times. Here the standard deviation is based on the distribution of country-level estimates. As data producers might not be used to thinking in standard deviations from the mean, we provide examples of what such deviations imply.

In further results we show how these errors change (i) if one is interested in regional statistics, (ii) if data are imputed, (iii) if the probability of data missing is correlated with the indicator of interest, (iv) if one uses the share of countries rather than the share of population as a coverage threshold, and (v) if one has specific coverage requirements for populous countries, such as India. We end with recommendations on when to produce global statistics. We hope these recommendations can be used to ensure that global statistics are only made available when the accuracy is deemed sufficiently high. This has implications for international organizations and researchers producing cross-country data sets that are aggregated to create a global statistic. By consequence, the recommendations have implications for any users of such global statistics, including academia, the media, and policy makers.

To our knowledge, we are the first to study when there is enough data to create a global statistic. Yet, our paper relates to several streams of literature, such as the challenges of measuring the SDGs (MacFeely 2018; Sachs 2012), missing data on SDG reporting (Dang & Serajuddin 2020; World Bank 2021), and making inference with missing data (Dang et al. 2019).

# Method

To quantify the impact of data availability on the precision of global statistics, we rely on the World Bank’s World Development Indicators (WDI). The WDI is arguably the world’s largest database of relevant countryyear indicators spanning a wide range of topics. The WDI contains information on around 1,400 indicators covering topics such as poverty, health, agriculture, education, climate change, infrastructure and more. We select 165 different indicators that for a given year have near universal coverage (>99% of the world’s population). We diversified the indicators to cover as many different topics as possible. We focus on 2