World Bank Statistical Capacity Building Project -- The World Bank's Statistical Capacity Building Project "provides resources to help ... develop better statistical capacity that advances the national and international monitoring of development policies and goals." The project is in part an outgrowth of "outcomes-based" approaches to development that place greater emphasis on attemping to actually measure development and the impact of national and international policies intended to promote it. The resources here include various reports on the quality of gathering of data/statistics in individual countries, as well as a database of "statistical capacity indicator" scores. You can also query and extract the Bank's data on statistical capacity at https://datacatalog.worldbank.org/dataset/data-statistical-capacity. Keep these site in mind when considering different topics for research - they will help you get a sense of where data availability will be a problem for a particular country.
"Data Quality in Research: What If We're Watering the Garden While the House Is On Fire?" -- A commentary from a World Bank economist on the implications of data quality for policy analysis and recommendations and on the need for researchers to pay greater attention to how data are collected.
The HRV Transparency Project -- The HRV Transparency Project has developed an index of government transparency "focuses on the availability of credible aggregate economic data" that "does so by examining patterns of missing data and treating transparency as the latent term which best reflects the tendency to disclose (...) Our measure provides observations for 125 countries from 1980-2010 and can be used to measure relationships between transparency and other issues such as democracy, accountability, or political instability." Data from this project are also available at http://dx.doi.org/10.7910/DVN/24274.
"Improving Data Quality: Actors, Incentives, and Capabilities" -- This article from Political Analysis on the effects of incentives and resources on data collection is a worthwhile read on determinants of data availability and how preferences, incentives, and institutional contexts combine to affect the data-gathering behavior (or lack thereof!) of governments, inter-governmental organizations, and individuals.
"The Political Economy of Bad Data: Evidence from African Survey & Administrative Statistics" -- This working paper from the Center for Global Development asseses the quality of administrative data from African countries on the provision of various public service by comparing official data on usage of those services to household data on their usage. The paper is an example of how incentives can affect the quality of collected data. Replication data from this paper are available at http://dx.doi.org/10.7910/DVN/26712.
"Statistical Tragedy in Africa? Evaluating the Data Base for African Economic Development" -- This special issue of the Journal of Development Studies is also devoted to issues of and implications of data availability and quality in African countries.
"Development by Numbers" -- This analysis from NYU's Development Research Institute "guides you through the availability, reliability and validity problems of the most important numbers in development: GDP, Poverty Headcounts, Purchasing Power Parities, Population and different indicators relating to the MDGs and SDGs. Here we will discuss briefly some of the issues that relate to measuring poverty."