Publication: Estimation of Normal Mixtures in a Nested Error Model with an Application to Small Area Estimation of Poverty and Inequality
Loading...
Published
2014-07
ISSN
Date
2014-08-15
Author(s)
Elbers, Chris
Editor(s)
Abstract
This paper proposes a method for estimating distribution functions that are associated with the nested errors in linear mixed models. The estimator incorporates Empirical Bayes prediction while making minimal assumptions about the shape of the error distributions. The application presented in this paper is the small area estimation of poverty and inequality, although this denotes by no means the only application. Monte-Carlo simulations show that estimates of poverty and inequality can be severely biased when the non-normality of the errors is ignored. The bias can be as high as 2 to 3 percent on a poverty rate of 20 to 30 percent. Most of this bias is resolved when using the proposed estimator. The approach is applicable to both survey-to-census and survey-to-survey prediction.
Link to Data Set
Citation
“Elbers, Chris; van der Weide, Roy. 2014. Estimation of Normal Mixtures in a Nested Error Model with an Application to Small Area Estimation of Poverty and Inequality. Policy Research Working Paper;No. 6962. © http://hdl.handle.net/10986/19362 License: CC BY 3.0 IGO.”
Digital Object Identifier
Associated URLs
Associated content
Other publications in this report series
Publication Climate and Social Sustainability in Fragility, Conflict, and Violence Contexts(Washington, DC: World Bank, 2026-01-07)Climate change is widely recognized as a driver of violent conflict, but its broader social effects remain less understood. Ignoring these dimensions risks a vicious cycle where climate policies might undermine socially just adaptation. Evidence is still limited on how climate shocks influence political participation, trust, or migration. This paper helps fill that gap by examining links between climate change, conflict, and social sustainability, with a focus on inclusion, resilience, cohesion, and legitimacy. Using secondary data from 2019–24, the study applies simple correlation-based methods to test three hypotheses on the nature, severity, and composition of these associations. The analysis combines multiple climate impact measures, new conflict classifications, recent social sustainability frameworks, and controls for population and geography. The results reveal strong correlations—not causation—between climate events and contexts of fragility, conflict, and violence. Climate impacts are most pronounced in both national and subnational conflict settings. The study also finds robust links between fragility, conflict, and violence and low levels of social sustainability, reflecting its role as both a driver and consequence of conflict. Some dimensions—such as violent events and insecurity—appear weaker in areas most affected by climate shocks. Two of the hypotheses are supported, and one remains inconclusive.Publication The Macroeconomic Implications of Climate Change Impacts and Adaptation Options(Washington, DC: World Bank, 2025-05-29)Estimating the macroeconomic implications of climate change impacts and adaptation options is a topic of intense research. This paper presents a framework in the World Bank's macrostructural model to assess climate-related damages. This approach has been used in many Country Climate and Development Reports, a World Bank diagnostic that identifies priorities to ensure continued development in spite of climate change and climate policy objectives. The methodology captures a set of impact channels through which climate change affects the economy by (1) connecting a set of biophysical models to the macroeconomic model and (2) exploring a set of development and climate scenarios. The paper summarizes the results for five countries, highlighting the sources and magnitudes of their vulnerability --- with estimated gross domestic product losses in 2050 exceeding 10 percent of gross domestic product in some countries and scenarios, although only a small set of impact channels is included. The paper also presents estimates of the macroeconomic gains from sector-level adaptation interventions, considering their upfront costs and avoided climate impacts and finding significant net gross domestic product gains from adaptation opportunities identified in the Country Climate and Development Reports. Finally, the paper discusses the limits of current modeling approaches, and their complementarity with empirical approaches based on historical data series. The integrated modeling approach proposed in this paper can inform policymakers as they make proactive decisions on climate change adaptation and resilience.Publication Institutional Capacity for Policy Implementation: An Analytical Framework(Washington, DC: World Bank, 2026-01-07)State capacity is an important prerequisite for policy implementation, yet at the country level it is difficult to measure, assess, and reform. This paper proposes a focus on institutional capacity: the ability of public institutions to implement the specific policy mandates for which they are responsible. Based on a review of existing literature, the paper defines the different dimensions that compose institutional capacity and groups them into two cross-cutting categories: organizational dimensions (personnel, financial resources, information systems, and management practices) and governance dimensions (transparency, independence, and accountability). The paper proposes measures for organizational and governance dimensions using existing data, shows intra-institutional variation of these measures within countries, and discusses how new data could be collected for better measurement of these concepts. Finally, the paper illustrates how the framework can be used to diagnose the sources of common problems related to weak policy implementation.Publication South Africa’s Fragmented Cities: The Unequal Burden of Labor Market Frictions(Washington, DC: World Bank, 2026-01-08)Using high-resolution administrative, census, and satellite data, this paper shows that South African cities are characterized by spatial mismatches between where people live and where jobs are located, relative to 20 global peers. Areas within 5 kilometers of commercial centers have 9,300 fewer residents per square kilometer than expected, which is 60 percent below the global median. Poor, dense neighborhoods are most affected. In Johannesburg, a 10-percentile increase in distance from the nearest business hub corresponds to a 3.7-percentile drop in asset wealth (a proxy of household wellbeing) and 4.9-percentile drop in employment. In Cape Town, the declines are 4.0 and 3.7 percentiles, respectively. Employment is 87 percent lower in the poorest decile than the richest in Johannesburg and 61 percent lower in Cape Town. These findings suggest that South Africa’s spatial organization of people and economic activity constrains agglomeration and reinforces inequality. This methodology provides a scalable and standardized data-driven framework to analyze spatial accessibility and agglomeration frictions in complex, data-constrained urban systems.Publication Investment in Emerging and Developing Economies(Washington, DC: World Bank, 2026-01-07)The world faces a pressing challenge to meet key development objectives amid slowing growth and rising macroeconomic and geopolitical risks. With the number of job seekers rising rapidly, infrastructure shortfalls continuing to be large, and climate costs mounting, the case for a significant investment push has never been stronger. Yet the capacity to respond in many emerging markets and developing economies has eroded. Since the global financial crisis, investment growth has slowed to about half its pace in the 2000s, with both public and private investment weakening. Foreign direct investment inflows—a critical source of capital, technology, and managerial know-how—have also fallen sharply and become increasingly concentrated, leaving low-income countries with only a marginal share. The risks of further retrenchment are significant, as trade tensions, policy uncertainty, and elevated debt levels continue to weigh on investment. Reigniting momentum will require ambitious domestic reforms to strengthen institutions, rebuild macro-fiscal stability, and deepen trade and investment integration—the foundations of a supportive business climate. At the same time, international cooperation is indispensable. A renewed commitment to a predictable system of cross-border trade and investment flows, combined with scaled-up financial support and sustained technical assistance, is essential to help emerging markets and developing economies—especially low-income countries and economies in fragile and conflict situations—bridge financing gaps and implement the domestic reforms needed to restore investment as an engine of growth, jobs, and development.
Journal
Journal Volume
Journal Issue
Collections
Related items
Showing items related by metadata.
Publication Estimating the Gravity Model When Zero Trade Flows are Frequent and Economically Determined(World Bank, Washington, DC, 2015-06)This paper evaluates the performance of alternative estimators of the gravity equation when zero trade flows result from economically-based data-generating processes with heteroscedastic residuals and potentially-omitted variables. In a standard Monte Carlo analysis, the paper finds that this combination can create seriously biased estimates in gravity models with frequencies of zero frequently observed in real-world data, and that Poisson Pseudo-Maximum-Likelihood models can be important in solving this problem. Standard threshold–Tobit estimators perform well in a Tobit-based data-generating process only if the analysis deals with the heteroscedasticity problem. When the data are generated by a Heckman sample selection model, the Zero-Inflated Poisson model appears to have the lowest bias. When the data are generated by a Helpman, Melitz, and Rubinstein-type model with heterogeneous firms, a Zero-Inflated Poisson estimator including firm numbers appears to provide the best results. Testing on real-world data for total trade throws up additional puzzles with truncated Poisson Pseudo-Maximum-Likelihood and Poisson Pseudo-Maximum-Likelihood estimators being very similar, and Zero-Inflated Poisson and truncated Poisson Pseudo-Maximum-Likelihood identical. Repeating the Monte Carlo analysis taking into account the high frequency of very small predicted trade flows in real-world data reconciles these findings and leads to specific recommendations for estimators.Publication Replicating Replication : Due Diligence in Roodman and Morduch’s Replication of Pitt and Khandker (1998)(World Bank, Washington, DC, 2012-11)"The Impact of Microcredit on the Poor in Bangladesh: Revisiting the Evidence," by David Roodman and Jonathan Morduch (2011) is the most recent of a sequence of papers and postings that seeks to refute the findings of the Pitt and Khandker (1998) article "The Impact of Group-Based Credit on Poor Households in Bangladesh: Does the Gender of Participants Matter?" that microcredit for women had significant, favorable effects on poverty reduction. In this paper the authors show that these latest Roodman and Morduch claims are based on seriously flawed econometric methods and theory and a lack of due diligence in formulating models and interpreting output from packaged software. On the basis of Roodman and Morduch's preferred two-stage least squares regression, an alternative calculation of the standard errors would lead one to conclude that the problem with Pitt and Khandker is that they underestimate the positive and statistically significant effect of women's credit on household consumption. As in their previous efforts, the methods of Roodman and Morduch are shown to bias the findings in the direction of rejecting the results of Pitt and Khandker. We also further examine two aspects of our instrumental variable approach that have been attacked by Roodman and Morduch. The first is the validity of the exclusion restrictions underlying the use of interactions between program choice and the set of exogenous variables (including the village fixed effects) as instruments. The second is the application of the "one-half acre" program eligibility rule. The authors show that identification does not require both of these, and present new results dropping each assumption in turn. The results originally reported in the Pitt and Khandker paper hold up extremely well in this new analysis.Publication A Practical Comparison of the Bivariate Probit and Linear IV Estimators(2011-03-01)This paper presents asymptotic theory and Monte-Carlo simulations comparing maximum-likelihood bivariate probit and linear instrumental variables estimators of treatment effects in models with a binary endogenous treatment and binary outcome. The three main contributions of the paper are (a) clarifying the relationship between the Average Treatment Effect obtained in the bivariate probit model and the Local Average Treatment Effect estimated through linear IV; (b) comparing the mean-square error and the actual size and power of tests based on these estimators across a wide range of parameter values relative to the existing literature; and (c) assessing the performance of misspecification tests for bivariate probit models. The authors recommend two changes to common practices: bootstrapped confidence intervals for both estimators, and a score test to check goodness of fit for the bivariate probit model.Publication PPML Estimation of Dynamic Discrete Choice Models with Aggregate Shocks(World Bank, Washington, DC, 2013-06)This paper introduces a computationally efficient method for estimating structural parameters of dynamic discrete choice models with large choice sets. The method is based on Poisson pseudo maximum likelihood (PPML) regression, which is widely used in the international trade and migration literature to estimate the gravity equation. Unlike most of the existing methods in the literature, it does not require strong parametric assumptions on agents' expectations, thus it can accommodate macroeconomic and policy shocks. The regression requires count data as opposed to choice probabilities; therefore it can handle sparse decision transition matrices caused by small sample sizes. As an example application, the paper estimates sectoral worker mobility in the United States.Publication Micro-Level Estimation of Welfare(World Bank, Washington, DC, 2002-10)The authors construct and derive the properties of estimators of welfare that take advantage of the detailed information about living standards available in small household surveys and the comprehensive coverage of a census or large sample. By combining the strengths of each, the estimators can be used at a remarkably disaggregated level. They have a clear interpretation, are mutually comparable, and can be assessed for reliability using standard statistical theory. Using data from Ecuador, the authors obtain estimates of welfare measures, some of which are quite reliable for populations as small as 15,000 households--a "town." They provide simple illustrations of their use. Such estimates open up the possibility of testing, at a more convincing intra-country level, the many recent models relating welfare distributions to growth and a variety of socioeconomic and political outcomes.
Users also downloaded
Showing related downloaded files
Publication World Development Report 2024(Washington, DC: World Bank, 2024-08-01)Middle-income countries are in a race against time. Many of them have done well since the 1990s to escape low-income levels and eradicate extreme poverty, leading to the perception that the last three decades have been great for development. But the ambition of the more than 100 economies with incomes per capita between US$1,100 and US$14,000 is to reach high-income status within the next generation. When assessed against this goal, their record is discouraging. Since the 1970s, income per capita in the median middle-income country has stagnated at less than a tenth of the US level. With aging populations, growing protectionism, and escalating pressures to speed up the energy transition, today’s middle-income economies face ever more daunting odds. To become advanced economies despite the growing headwinds, they will have to make miracles. Drawing on the development experience and advances in economic analysis since the 1950s, World Development Report 2024 identifies pathways for developing economies to avoid the “middle-income trap.” It points to the need for not one but two transitions for those at the middle-income level: the first from investment to infusion and the second from infusion to innovation. Governments in lower-middle-income countries must drop the habit of repeating the same investment-driven strategies and work instead to infuse modern technologies and successful business processes from around the world into their economies. This requires reshaping large swaths of those economies into globally competitive suppliers of goods and services. Upper-middle-income countries that have mastered infusion can accelerate the shift to innovation—not just borrowing ideas from the global frontiers of technology but also beginning to push the frontiers outward. This requires restructuring enterprise, work, and energy use once again, with an even greater emphasis on economic freedom, social mobility, and political contestability. Neither transition is automatic. The handful of economies that made speedy transitions from middle- to high-income status have encouraged enterprise by disciplining powerful incumbents, developed talent by rewarding merit, and capitalized on crises to alter policies and institutions that no longer suit the purposes they were once designed to serve. Today’s middle-income countries will have to do the same.Publication Digital Africa(Washington, DC: World Bank, 2023-03-13)All African countries need better and more jobs for their growing populations. "Digital Africa: Technological Transformation for Jobs" shows that broader use of productivity-enhancing, digital technologies by enterprises and households is imperative to generate such jobs, including for lower-skilled people. At the same time, it can support not only countries’ short-term objective of postpandemic economic recovery but also their vision of economic transformation with more inclusive growth. These outcomes are not automatic, however. Mobile internet availability has increased throughout the continent in recent years, but Africa’s uptake gap is the highest in the world. Areas with at least 3G mobile internet service now cover 84 percent of Africa’s population, but only 22 percent uses such services. And the average African business lags in the use of smartphones and computers as well as more sophisticated digital technologies that catalyze further productivity gains. Two issues explain the usage gap: affordability of these new technologies and willingness to use them. For the 40 percent of Africans below the extreme poverty line, mobile data plans alone would cost one-third of their incomes—in addition to the price of access devices, apps, and electricity. Data plans for small- and medium-size businesses are also more expensive than in other regions. Moreover, shortcomings in the quality of internet services—and in the supply of attractive, skills-appropriate apps that promote entrepreneurship and raise earnings—dampen people’s willingness to use them. For those countries already using these technologies, the development payoffs are significant. New empirical studies for this report add to the rapidly growing evidence that mobile internet availability directly raises enterprise productivity, increases jobs, and reduces poverty throughout Africa. To realize these and other benefits more widely, Africa’s countries must implement complementary and mutually reinforcing policies to strengthen both consumers’ ability to pay and willingness to use digital technologies. These interventions must prioritize productive use to generate large numbers of inclusive jobs in a region poised to benefit from a massive, youthful workforce—one projected to become the world’s largest by the end of this century.Publication Remarks to the G20 Finance Ministers and Central Bank Governors Meeting(World Bank, Washington, DC, 2020-11-20)World Bank Group President David Malpass said that while some countries are recovering, the pandemic is still taking a terrible toll, with poverty levels rising sharply. He highlighted on the health emergency response programs in one hundred twelve countries using a fast-track mechanism that is now able to access a further window of twelve billion in funding for vaccine purchases and delivery. He also mentioned that the World Bank is already at work in cooperation with WHO, UNICEF, the Global Fund and GAVI on rapid vaccine deployment readiness assessments for one hundred countries. He spoke about IFC working in coordination with CEPI to invest a further four billion in manufacturing and distribution of vaccines and products that support vaccination programs. He recognized that fragile conflict and violence (FCV) states are most in need, and World Bank's engagement with them. Under his Presidency, the World Bank Group has invested more in climate finance than at any time in its history. He mentioned that IDA is frontloading its financing to make more resources available for the poorest countries. He highlighted on an important step that the G20 call on DSSI beneficiary countries to commit to disclose all public sector financial commitments. The Development Committee that asked the Bank and the IMF to propose more actions to address the unsustainable debt burdens of low- and middle-income countries. He concluded that the fuller transparency is the only way to balance the interests of the people with the interests of those signing the debt and investment contracts.Publication South Asia Development Update, October 2024: Women, Jobs, and Growth(Washington, DC: World Bank, 2024-10-10)South Asia’s growth is on track to exceed earlier expectations, in a broad-based upturn. The region is expected to remain the fastest-growing among emerging market and developing economies (EMDEs). Several risks could upend this generally promising outlook, including extreme weather events, social unrest, and policy missteps, such as reform delays. But South Asian countries also have considerable untapped potential that could help them further boost productivity growth and employment and adapt to climate change. In particular, with about two-thirds of the region’s working-age women out of the labor force, raising female employment rates to those of men could increase per capita income by as much as one-half. Measures to accelerate job creation, remove obstacles to women working, and equalize gender rights would be more effective if combined with a shift toward social norms that looked more favorably on working women. Also, most South Asian countries rank among the EMDEs least open to global trade and investment. Greater openness could boost women’s employment, spur the growth of firms, and allow the region to take better advantage of the reshaping of global supply chains and trade. Reducing the cost of conducting business could help the region better harness large-scale remittance inflows.Publication World Bank East Asia and the Pacific Economic Update, October 2024: Jobs and Technology(Washington, DC: World Bank, 2024-10-07)East Asia and the Pacific, seen in the context of the world economy, stands out as a paragon of development. Despite the recent ravages of the pandemic and the persistent tensions of geopolitics, the region is growing at stably high rates and the benefits are widely shared. But compared to its own past and potential, the region’s economic performance is less impressive. Growth is still below pre-pandemic rates, except in Indonesia, and output has not yet recovered to pre-pandemic levels in several countries, especially in the Pacific. This Economic Update highlights three key developments: shifting regional growth dynamics as China’s growth slows, changing trade patterns due to global tensions, and the impact of technologies such as robots, artificial intelligence, and digital platforms on jobs. The report calls for productivity-enhancing structural reforms to strengthen domestic growth drivers through; deeper international trade agreements to foster more open and stable trade regimes; deeper technical, digital, and soft skills while addressing impediments to labor mobility, factor price distortions and expanding social protection for workers in the digital informal economy to boost productivity and employment.