We study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data. Identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database, when such distribution is common to the two data sets. The auxiliary sample can be independent of the primary sample, or can be a subset of it. For both cases, we derive bounds when the probability of missing data given the proxy variables is unknown, or known, or belongs to a correctly specified parametric family. We find that the conditional probability is not ancillary when the two samples are independent. For all cases, we discuss efficient semiparametric estimators. An estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting.Comment: Published in at http://dx.doi.org/10.1214/009053607000000947 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org
We describe findings from the first large-scale cluster randomized controlled trial in a developing country that evaluates the uptake of a health-protecting technology, insecticide-treated bednets (ITNs), through micro-consumer loans, as compared to free distribution and control conditions. Despite a relatively high price, 52 percent of sample households purchased ITNs, highlighting the role of liquidity constraints in explaining earlier low adoption rates. We find mixed evidence of improvements in malaria indices. We interpret the results and their implications within the debate about cost sharing, sustainability and liquidity constraints in public health initiatives in developing countries. (JEL D12, G21, H51, I12, I18, O15, O18)
Household expenditure survey data cannot yield precise estimates of poverty or inequality for small areas for which no or few observations are available. Census data are more plentiful, but typically exclude income and expenditure data. Recent years have seen a widespread use of small-area "poverty maps" based on census data enriched by relationships estimated from household surveys that predict variables not covered by the census. These methods are used to estimate putatively precise estimates of poverty and inequality for areas as small as 20,000 households. In this paper we argue that to usefully match survey and census data in this way requires a degree of spatial homogeneity for which the method provides no basis, and which is unlikely to be satisfied in practice. The relationships that are used to bridge the surveys and censuses are not structural but are projections of missing variables on a subset of those variables that happen to be common to the survey and the census supplemented by local census means appended to the survey. As such, the coefficients of the projections will generally vary from area to area in response to variables that are not included in the analysis. Estimates of poverty and inequality that assume homogeneity will generally be inconsistent in the presence of spatial heterogeneity, and error variances calculated on the assumption of homogeneity will underestimate mean squared errors and overestimate the coverage of calculated confidence intervals. We use data from the 2000 census of Mexico to construct synthetic "household surveys" and to simulate the poverty mapping process. In this context, our simulations show that while the poverty maps contain useful information, their nominal confidence intervals give a misleading idea of precision. JEL: I32, C31, C42 two referees, seminar participants at various institutions and especially Peter Lanjouw for valuable comments. We are also grateful to IPUMS for access to the 2000 Mexican Census extract. Maria Eugenia Genoni provided excellent research assistance. We are solely responsible for all errors and omissions.
Applied economists are often interested in studying changes over time of important economic indicators, such as inequality or poverty, but such comparisons can be made impossible by changes in data collection methodology. We describe an easily implemented procedure to recover comparability that can be adopted whenever the statistic of interest satisfies a moment condition, when the researcher has available a set of auxiliary variables whose reports are not affected by the different survey design, and whose relation with the main variable of interest is stable over time. We analyze the asymptotic properties of the estimator taking into account the presence of clustering, stratification, and sampling weights, which characterize most household surveys. We use the 1999-2000 Round of the Indian National Sample Survey as an empirical illustration. Due to important changes in the adopted questionnaire, the unadjusted figures are likely to understate poverty relative to the previous rounds. We use previous waves of the same survey to provide evidence supporting the plausibility of the identifying assumptions and conclude that most of the very large reduction in poverty implied by the unadjusted figures is real.
We use data from a randomized controlled trial conducted in 2003-2006 in rural Amhara and Oromiya (Ethiopia) to study the impacts of increasing access to microfinance on a number of socioeconomic outcomes, including income from agriculture, animal husbandry, nonfarm self-employment, labor supply, schooling and indicators of women's empowerment. We document that despite substantial increases in borrowing in areas assigned to treatment the null of no impact cannot be rejected for a large majority of outcomes. (JEL G21, I20, J13, J16, O13, O16, O18) B eginning in the 1970s, with the birth of the Grameen Bank in Bangladesh, microcredit has played a prominent role among development initiatives. Many proponents claim that microfinance has had enormously positive effects among borrowers. However, the rigorous evaluation of such claims of success has been complicated by the endogeneity of program placement and client selection, both common obstacles in program evaluations. Microfinance institutions (MFIs) typically choose to locate in areas predicted to be profitable, and/or where large impacts are expected. In addition, individuals who seek out loans in areas served by MFIs and that are willing and able to form joint-liability borrowing groups (a model often preferred by MFIs) are likely different from others who do not along a number of observable and unobservable factors. Until recently, the results of most evaluations could not be interpreted as conclusively causal because of the lack of an appropriate control group (see Brau and Woller 2004 and Armendáriz de Aghion and Morduch 2005 for comprehensive early surveys). In this context, randomized controlled trials (RCTs) provide an ideal research design to evaluate the impact of microcredit.In this paper we present the results of one of the few existing RCTs that evaluate the impact of introducing access to microloans in poor communities in a developing country after the early contribution of Banerjee et al. (2014). We study a large-scale clustered RCT conducted in rural Amhara and Oromiya (Ethiopia) between 2003 and 2006. The main purpose of the RCT was to evaluate whether the Duflo (the Editor), two anonymous referees and seminar participants at several seminars and workshops for comments and suggestions. All errors and omissions are our own. The trial described in the paper has been registered after the conclusion of the study with the AER RCT Registry, with registry number AEARCTR-0000305.
Recent years have seen widespread use of small-area maps based on census data enriched by relationships estimated from household surveys that predict variables, such as income, not covered by the census. The purpose is to obtain putatively precise estimates of poverty and inequality for small areas for which no or few observations are available in the survey. We argue that to usefully match survey and census data in this way requires a degree of spatial homogeneity for which the method provides no basis and which is unlikely to be satisfied in practice. We document the potential empirical relevance of such concerns using data from the 2000 census of Mexico. Copyright by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.
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