Bayesian Models for the Analyzes of Noisy Responses From Small Areas: An Application to Poverty Estimation

Manandhar, Binod

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Bayesian Models for the Analyzes of Noisy Responses From Small Areas: An Application to Poverty Estimation

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We implement techniques of small area estimation (SAE) to study consumption, a welfare indicator, which is used to assess poverty in the 2003-2004 Nepal Living Standards Survey (NLSS-II) and the 2001 census. NLSS-II has detailed information of consumption, but it can give estimates only at stratum level or higher. While population variables are available for all households in the census, they do not include the information on consumption; the survey has the `population' variables nonetheless. We combine these two sets of data to provide estimates of poverty indicators (incidence, gap and severity) for small areas (wards, village development committees and districts). Consumption is the aggregate of all food and all non-food items consumed. In the welfare survey the responders are asked to recall all information about consumptions throughout the reference year. Therefore, such data are likely to be noisy, possibly due to response errors or recalling errors. The consumption variable is continuous and positively skewed, so a statistician might use a logarithmic transformation, which can reduce skewness and help meet the normality assumption required for model building. However, it could be problematic since back transformation may produce inaccurate estimates and there are difficulties in interpretations. Without using the logarithmic transformation, we develop hierarchical Bayesian models to link the survey to the census. In our models for consumption, we incorporate the `population' variables as covariates. First, we assume that consumption is noiseless, and it is modeled using three scenarios: the exponential distribution, the gamma distribution and the generalized gamma distribution. Second, we assume that consumption is noisy, and we fit the generalized beta distribution of the second kind (GB2) to consumption. We consider three more scenarios of GB2: a mixture of exponential and gamma distributions, a mixture of two gamma distributions, and a mixture of two generalized gamma distributions. We note that there are difficulties in fitting the models for noisy responses because these models have non-identifiable parameters. For each scenario, after fitting two hierarchical Bayesian models (with and without area effects), we show how to select the most plausible model and we perform a Bayesian data analysis on Nepal's poverty data. We show how to predict the poverty indicators for all wards, village development committees and districts of Nepal (a big data problem) by combining the survey data with the census. This is a computationally intensive problem because Nepal has about four million households with about four thousand households in the survey and there is no record linkage between households in the survey and the census. Finally, we perform empirical studies to assess the quality of our survey-census procedure.

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