Kernel Density Estimation Based on Grouped Data: The Case of Poverty Assessment, Issues 2008-2183
International Monetary Fund, African Department, 2008 - Income distribution - 34 pages
We analyze the performance of kernel density methods applied to grouped data to estimate poverty (as applied in Sala-i-Martin, 2006, QJE). Using Monte Carlo simulations and household surveys, we find that the technique gives rise to biases in poverty estimates, the sign and magnitude of which vary with the bandwidth, the kernel, the number of datapoints, and across poverty lines. Depending on the chosen bandwidth, the $1/day poverty rate in 2000 varies by a factor of 1.8, while the $2/day headcount in 2000 varies by 287 million people. Our findings challenge the validity and robustness of poverty estimates derived through kernel density estimation on grouped data.
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Bias in the poverty headcount ratio versus location of poverty line
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$2/day poverty amount of smoothing ascending order average income Bias of poverty biases associated boundary bias canonical bandwidths countries datapoints datasets decile means density biases Epanechnikov Gaussian Epanechnikov kernel estimate poverty estimated density estimated quantity estimates from grouped Figure Gaussian kernel give rise global poverty estimates grouped data higher poverty lines hybrid bandwidth income averages income distributions income levels Input data kernel density estimation l/day poverty line Log-normal distribution Lorenz curve median million Minoiu Monte Carlo simulations multimodal distribution nationally representative household Nicaragua nonparametric normal distribution number of quantile optimal bandwidth order statistics percent percentage points population quantiles poverty analysis poverty gap poverty headcount ratio poverty indicators Poverty Log-normal poverty measures poverty rates quantile means quintile represent the ratio representative household surveys S3 bandwidth Sala-i-Martin sample small number Squared Log-normal survey-based Tanzania trimmed means true counterpart True Density underlying distribution unimodal distributions unit data weighting function world poverty