Kernel Density Estimation Basedon Grouped Data: The Case of Poverty Assessment
International Monetary Fund, Jul 1, 2008 - Business & Economics - 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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$1/day poverty line $2/day poverty amount of smoothing average income Bias of poverty biases associated boundary bias canonical bandwidths countries datapoints datasets decile means density biases Epanechnikov kernel estimate poverty estimated density estimated quantity estimates from grouped Figure Gaussian kernel give rise global poverty estimates grouped data headcount Dagum higher poverty lines hybrid bandwidth income averages income distributions income levels Input data kemel kernel density estimation 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 oversmoothed bandwidth 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 survey-based Tanzania trimmed means true counterpart True Density underlying distribution unimodal distributions unit data weighting function world poverty