{smcl} {* *! version 1.0.0 17Oct2016 Long Hong} {cmd: help survbound} {hline} {title: Title} {phang} {bf: survbound} - Non-parametric Gini index estimation for censored data {title: Syntax} {phang} {cmd: survbound} {it:varname} {cmd:,} {cmdab:thres:hold(}{it:real}{cmd:)} {cmd:censorpct(}{it:real}{cmd:)} [{cmd:grid(}{it:integer}{cmd:)}] {synoptset 16 tabbed}{...} {synopthdr: Options} {synoptline} {synopt:{it:threshold}} Threshold. Exact values below the threshold are unknown due to left-censoring; the value should {bf:not} be larger than the minimum value of the observation. {p_end} {synopt:{it:censorpct}} Left-censoring percentage. Input a value in {bf:(0,1)} for the percentage of the left-censored observations. {p_end} {synopt:{it:grid}(optional)} Allow "grid search". Input a positive integer. {p_end} {synoptline} {title: Description} {pstd}{cmd:survbound} estimates the Gini index non-parametrically for left-censored data with a fixed threshold. {p_end} {title: Example} {pstd} We illustrate by using the historical household income in England (Alfani and Garcia Montero, 2017). Since the income data are tax-based, 30% of the household's incomes are not documented because their incomes are below the tax-paying threshold, 10 shilings. Without knowing the distribution, we can use {cmd:survbound} to estimate the lower and upper bounds of the Gini index as follows. {p_end} {com}. survbound income, thres(10) censorpct(0.30) grid(10) {res} {txt}Non-Parametric Gini Numeric Boundaries: {res} {txt}{space 0}{hline 21}{c TT}{hline 11}{hline 11}{hline 11} {space 0}{space 0}{ralign 20:}{space 1}{c |}{space 1}{ralign 9:Lower(A)}{space 1}{space 1}{ralign 9:Upper(A)}{space 1}{space 1}{ralign 9:Upper(G)}{space 1} {space 0}{hline 21}{c +}{hline 11}{hline 11}{hline 11} {space 0}{space 0}{ralign 20:Non-Parametric Gini}{space 1}{c |}{space 1}{ralign 9:{res:{sf: .4275492}}}{space 1}{space 1}{ralign 9:{res:{sf: .5787303}}}{space 1}{space 1}{ralign 9:{res:{sf: .5389827}}}{space 1} {space 0}{hline 21}{c BT}{hline 11}{hline 11}{hline 11} Lower(A): Analytic lower bound Upper(A): Analytic upper bound Upper(G): Upper bound approximation by Grid-search {title: Saved Results} {pstd}{cmd:survbound} saves the following in {cmd: r()}{p_end} {pstd}Scalars{p_end} {synoptset 16 tabbed} {synopt: {cmdab:r(lower_a)}} Analytical lower bound {p_end} {synopt: {cmdab:r(upper_a)}} Analytical upper bound {p_end} {synopt: {cmdab:r(upper_g)}} Upper bound approximation by "grid search"{p_end} {title: Author} {pstd}Long Hong{p_end} {pstd}Department of Economics{p_end} {pstd}University of Wisconsin - Madison{p_end} {pstd}Madison, WI, USA{p_end} {pstd}{browse "mailto:long.hong@wisc.edu":long.hong@wisc.edu} {title:References} {pstd}Alfani, G. and Garcia Montero, H. (2017). Wealth Inequality in Preindustrial England:A Long-Term View (Thirteenth to Seventeenth Centuries), {it:forthcoming}.{p_end} {pstd}Sajaia, Z. (2007). FASTGINI: Stata module to calculate Gini coefficient with jackknife standard errors, {it: Statistical Software Components S456814}, Boston College Department of Economics. {p_end}