*! version 1.0.0 17Oct2016 Long Hong

help survbound

Title

survbound - Non-parametric Gini index estimation for censored data

Syntax

survbound varname , threshold(real)
censorpct(real) [grid(integer)]

Options

threshold Threshold. Exact values below the threshold are unknown due to
left-censoring; the value should not be larger
than the minimum value of the observation.

censorpct Left-censoring percentage. Input a value in (0,1) for
the percentage of the left-censored observations.

grid(optional) Allow "grid search". Input a positive integer.

Description

survbound estimates the Gini index non-parametrically for
left-censored data with a fixed threshold.

Example

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 survbound to
estimate the lower and upper bounds of the Gini index as follows.

. survbound income, thres(10) censorpct(0.30) grid(10)

Non-Parametric Gini Numeric Boundaries:

+

| Lower(A) Upper(A) Upper(G)

+

Non-Parametric Gini | .4275492 .5787303 .5389827

+

Lower(A): Analytic lower bound
Upper(A): Analytic upper bound
Upper(G): Upper bound approximation by Grid-search

Saved Results

survbound saves the following in r()

Scalars

r(lower_a) Analytical lower bound

r(upper_a) Analytical upper bound

r(upper_g) Upper bound approximation by "grid search"

Author

Long Hong

Department of Economics

University of Wisconsin - Madison

Madison, WI, USA

long.hong@wisc.edu

References

Alfani, G. and Garcia Montero, H. (2017).
Wealth Inequality in Preindustrial England:A Long-Term View
(Thirteenth to Seventeenth Centuries), forthcoming.

Sajaia, Z. (2007). FASTGINI: Stata module to calculate Gini coefficient
with jackknife standard errors, Statistical Software Components S456814,
Boston College Department of Economics.