*! version 1.0.0 15Apr2017 Long Hong

help survlsl

Title

survlsl - Estimation of the Gini index for log-scale-location parametric models

Syntax

survlsl varname, threshold(real)
censorpct(real) model(string)

Options

threshold Threshold. Exact values below threshold are unknown due to
left- censoring or truncation. The value should not be
larger than the minimum value of the observations.

censorpct Left-censoring percentage. Input 0 if the data are
left-truncated; input a value in (0,1) if the
data are left-censored.

model Three models are available: lognormal, weibull,
and loglogistic. Please type the exact name in full.

Description

survlsl estimates the Gini index using log-scale-location
parametric models for left- censored or truncated data with a fixed threshold.
The current version contains Log-normal, Weibull, and log-logistic models.

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. Assuming that the incomes follow a log-normal distribution, we can use
survlsl to estimate the Gini index as follows.

. survlsl income, thres(10) censorpct(0.30) model(lognormal)

(...MLE inerations omitted...)
(...Estimated parameters omitted...)

Left Censored Model

Estimated Parameters:
MLE location = 2.94
MLE scale = .9912

Parametric Gini = .5166

Parametric Gini 95% Confidence Interval:
C.I. 1 is derived from the delta method;
C.I. 2 is derived from a direct approach.

+

| Lower Upper

+

Conf Interval 1 | .5079 .5253
Conf Interval 2 | .5079 .5253

+

If the data were instead truncated, please use censorpct(0) to flag this case.

Saved Results

survlsl saves the following in r()

Scalars

r(gini) Gini index calculated using parametric models

r(alpha) Location estimate for log-normal; scale estimate
for Wellbull or log-logistic

r(beta) Scale estimate for log-normal; shape estimate for
Wellbull or log-logistic

Matrices

r(estimates) maximum likelihood estimates

r(variances) Variance-covariance matrix

r(conf_interval) Confidence intervals

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.

Bonetti, M., Gigliarano, C. and Basellini U. (2015). Longevity and
concentration in survival times: the log-scale-location family of failure
time models Lifetime Data Analysis