*! version 1.0.02 5feb2015
help ginireg

Title

ginireg -- Progam to estimate Gini regression

Syntax

Standard:

ginireg
depvar regressors
[weight] [if exp] [in range]
[ , nogini(varlist)
extended(varlist) nu(#) vce(jackknife)
noconstant ]

IV estimation:

ginireg
depvar [exogenous regressors] (endogenous regressors = excluded instruments)
[weight] [if exp] [in range]
[ , nogini(varlist)
extended(varlist) nu(#) vce(jackknife)
noconstant ]

Options

nogini(varlist)
do not apply Gini (rank) transformation to variables in varlist

extended(varlist)
regressors for extended Gini transformationvarlist

nu(#)
extended Gini parameter (default=2)

vce(jackknife)
jackknife VCE

noconstant
suppress constant from regression

Postestimation:

predict [type] newvar [if] [in] [,
resid xb ]

estat graph_type
[ , nlma
graph_options ]

Postestimation options

graph_type
either lmaresid for LMA graph of residuals
or lmayyhat for LMA graph of dependent variable and fitted value,
in both cases vs. all independent variables.

nlma
report Normalized LMA graph instead of default LMA graph

graph_options
options to pass to underlying call to graph combine

ginireg may be used with time-series or panel data,
in which case the data must be tsset first; see help tsset.

All varlists may contain time-series operators,
but factor variables are not currently supported; see help varlist.

Contents

Description

Examples of usage

Saved results

References

Acknowledgements

Citation of ginireg

Description

ginireg is a routine for estimating Gini regressions.
It can run standard Gini,
mixed OLS/Gini,
instrumental variables (IV) Gini
and extended Gini regressions.
The ability to mix regression methods enables finding
the implicit assumptions that affect the sign or magnitude of the estimates.

Gini regression can be interpreted in various ways.
The Gini regression has its origin in Corrado Gini's (1912) introduction
of the Gini Mean Difference (GMD) as an alternative to the variance.
The population GMD is defined as GMD = E{|X_i-X_j|} , i.e.,
the expected absolute difference between two realizations
of an i.i.d. random variable.
It can be shown (see Yitzhak-Schechtman 2013, p. 18)
that the GMD can be equivalently defined as
GMD = 4*cov(X,F(X)) },
where F(X) is the population cumulative distribution function (CDF).
One intuition for the Gini regression is that
it replaces the standard notion of variance with the Gini notion of variance.

An alternative interpretation that also makes clear the methods of computation
is that the basic Gini regression of Y on a set of regressors X
is an IV regression with regressors X and instruments F(X),
where here F(X) represents the empirical CDF.
Mixed Gini regression is equivalent to partitioning the regressors X into two sets, X_1 and X2,
and estimating by IV treating X_1 as exogenous (OLS regressors)
and treating X_2 as endogenous with instruments F(X_2) (Gini regressors).
Pure Gini IV is IV with regressors X and instruments F(Z);
general Gini IV is IV with regressors partitioned into X_1, X_2
and a mix of instruments F(X_1) and F(Z).
ginireg can also estimate Extended Gini regressions.
For a full discussion of these estimators see Yitzhak-Schechtman (2013).

The default VCE is the classical VCE.
Jackknife SEs are available with the vce(jackknife) option.

The nogini(varlist) option may be used
to suppress the Gini transformation for the variables listed.
The untransformed variables may be either regressors or instruments
(in the case of IV estimation).
For example, nogini(X_2) will perform
the basic Mixed Gini estimation described above.
To peform Extended Gini regression,
the variables subject to the extended Gini tranform
extended(varlist) need to be specified
along with the Extended Gini parameter nu(#).
Standard Gini regression is equivalent
to Extended Gini estimation with nu=2.

ginireg reports several goodness-of-fit measures
that parallel the standard OLS measure of R-squared.
Denote the predicted value of the dependent variable by Yhat.
Then

GR = cov(Yhat,F(Yhat))/cov(Y,F(Y))

Gamma YYhat = cov(Y,F(Yhat))/cov(Y,F(Y))

Gamma YhatY = cov(Yhat,F(Y))/cov(Yhat,F(Yhat))

For further discussion of these measures
see Yitzhaki-Schechtman (2013), pp. 18, 53, 159-60.

The LMA curve (Line of independence Minus the Absolute concentration)
and Normalized LMA (NLMA) can be obtained following ginireg estimation
using estat.
Either the regression residuals (lmaresid)
or the dependent variable and fitted values (lmayyhat)
can be requested.
Additional options for the underlying Stata graphics command
can also be added.
The ginilma command must also be installed
for this option to be available.
See the online help for ginilma
or Yitzkaki-Schechtman (2012)
for further discussion of the LMA and NLMA curves.

Examples

Load Mroz cross-sectional dataset on female labor force participation

. use http://fmwww.bc.edu/ec-p/data/wooldridge/mroz.dta

Standard Gini estimation - labor force participation vs. age, education

. ginireg inlf age

. ginireg inlf age, vce(jackknife)

. ginireg inlf age educ

IV Gini estimation

. ginireg inlf age (educ = motheduc fatheduc huseduc)

Postestimation - LMA and NLMA for residuals or dependent variable/fitted values

Gini regression of labor force participation vs. age

. ginireg inlf age

. estat lmar

. estat lmay

Gini regression of labor force participation vs. age, education

. ginireg inlf age educ

. estat lmar

. estat lmay, nlma

Mixed Gini estimation

Gini estimation of a wage equation in levels

. ginireg wage age educ kidslt6 kidsge6

. estat lmay, nlma

Mixed Gini estimation of a wage equation with both Gini and OLS regressors

. ginireg wage age educ kidslt6 kidsge6 exper expersq, nogini(exper expersq)

Saved results

ginireg saves the following in e():

scalars

e(N) sample size

e(nu) extended Gini parameter

e(gr) Gini regression goodness-of-fit measure

e(gyyh) cov(y,f(yhat))/cov(y,f(y))

e(gyhyh) cov(yhat,f(yat))/cov(yhat,f(yhat))

macros

e(cmd) ginireg

e(depvar) name of dependent variable

e(gini_inexog) Gini regressors

e(nogini_inexog) standard (least squares) regressors

e(endo) endogenous regressors

e(gini_exexog) Gini instruments

e(nogini_exexog) standard (least squares) instruments

e(extended) extended Gini regressors

e(predict) ginireg_p

e(estat_cmd) ginireg_estat

e(properties) b V

matrices

e(b) coefficient vector

e(V) variance-covariance matrix of the estimators

functions

e(sample)

References

Yitzhaki, Shlomo and Schechtman, E. 2013.
The Gini Methodology: A Primer on a Statistical Methodology.
Springer.

Yitzhaki, Shlomo and Schechtman, E. 2012.
Identifying monotonic and non-monotonic relationships.
Economics Letters 116 (2012) 23–25.

Acknowledgements

I am grateful to Shlomo Yitzhaki for guidance and many helpful discussions
about Gini regression and its implementation.

Citation of ginireg

ginireg is not an official Stata command. It is a free contribution
to the research community, like a paper. Please cite it as such:

Schaffer, M.E. 2015.
ginireg: Program to estimate Gini regression.
http://ideas.repec.org/c/boc/bocode/s457958.html

Author

Mark E Schaffer, Heriot-Watt University, UK
m.e.schaffer@hw.ac.uk

Also see

Help: ginilma (if installed)