{smcl}
{* 04sep2007}{...}
{hline}
help for {hi:progres}
{hline}

{title:Distributive effects of an income tax -- Measures of progressivity, vertical equity and reranking}

{p 8 14 2}
{cmdab:progres}
{it:pretaxvar posttaxvar} 
[{it:weight}] 
[{cmd:if} {it:exp}] 
[{cmd:in} {it:range}] 
[{cmd:,}
 {cmdab:p:aram(}{it:real 2.0}{cmd:)}
 {cmdab:f:ormat}{cmd:(%}{it:fmt}{cmd:)}
 ]

{p 8 8 2}
{cmd:aweights} and {cmd:fweights} are allowed; see help {help weights:weights}.


{title:Description}

{p 4 4 2}
{cmd:progres} is a module for assessing the distributive effects of an income tax.
{cmd:progres} takes unit-record data on pre-tax and post-tax income 
and computes several classic measures of (net) redistributive effects,
progressivity, vertical equity and reranking (horizontal inequity). All indices
are derived from (generalized) Gini coefficients of inequality and (generalized)
concentration coefficients.

{p 4 4 2}
{it:pretaxvar} is pre-tax income (X) and {it:posttaxvar} is post-tax income (Y).
Tax payments (T) are determined from the difference between {it:pretaxvar} and {it:posttaxvar}. 
Measures computed by {cmd:progres} are:

{p 5 5 2}
- The Kakwani (1977) index of tax progressivity: K =  C(T) - G(X)

{p 5 5 2}
- The Musgrave-Thin (1948) index of redistributive effect: MT = (1-G(Y))/(1-G(X))

{p 5 5 2}
- The Reynolds-Smolensky (1977) index of redistributive effect: RS = G(X) - G(Y)

{p 5 5 2}
- The Vertical Equity measure: VE = G(X) - C(Y) = g/(1-g) * K  , where g is the average tax rate.

{p 5 5 2}
- The Reranking effect: R = VE - RS = G(Y) - C(Y) 

{p 5 5 2}
- The Atkinson (1980)-Plotnick (1981) index of horizontal inequity:  AP = 0.5 * R/G(Y)

{p 5 5 2}
- The Suits' (1977) index if progressivity: S = 1- L/K where K denotes the area below the line of proportionality, and L denotes the area below the Lorenz curve of tax payments against income.

{p 4 4 2}
{it:pretaxvar} is required to be non-negative. Observations with {it:pretaxvar}<0 are
automatically discarded in computations.
    

{title:Options}

{p 4 8 2} 
{cmdab:p:aram(}{it:real 2.0}{cmd:)} sets the generalized Gini inequality aversion coefficient. Default is 2 leading to the classical Gini and concentration coefficients.
Greater inequality aversion can be adopted by setting param larger than 2.

{p 4 8 2} 
{cmdab:f:ormat(%}{it:fmt}{cmd:)} specifies the results display format. Default is %5.4f.


{title:Saved results} 

{p 4 8 2} 
All computed indices listed above are stored in real scalars:  

    r(Kakwani), r(MusThin), r(ReySmol),
    r(VE), r(R), r(AP), r(AtkPlot), r(Suits).
    
{p 4 8 2} 
Additionally, the average tax rate and the generalized Gini and 
concentration coefficients of pre-tax income, post-tax income and
tax are stored in 

    r(ATR), r(G_pre), r(G_post), r(C_post), r(C_tax).

{p 4 8 2} 
Furthermore, the (weighted) number of observations and the variables used are stored in

    r(N), r(sum_w), r(posttaxvar), r(pretaxvar).


{title:Examples}

{p 4 8 2}{cmd:. progres gross_inc std_dispy}

{p 4 8 2}{cmd:. progres gross_inc std_dispy [aw=coweight] , param(3.0)}


{title:References}

{p 1 5 2}Atkinson, A. (1980), Horizontal Inequity and the Distribution of the Tax Burden in H. Aaron & M. Boskin (eds.), The Economics of Taxation, pp.3-18.

{p 1 5 2}Kakwani, N.C. (1977). Measurement of Tax Progressivity: An International Comparison, Economic Journal 87: 71-80.

{p 1 5 2}Lambert, P. J. (2001): The distribution and redistribution of income, Manchester University Press, 3rd edition.

{p 1 5 2}Musgrave, R.A. and Thin, T. (1948). Income tax progression 1929-48, Journal of Political Economy 56: 498-514.

{p 1 5 2}Ochmann, R. and Peichl, A. (2006): Measuring Distributional Effects of Fiscal Reforms, Finanzwissenschaftliche Diskussionsbeiträge 06-9, Köln.

{p 1 5 2}Plotnick, R. (1981), A Measure of Horizontal Inequity in Review of Economics and Statistics, vol.63, p.283-288.

{p 1 5 2}Reynolds, M. and Smolensky, E. (1977). Public Expenditures, Taxes, and the Distribution of Income: The United States, 1950, 1961, 1970, Academic Press, New York.

{p 1 5 2}Suits, D. (1977). Measurement of Tax Progressivity, American Economic Review 67: 747-752.


{title:Authors}

   Andreas Peichl
   Cologne Center for Public Economics
   University of Cologne, Germany
   a.peichl@uni-koeln.de
   www.cpe-cologne.de

   Philippe Van Kerm
   CEPS/INSTEAD
   Luxembourg
   philippe.vankerm@ceps.lu

   Useful comments and testing by Christoph Haas are gratefully acknowledged.

{* Version 1.0.0 2007-09-04}