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Distributive effects of an income tax -- Measures of progressivity, vertical eq
> uity and reranking

        progres pretaxvar posttaxvar [weight] [if exp] [in range] [,
              param(real 2.0) format(%fmt) ]

        aweights and fweights are allowed; see help weights.


Description

    progres is a module for assessing the distributive effects of an income
    tax.  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.

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

     - The Kakwani (1977) index of tax progressivity: K = C(T) - G(X)

     - The Musgrave-Thin (1948) index of redistributive effect: MT =
     (1-G(Y))/(1-G(X))

     - The Reynolds-Smolensky (1977) index of redistributive effect: RS =
     G(X) - G(Y)

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

     - The Reranking effect: R = VE - RS = G(Y) - C(Y)

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

     - 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.

    pretaxvar is required to be non-negative. Observations with pretaxvar<0
    are automatically discarded in computations.


Options

    param(real 2.0) 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.

    format(%fmt) specifies the results display format. Default is %5.4f.


Saved results 

    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).
    
    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).

    Furthermore, the (weighted) number of observations and the variables used
        are stored in

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


Examples

    . progres gross_inc std_dispy

    . progres gross_inc std_dispy [aw=coweight] , param(3.0)


References

 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.

 Kakwani, N.C. (1977). Measurement of Tax Progressivity: An International
     Comparison, Economic Journal 87: 71-80.

 Lambert, P. J. (2001): The distribution and redistribution of income,
     Manchester University Press, 3rd edition.

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

 Ochmann, R. and Peichl, A. (2006): Measuring Distributional Effects of
     Fiscal Reforms, Finanzwissenschaftliche Diskussionsbeiträge 06-9, Köln.

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

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

 Suits, D. (1977). Measurement of Tax Progressivity, American Economic Review
     67: 747-752.


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.