ADECOMP

Description

adecomp implements the Shapley decomposition of changes in a welfare indicator as proposed by Azevedo, Sanfelice and Nguyen (2012). Following Barros et al. (2006), the method takes advantage of the additivity property of a welfare aggregate to construct counterfactual unconditional distributions by changing each component at a time, calculating their contribution to observed changes in poverty and inequality.

The approach calculates the decomposition across all possible paths and takes the average — the Shapley-Shorrocks estimates — resolving the path-dependence problem common in micro-decomposition methods.

The equation() option captures the relationship between the welfare variable and its components, where component variables are denoted by c# and separated by arithmetic operators.

Examples

* Basic decomposition with poverty and inequality indicators
adecomp percapitainc laborinc nonlaborinc, by(year) ///
    equation(c1+c2) indicator(fgt0 fgt1 fgt2 gini theil) varpl(pline)

* Decomposition with growth incidence curve
adecomp percapitainc laborinc nonlaborinc, by(year) ///
    equation(c1+c2) indicator(fgt0) varpl(pline) gic(100)

* Multi-component income decomposition
adecomp percapitainc padults laborinc capitalinc pensioninc transferinc othersinc, ///
    by(year) equation(c1*(c2+c3+c4+c5+c6)) indicator(fgt0) varpl(pline)

References

• Azevedo, J.P., Nguyen, M.C. and Sanfelice, V. (2012). “Shapley decomposition by components of a welfare aggregate.” Washington, DC: World Bank.
• Azevedo, J.P., Inchauste, G. and Sanfelice, V. (2013). “Decomposing the recent inequality decline in Latin America.” Policy Research Working Paper 6715, World Bank.
• Barros, R.P. de, Carvalho, M., Franco, S. and Mendoça, R. (2006). “Uma Análise das Principais Causas da Queda Recente na Desigualdade de Renda Brasileira.” Revista Econômica, 8(1), 117–147.
• Inchauste, G., Azevedo, J.P. et al. (2014). Understanding Changes in Poverty. World Bank.
• Shapley, L. (1953). “A value for n-person games.” In Kuhn and Tucker (eds.), Contributions to the Theory of Games, Vol. 2, Princeton University Press.

Citation

Azevedo, J.P., Nguyen, M.C. and Sanfelice, V. (2012). “ADECOMP: Stata module to estimate Shapley Decomposition by Components of a Welfare Measure.” Statistical Software Components S457562, Boston College Department of Economics.