The players may form coalitions these are subsets s of n that appropri ate themselves a part of the surplus and redistribute it between their members. Shapley value decomposition of r 2 and develops a fortran computer program that executes it. The marginal effects in subgroup decomposition of the gini. Changes in income inequalities are driven largely by changes in betweenzone inequalities. Shapley value regression is computationally and memory intensive, so if you have a lot of variables, i recommend forcing the variables whose importance measure isnt necessary. On this decomposition in matrix analysis books, the case is m n, called ldl decomposition, which is derived from triangular decomposition lu decomposition. Shapley value regression is perhaps the best methods to combat this problem.
Stata module to perform additive decomposition of sample statistic. Stanislav kolenikov statistical software components from boston college department of economics. The shapley value shapley, 1953 provides a popular answer to this question. Pdf shapley inequality decomposition by factor components. Shapley inequality decomposition, including the nested shapley chantreuil and trannoy 1999 and the owen decomposition shorrocks 1999, based on dening a hierarchical structure of incomes. The tce values by using shapley values in this example for x 1, x 2, and x 3 are 1187. The decomposition is performed using the shapley value. Regression based shapley value decomposition rbdineq. A shapleybased decomposition of the rsquare of a linear. Dear statalisters i am running a regression based decomposition by using command rbdineq. Multicollinearity and sparse data in key driver analysis.
Its principal application is to resolve a weakness of linear regression, which is that it is not reliable when predicted variables are moderately to highly correlated. This paper investigates the evolution of sri lankas expenditure distribution in the period 19802002 and uses three decomposition methodologiesthe fields, the shapley value decomposition. Their use is particularly widespread in studies of poverty and inequality. Once combined with conventional decomposition methods or the shapley value approach of shorrocks 1999, what is being proposed becomes a most general and powerful framework for regressionbased inequality decomposition. Decomposition procedures for distributional analysis. Citeseerx decomposition procedures for distributional. The present paper simplifies the algorithm of shapley value decomposition of r 2 and develops a fortran computer program that executes it. This program performs exact additive decomposition of a sample statistic by effects specified in factor list. Shapley decomposition is based on the wellknown concept of shapley value in cooperative game theory shapley, 1953. Empirical examples are provided to demonstrate the use of the procedure, and to contrast our results with those.
The advantages of the proposed methodology over the shapley value approach to gini subgroup decomposition are stated. This paper examines the shapley inequality decomposition. And with recent advancements in shapley value calculations for gradient boosted decision trees and neural networks, computing our proposed metric after model training can come with minimal computational overhead. Stata module to estimate shapley value of growth and distribution components of changes in poverty indicators. The idea of shapley value is to remove from time to time the contribution of all possible combinations of considered factors for determining their marginal contribution. Just type ssc install fmiss in stata to install it. Regressionbased approaches for the decomposition of. The concept of shapley value was introduced in cooperative collusive game theory where agents form collusion and cooperate with each other to raise the value of a game in their favour and later divide it.
Nov 15, 2006 this note suggests a new way of determining the exact contributions of the explanatory variables to the rsquare of a linear regression. Apr 18, 2016 shapley value regression is computationally and memory intensive, so if you have a lot of variables, i recommend forcing the variables whose importance measure isnt necessary. This note suggests a new way of determining the exact contributions of the explanatory variables to the rsquare of a linear regression. A shapleybased decomposition of the r square of a linear. Im asking m stata, see sysuse dir id take another look and see if anything jumps off the page at me. Some possible checks for income separation are described and an illustrative example using canadian data is provided. The command dfgts decomposes the allevation of fgt poverty by income components and provides standard errors on elements of the decompositions. Regressionbased approaches for the decomposition of income. Decomposes the gini index by income sources with the shapley approach. Shapley2 is a postestimation command to compute the shorrocksshapley decomposition of any statistic of the model normally the r squared. The studies by wan 2004, wan and zhou 2005 and wan et al.
It also retrieves regression coefficients from the shapley value. Regression based shapley value decomposition rbdineq stata. Shapley2 is a postestimation command to compute the shorrocks shapley decomposition of any statistic of the model normally the r squared. Output per worker employment to working aged population ratio working aged population to total population decomposition of the change ingdp uses shapley approach to divide each component as with all such decompositions, this does not provide a direct causal interpretation. The proposed solution to the general decomposition problem turns out to formally equivalent to the shapley value, and is therefore referred to as the shapley decomposition. Although chantreuil and trannoy 1999 and sastre et trannoy 2002 limited their application of the shapley value to the decomposition of income. Some methodological issues article pdf available in journal of economics 9s1 december 2002 with 1,484 reads how we measure reads. Shapley value regression significantly ameliorates the deleterious effects of collinearity on the estimated parameters of a regression equation. Individual members of the coalition share this gain as detailed out in table4. We undertake a spatial and intertemporal decomposition of the sgini inequality index using the shapley valuebased approach, and both moneymetric and child health indicators collected by the governments statistics office in 1996 and 2001.
Shapley value imputation shapley value regression has its origins in a game theory. Studies have shown that the two, despite being constructed in very different ways, provide surprisingly similar scoresgromping, u. Shapley value regression is a technique for working out the relative importance of predictor variables in linear regression. Stata module to estimate shapley decomposition by components of a welfare measure description. Shapley2 can be used for most estimation commands, e. Find the shapleyowen decomposition for the linear regression for the data in range a3. A short summary of the concept of shapley decomposition 1 the case of two variables. To this end, the present paper has made two contributions, first in simplifying the algorithm to compute the shapley value decomposition of r2 as fair shares to individual regressor variables and secondly a computer program that works it out. Shapleyowen decomposition real statistics using excel. This procedure was implemented with the distributive analysis stata package dasp 2.
Citeseerx document details isaac councill, lee giles, pradeep teregowda. Decomposition analysis provides help in the difficult task of explaining how economies trends and government policies affect the distribution of income. Gdp value added per capita can be decomposed into 3 parts. The players may form coalitions these are subsets s of n that appropriate themselves a part of the surplus and redistribute it between their. A shapleybased decomposition of the rsquare of a linear regression israeli, osnat, 2007 on the shapley value and decompositions of the gender gap. The marginal effects in subgroup decomposition of the gini index. Shapleyvalue decomposition in empirical applications raises some dilemmas that cannot be solved on purely theoretical grounds. Following this theory of sharing of the value of a game, the shapley value regression decomposes the r2 read it r square of a conventional regression which is considered as the value of the collusive cooperative game such that the mean expected marginal contribution of every predictor variable agents in collusion to explain the variation. Shapley regression and relative weights are two methods for estimating the importance of predictor variables in linear regression. An algorithm for computing the shapley value abdelkrim araar and jeanyves duclos january 12, 2009 1 the shapley value consider a set n of n players that must divide a given surplus among them selves. Shapley inequality decomposition by factor components. We first calculate the r 2 values of all subsets of x 1, x 2, x 3 on y, using the real statistics rsquare function.
Decomposing the change in gdp per capita world bank. To install the shapley decomposition of the hoi enter in the command window ssc install hoishapley. What is shapley value regression and how does one implement. Let ia,b be a function depending on two variables a and b. Also, you will find that some special characters that are legal in spss names do not work in the r code, but ordinary accented characters should be okay. To perform the shapley decomposition, the effects are eliminated one by one, and marginal effects from each exclusion are weighted in such a way that all exclusion trajectories have equal weights. Decomposition of shapley value of regression analysis. Shapley value regression is one of the best methods to combat this adversity to empirical analysis. A shapleybased decomposition of the rsquare of a linear regression a shapleybased decomposition of the rsquare of a linear regression israeli, osnat 20061115 00. As argued by sastre and trannoy 2002, provided all ambiguities about di. Compared to the user written command shapley, shapley2 is faster and enables you to compute the shapley value by groups of variables. Inequality decomposition in the distribution of income and. The proposed methodology combines the socalled shapley approach chantreuil and trannoy, inequality decomposition values.
Some methodological issues article pdf available in journal of economics 9s1 december 2002 with 1,484 reads how we. It also retrieve regression coefficients from the shapley value. Yitzhakis 1985 elasticity for gini incomesource decomposition, entails easy and transparent computations. An algorithm for computing the shapley value abdelkrim araar and jeanyves duclos january 12, 2009 1 the shapley value consider a set n of n players that must divide a given surplus among themselves. Another value addition of this paper is the construction and use of synthetic. Shapley decomposition if we want to estimate the marginal contribution of each circumstance to inequality we use the shapley decomposition see shorrocks, 2002. Aug 26, 2019 and with recent advancements in shapley value calculations for gradient boosted decision trees and neural networks, computing our proposed metric after model training can come with minimal computational overhead. Decomposition techniques are used in many fields of economics to help disentangle and quantify the impact of various causal factors. A regressionbased decomposition analysis boniface ngah epo and francis menjo baye1. Rongve 1995 and chantreuil and trannoy 1997 have both. In this context, recent studies have proposed the application of the shapley value allocation method, a concept from cooperative game theory, to the decomposition of inequality.
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