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View/save PDF version of this document - La Strada International

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with its neat correspondence to the Lorenz curve and easy-to-interpretdecompositions <strong>of</strong> remittance effects. This is the measure we use in thepresent study.Following Lerman and Yitzhaki (1985), the Gini coefficient for totalincome inequality, G, can be represented as:G =K∑k=RkGkSk1 (1)where S krepresents the share <strong>of</strong> component k in total income, G kis thesource Gini, corresponding to the distribution <strong>of</strong> income from source k,and R kis the Gini correlation <strong>of</strong> income from source k with the distribution<strong>of</strong> total income. 2Equation (1) permits us to decompose the influence <strong>of</strong> any incomecomponent, in our case remittances, upon total income inequality, as theproduct <strong>of</strong> three easily interpreted terms:a) how important the income source is with respect to total income (S k)b) how equally or unequally distributed the income source is (G k)c) whether or not the income source is correlated with total income (R k).For example, if remittances represent a large share <strong>of</strong> total income, theymay potentially have a large impact on inequality. (If their share in totalincome is nil, so must be their contribution to inequality.) However, if theyare perfectly equally distributed (G k= 0), they cannot influence inequalityeven if their magnitude is large. If remittances are large and unequallydistributed (S kand G kare large), they may either increase or decreaseinequality, depending upon which households, at which points in the incomedistribution, receive them. If remittances are unequally distributed and flowdisproportionately towards households at the top <strong>of</strong> the income distribution(R kis positive and large), their contribution to inequality will be positive.However, if they are unequally distributed but target poor households,remittances may have an equalizing effect on the rural income distribution,and the Gini index may be lower with than without remittances.108Using the Gini decomposition, we can estimate the effect <strong>of</strong> small changesin remittances on inequality, holding income from all other sources constant2The properties <strong>of</strong> R kare the following:a) -1 ≤ R k≤ 1. R kequals zero if y kand Y are independent, and it equals 1(-1) if y kis an increasing(decreasing) function <strong>of</strong> total income.b) If y kand Y are normally distributed, then R kis equal to the Pearson correlation coefficient

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