Linear SAM models for inequality changes analysis: an application to the Extremadurian economy

Abstract

Social accounting matrices are adequate databases for the economic modelling. These matrices emphasize the role of households in the economy, and so, they usually disaggregate the household sector into several groups. This disaggregation allows social accounting matrices to be used for diverse income distribution analysis. The objective of this work is to use the linear SAM models to study how inequality is modified by several exogenous injections of income. The set of multipliers and indicators presented is applied to the economy of Extremadura – a region situated in the southwest of Spain. In particular, together with the accounting multipliers, two redistributed income matrices are presented to show how changes in final demand and in income transfers cause opposite effects in inequality. For contrasting these results, Gini and Theil indices are also used. Finally, a major reduction in both would result from an appropriate re-allocation of transfers.

Acknowledgements

The first author acknowledges the financial support received from Ministerio de Ciencia y Tecnología (SEC2003-06080) and Generalitat de Catalunya (2004XT0095).

Notes

¹ Social accounting matrices are also typically used to calibrate the parameters of computable general equilibrium models.

² There nevertheless exist alternative closure assumptions. See Reinert et al . (1993).

³ A generic element Ma _ij of the said matrix reflects the increment that will accrue in the income of endogenous account i if endogenous account j receives an additional monetary unit of income from the exogenous accounts. For a more detailed analysis of this model, see Pyatt and Round (1979). These authors also present a procedure for the decomposition of the multipliers, giving the necessary existence conditions of the resulting matrices.

⁴ See also Polo et al . (1990), Roland-Holst (1990) and Llop and Manresa (2004). Moreover, Cohen and Tuyl (1991) proposed a different approach for income redistribution analysis, presenting various relative distributive measures. See also, De Miguel and Manresa (2004).

⁵ A generic element R _ij of the said matrix indicates the direction and magnitude of the change in relative income of account i resulting from a unitary exogenous injection received by account j. It can be demonstrated that the different columns of this matrix R sum to zero, independently of how the distribution is made between endogenous and exogenous accounts. The process of income redistribution could therefore be regarded as a zero-sum game.

⁶ Due to the absence of a Regional Statistical Institute, the lack of statistical information is especially serious in Extremadura. These statistical limitations have determined the degree of detail of the SAMEXT90 matrix – it would have been appropriate to disaggregate the labour factor – and have prevented the construction of a SAM referred to a more recent period. For example, it is important to note that there is only one input-output table for the Extremadura economy, also referred to the year 1990. For more detailed information on the Extremadura matrix, see De Miguel et al . (1998) and De Miguel (2003).

⁷ ‘Elements of the matrix R are in a one-to-one correspondence with those of the original M ( Ma ), and the normalization of incomes can be chosen for the subgroup of endogenous institutions under study’ (Roland-Holst, 1990, p. 129).

⁸ It can be shown that the columns of this redistributed income matrix also sum to zero.

⁹ The weights used in this case are those of the exogenous injections received by the different households groups.

¹⁰ Although not presented here for the sake of clarity, these indices can also be calculated by differentiating between active workers (accounts 3–9 in the matrix) and retirees (accounts 10–13). It is also possible to differentiate between high and low incomes directly, i.e., applying the distinction to the active farming-linked households (accounts 1 and 2), the households of active workers in other sectors (accounts 3–7), of rural retirees (groups 8 and 9), and of urban retirees (groups 10 and 11). The results that we obtained in these cases showed the same tendency as described in the text.

¹¹ By using a different methodological approach, Assane and Grammy (2003) analyse the causal relationship between growth and inequality.

¹² The Gini index is more sensitive to the changes in the centre of the distribution (Sen, 1997), while the Theil index, with the parameter c set to zero, is more sensitive to changes in the extremes (Shorrocks, 1980).

¹³ Indeed, in the initial situation reflected by SAMEXT90, the incorporation of transfers leads to a major reduction in inequality. In particular, the initial Gini and Theil indices for primary incomes are 0.5837 and 0.9456, respectively, both clearly greater than the final income indices (0.4902 and 0.5131). The reduction in the Theil index is far greater because the transfers fundamentally affect the household groups situated at the lower tail of the distribution.

¹⁴ Isla et al . (2002) present a similar analysis for Andalusian economy.

¹⁵ The inequality indices were minimized by solving the corresponding optimization problem, using GAMS (General Algebraic Modelling System) software.