MODIFIED GENERALISED FOSTER-GREER-THORBECKE INDEX IN UNIDIMENSIONAL POVERTY IN NIGERIA

Abstract

Unidimensional poverty analysis is the use of income or expenditure as an indicator for poverty. This approach relies heavily on the use of the Poverty Line (PL) as an arbitrary classification threshold to classify households into poor and non-poor groups. However, the major criticism of this approach is its sensitivity to extreme observations. Also, the existing Foster-Greer-Thorbecke (FGT) index is limited by its exclusion of variations among the poor. Therefore, this study was aimed at developing a Modified Generalised Foster-Greer-Thorbecke (MGFGT) poverty index and hybrid PL. The existing Foster-Greer-Thorbecke (FGT) poverty index was modified by choosing the Indicator Function (IF), I(y < z), where z is PL and y is the Per Capita Household Expenditure (PCHE) to represent starving, extremely poor, moderately poor and non-poor households instead of the poor and non-poor households of the original IF. The Poverty Gap Ratio (PGR), ((z-y)/z) was redefined as |(y-z)/z|. The PL was also redefined as z_H=z_r^β z_a^(1-β) where z_His the hybrid PL, z_r is the relative PL, z_a is the absolute PL and β (0< β <1) is the elasticity of the hybrid PL with respect to PCHE. Four relative PLs: mean PCHE (Zr1), (2/3)*mean PCHE (Zr2), median PCHE (Zr3), and (2/3)*median PCHE (Zr4) were used for each β to determine z_H and the Modified Head Count Index (MHCI), Modified Poverty Gap Index (MPGI), and Modified Square Poverty Gap Index (MSPGI), respectively using the consumption expenditure data obtained from the 2012/2013 General Household Survey (GHS) of the National Bureau of Statistics. These indices were accessed using the minimum variance criterion. A supplementary simulated dataset with 5000 replications was used to investigate the statistical distributions of the MHCI, MPGI and MSPGI with their basic moments. The statistical distributions were further assessed for their suitability based on the Kolmogrov-Smirnov goodness of fit (GOF) test at α0.05. The MGFGT was P_α^*=1/N ∑_1^N▒〖|(y-z_H)/z_H |^α I^* (y≤z_H)〗, where α is the sensitivity of the index to poverty and I^* (y≤z_H )is the modified IF with 3/6,2/6,1/6and 0 representing starving, extremely poor, moderately poor and non-poor households, respectively. The MGFGT became MHCI, MPGI and MSPGI for α = 0, 1 and 2, respectively. The estimates of Zr1, Zr2, Zr3 and Zr4 at β = 0.6 with their corresponding hybrid PLs were N110,984.97, N73,989.90, N85,906.95, N57,271.35; and N12,135,653.00, N9,514,991.00, N10,406,910.00, N8,159, 565.70, respectively. The estimates of MHCI, MPGI and MSPGI for the four hybrid PLs at β = 0.6 were 0.5000, 0.4954, 0.4909; 0.4999, 0.4822, 0.4656; 0.4999, 0.4947, 0.4946; and 0.5000, 0.4932, 0.4866, respectively. The approximate estimate of 50% from the estimates of the indices suggested that approximately 50% of the household experienced starvation. These estimates further indicated the robustness of the indices. The GOF test validated the Weibull distribution for fitting the MHCI and Frechet distribution for fitting both the MPGI and MSPGI. The modified generalised Foster-Greer-Thorbecke poverty index allowed the inclusion of variations among the poor. There was further reduction in the negative effects of arbitrariness and sensitivity in unidimensional poverty analysis