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1 Michel Tenenhaus & Carlo Lauro A SEM approach for composite indicators building Michel Tenenhaus & Carlo Lauro

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2 Economic inequality and political instability Data from Russett (1964), in GIFI Economic inequality Agricultural inequality GINI : Inequality of land distributions FARM : % farmers that own half of the land (> 50) RENT : % farmers that rent all their land Industrial development GNPR : Gross national product per capita ($ 1955) LABO : % of labor force employed in agriculture Political instability INST : Instability of executive (45-61) ECKS : Nb of violent internal war incidents (46-61) DEATH : Nb of people killed as a result of civic group violence (50-62) D-STAB : Stable democracy D-UNST : Unstable democracy DICT : Dictatorship

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3 Economic inequality and political instability (Data from Russett, 1964) 47 countries

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4 GINI FARM RENT GNPR LABO Agricultural inequality (X 1 ) Industrial development (X 2 ) ECKS DEATH INST Political instability (X 3 ) 1 2 3 + + + + - + + + + - Economic inequality and political instability

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5 Building composite indicators 1.Separately for each block (without taking into account the other blocks). 2.For each block, taking into account all the other blocks (multi-block data analysis). 3.For each block, taking into account the causal model (Structural Equation Modelling).

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6 1. Using SEM for factor analysis Measurement model 1 2 3 1 2 3

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7 ULS algorithm S = Observed covariance matrix for MV Goodness-of-fit Index (Jöreskog & Sorbum): = PCA when

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8 First result This solution is not admissible because

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9 A solution The variance of residual e2 is fixed to a small value

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10 Result 2 The variance of residual e2 is fixed to a small value:

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11 Bootstrap Results Regression Weights: Composite indicator

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12 Principal component analysis with SEM The variance of the residuals are fixed to 0 :

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13 Result 3 The variance of the residuals are fixed to 0 :

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14 Bootstrap Results Regression Weights: Conclusion

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15 Result 4 The variance of the residuals are fixed to 0 :

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16 Bootstrap Results Regression Weights: Composite indicator

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17 2. Using SEM for multi-block data analysis

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18 Result 5 This solution is not admissible because

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19 Result 6 Var(e2) is fixed to a small value

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20 Result 7 MacDonald (1996) proposal All Var(e) are fixed to 0:

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21 Bootstrap Results Regression Weights: Conclusion

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22 Result 8 MacDonald (1996) Proposals: (1) All Var(e) are fixed to 0: (2) Composite indicator:

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23 3. Causal model estimation using SEM-ULS

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24 Result 9 This solution is not admissible because

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25 Result 10 Var(e2) is fixed to a small value

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26 Bootstrap Results Regression Weights: Conclusion

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27 Result 11 Var(e2) is fixed to a small value Composite indicator:

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28 Bootstrap Results Regression Weights: Conclusion

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29 Conclusion Agricultural inequality and Industrial development are drivers of political instability Russet hypotheses are validated: Other composite indicators:

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31 Conclusion Agricultural inequality above the average Industrial development below the average DICTATORSHIP

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