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

A SEM approach for composite indicators buildingMichel Tenenhaus & Carlo Lauro

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 Economic inequality and political instability Data from Russett (1964), in GIFI

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

Economic inequality and political instability Agricultural inequality (X1) GINI + + INST FARM + 1 + + + RENT ECKS 3 + GNPR + - DEATH 2 - LABO Political instability (X3) Industrial development (X2)

Building composite indicators • 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).

1. Using SEM for factor analysis Measurement model 1 1 2 2 3 3

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

This solution is not admissible because First result

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

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

Bootstrap Results Regression Weights: Composite indicator

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

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

Conclusion Bootstrap Results Regression Weights:

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

Composite indicator Bootstrap Results Regression Weights:

2. Using SEM for multi-block data analysis

This solution is not admissible because Result 5

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

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

Composite indicator: Result 8 MacDonald (1996) proposal All Var(e) are fixed to 0:

3. Causal model estimation using SEM-ULS

Result 9 This solution is not admissible because

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

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

Bootstrap Results Regression Weights: Conclusion

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

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