# If, we assume that a number of variables observed (latent variables), then what the method does is to extract a group of indicators to characterize a variable.

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If, we assume that a number of variables observed (latent variables), then what the method does is to extract a group of indicators to characterize a variable whose behavior has not been observed (Informality Index). Defining occupation following positions jobs: With this these, the index is obtained from informality relative proportions in which each position represents the employment of the total, thereby reducing the dimensionality of the original set of variables. Informal Sector X1 = Employees X2= Self-employed X3= Employers X4= Unpaid Workers X5= Other Workers Informal employment in formal X1 = Self-employment in agriculture or subsistence X2 = unpaid workers in different units Informal Sector X3 = Paid Domestic Service X4 = Salaried workers unprotected sectors working to formal X5 = Unprotected workers without remuneration fixed in formal ANNEX

Consider that: X1= Vector of weights TA NAICS subsector with order of 56x1: X2=Vector of weights TCP NAICS subsector with order 56x1: ANNEX Thus :

X3=Vector of weights Emp NAICS subsector with order56x1: X4=Vector of weights UW NAICS subsector with order of 56x1: ANNEX Thus :

ANNEX X5=Vector of weights OT NAICS subsector with order of 56x1: Thus :

Econometric Estimation in with Software Year of study: 2008 Principal Components of correlation: Eigenvalue Variance Prop. Cumulative Prop. Vector 1 order 5x1=Vector Characteristic (VC) Yields the following vector characteristic: ANNEX VariableVector 1 X1 q1q1 X2 q2q2 X3 q3q3 X4 q4q4 X5 q5q5

Squares of the elements of Vector Characteristic(CVC) Principal Component (CP) = (Vector Characteristic)*(square root of Eigen value) Weighting and Scoring=(Elements of Vector Characteristic)/(Principal Component) ANNEX

Proportion of Variance Explained Informality Index by Economic Activity Subsector, vector order 56x1 (Matrix X1, X2, X3, X4,X5 of order 56x5)*(Vector of Weights order 5x1) ANNEX

ANNEX Adding Weights Vector, vector order 56x1 =  by subsector of X1, X2, X3, X4 y X5 Average Weights Vector, vector order 56x1= by subsector de X1, X2, X3, X4 y X5 Yields some measures of central tendency: mean, standard deviation and variance of the Index of Informality by sector of Economic activity: Index of Informality Standardized by Subsector of Economic Activity (IIE) vector order 56x1 = Index of Informality (56x1) Mean ( ) Standard Deviation (σ) Variance (σ 2 )

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