Growth, Concentration, Inequality and Regional Policy in Mexico

Abstract

During the period from 1970 to 2010 the Mexican economy grew at an average rate of 3.3 %, a disappointing long run performance. To a large extent, this situation is due to the end of the import substitution industrialization period, during the late 1970s, and the subsequent transition to a new model based on exports, during the 1980s.

This work was carried out with the support of the Special University Chair “José Vasconcelos” FES-Acatlán and the DGAPA PAPIIT IN308911 “Economic regionalization program” in FE-UNAM. The authors want to thank to Cristina Vázquez Ruiz and Jaime Prudencio Vázquez for his valuable work of research documents, sources and for mapping.

Annex: Inequality Indicators

The next indicators are based on Ezcuarra and Rodriguez-Pose (2010):

The coefficient of variation (c), and the standard deviation of the logarithms (v), which are in the expressions (8.1) y (8.2):

$$ c=\frac{\sqrt{{\displaystyle \sum_{i=1}^n{p}_i{\left({x}_i-\mu \right)}^2}}}{\mu } $$

(8.1)

$$ v=\sqrt{{\displaystyle \sum_{i=1}^n{p}_i{\left(\operatorname{l}\mathrm{n}{x}_i-\tilde{\mu}\right)}^2}} $$

(8.2)

Where:

$$ \mu ={\displaystyle {\sum}_{i=1}^n{p}_i} $$

$$ \tilde{\mu}={\displaystyle {\sum}_{i=1}^n{p}_i}\operatorname{l}\mathrm{n}{x}_i $$

• p _i  = population share of region i in a given year.

• x _i  = per capita GDP of region i.

The Gini index (G) can be written as:

$$ G=\frac{{\displaystyle \sum_{i=1}^n{\displaystyle \sum_{i=1}^n{p}_i{p}_j\left|{x}_i-{x}_j\right|}}}{\mu } $$

(8.3)

The generalised entropy class of measures (GE) can be written as:

$$ GE\left(\theta \right)=\left\{\begin{array}{c}\hfill {\displaystyle \sum_{i=1}^n{p}_i \ln \left(\frac{\mu }{x_i}\right)};\theta =0\hfill \\ {}\hfill {\displaystyle \sum_{i=1}^n pi\left(\frac{ xi}{\mu}\right) \ln \left(\frac{ xi}{\mu}\right);\theta =1}\hfill \end{array}\right. $$

(8.4)

The Atkinson’s family of indices, A(ε), can be written as:

$$ A\left(\varepsilon \right)=\left\{\begin{array}{c}\hfill 1-{\left[{\displaystyle \sum_{i=1}^n{p}_i}{\left(\frac{x_i}{\mu}\right)}^{1-\varepsilon}\right]}^{\frac{1}{1-\varepsilon }};\varepsilon \ne 1\hfill \\ {}\hfill 1-{\displaystyle \prod_{i=1}^n{\left(\frac{x_i}{\mu}\right)}^{p_i};}\varepsilon =1\hfill \end{array}\right. $$

(8.5)

The Esteban and Ray’s measures of polarization are in the following expressions:

$$ {P}^{ER}\left(f,\propto, \rho \right)={\displaystyle {\sum}_{j=1}^m{\displaystyle {\sum}_{k=1}^m}}{p}_j^{1+\alpha } pk\left|\mu j-\mu k\right| $$

(8.6)

$$ {P}^{EGR}\left(f,\propto, {\rho}^{\ast },\beta \right)={P}^{ER}\left(f,\propto, {\rho}^{\ast}\right)-\beta \left[G(f)-G\left({\rho}^{\ast}\right)\right] $$

(8.7)

where:

∝ ∈ [1,1.6] parameter that reflects the degree of sensitivity to polarisation

β ≥ 0 is a weighting parameter for the error term in expression (8.7)

Finally, the modified conditional density estimator proposed by Hyndman et al. (1996) takes the following form:

$$ \overset{\wedge }{f}\left(y\left|x\right.\right)={\sum}_{j=1}^n{w}_j(x)\frac{1}{b}K\left(\frac{\left\Vert y-{Y}_j\left\Vert y\right.\right.}{b}\right) $$

(8.8)

Where:

^∧ _f (y|x) is the natural kernel estimator of the conditional density Y|X = x

K is the kernel function

‖_.‖ is a metrical distance

b controls the smoothness of each conditional density in the y direction

w _j can be estimated from:

$$ {w}_j(x)=K\left(\frac{\left\Vert x-{X}_j\right\Vert }{a}\right)/{\sum}_{i=1}^nK\left(\frac{\left\Vert x-{X}_i\right\Vert }{a}\right) $$

(8.9)

where a controls the smoothness of each conditional density in the x direction

All the indicators were calculated with DASP (Distributive Analysis Stata Package) in STATA.12 (Araar and Jean-Yves 2007), and using the Hyndman’s hdrcde package for R.