1. PARAMETRIC MODELS FOR PERSONAL INCOME DISTRIBUTION IN SPAIN
PARAMETRIC MODELS FOR PERSONAL INCOME DISTRIBUTION IN SPAIN. AN APPROXIMATION BY MEANS OF THE GENERALIZED BETA DISTRIBUTION OF SECOND KIND MODELOS PARAMÉTRICOS PARA LA DISTRIBUCIÓN PERSONAL DE LA RENTA EN ESPAÑA. UNA APROXIMACIÓN A PARTIR DE LA DISTRIBUCIÓN BETA GENERALIZADA DE SEGUNDA ESPECIE.
Mercedes Prieto Alaiz
Universidad de Valladolid
Carmelo García Pérez
Universidad de Alcalá
Presented at
XXXIII SIMPOSIO DE ANÁLISIS ECONÓMICO ZARAGOZA,
12 december 2008

2. Motivation
The main advantage of the parametric approach is that thousands or hundreds of thousands of observations could be concentrated in a small number of parameters
The regularities displayed by observed personal income distributions provide justification to describe them with the help of some statistical distribution functions

3. Motivation
Comparisons among income distributions (Bandourian, McDonald and Turley 2003)
Analysis of the impact of taxes and transfer payments on inequality (Dastrup, Hartshorn and McDonald 2007)
Study of the relationship between economic and social factors and income distribution (Parker 2000; Jäntti and Jenkins 2001).
Overcoming data censoring problems (Feng, S., Burkhauser, R., and Butler, J.S. ,2006)
The estimated parameters could be used

4. Objetive
Modelling income distribution by means of the generalised beta II (GBII) distribution a four-parameter distribution

5. Outline Parametric modelling of personal income distribution
1.1 The choice of parametric models for income distribution
1.2 The Estimation
1.3 The Goodness of fit
Data and Methodological Decisions
Results
Conclusions

6. 1. Parametric modelling of personal income distribution
Aim: to fit a functional form to expenditure data.
This is an inference problem
The choice of a functional form
The estimation of the unknown parameters
The analysis of the goodness of fit.

7. 1.1 The choice of a functional form
Properties
Right skewness
Convergence to the Pareto Law
Parsimonious parametric specification
Economic model foundation
Flexibility
Goodness of fit

8. 1.1 The choice of a functional form
One parameter → Pareto Law (Mandelbrot, 1960 )
Two parameters → Gamma and Lognormal (Salem and Mount, 1974)
Three parameters → Singh-Maddala (Singh and Maddala, 1976 ) and Dagum (Dagum, 1977)
Four parameters → Generalized Beta of Second Kind (McDonald 1984)

9. 1.1 The choice of a functional form

10. The choice of a functional form
q→∞
a→0
Gamma G
Beta II
S-M
GBII
Lognor
Gamma
Weibull
a=1
p=1
q=1
Dagum
Fisk

11. 1.2 The estimation tecnique
Likelihood estimation

12. 1.3 The analysis of goodness of fit
Nested models
Non-nested models
Kolmogorov-Smirnov
Cramer-von Mises
Anderson-Darling

13. 2. Data and Methodological Decisions
Main choices
Variable: Disposable income
Unit of analysis: Person
Equivalent Scale: Modified equivalent scale (1 first adult, 0.5 rest of the adults.0.3 children under 14)
Source of information
The European Union Statistics on Income and Living Conditions (EU-SILC) and 2005

14. 3 Results
Year 2003

15. 3 Results
Year 2004

16. 3 Results (Goodness of fit)

17. Results Quartile pp-plots (2004)
Fisk pp-plots
GBII pp-plots
Singh-Maddala pp-plots

18. 3. Results(Lorenz dominance)
From the non parametric approach, this test involves calculating the joint distribution of a finite number of the empirical Lorenz ordinates.
Problems
There is always some arbitrariness to choose the number of ordinates to be tested.
The joint distribution is computationally costly

19. 3. Results From the parametric approach Kleiber (1999)
X1 Lorenz dominates X2
X2 exhibits at least as much inequality as X1.

20. 3. Results
The distribution for the year 2003 Lorenz dominates the distribution for the year 2004.
There has been an increase in inequality during these two years

21. 4 Conclusions
As a conclusion we can say that parametric modelling is a useful approach for analysing income distribution.
This approach is very sensitive to the presence of misspecification errors which could lead to erratic conclusions.
The GBII is a good model for summarising the information contained in the income data.
The level of inequality for the year 2003 was less than that for the year 2004