economies Article Fréchet Distribution Applied to Salary Incomes in Spain from 1999 to 2014. An Engineering Approach to Changes in Salaries’ Distribution Santiago Pindado 1,*, Carlos Pindado 2 and Javier Cubas 1 1 Instituto Universitario de Microgravedad “Ignacio Da Riva” (IDR/UPM), ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza. del Cardenal Cisneros 3, 28040 Madrid, Spain;
[email protected] 2 Colegio de Ingenieros de Caminos, Canales y Puertos, Colegiado n◦ 13177, Almagro 42 - 1a Planta, 28010 Madrid, Spain;
[email protected] * Correspondence:
[email protected]; Tel.: +34-91-336-63-53 Academic Editor: Joydeep Bhattacharya Received: 20 December 2016; Accepted: 18 April 2017; Published: 1 May 2017 Abstract: The official data in relation to salaries paid in Spain from 1999 to 2014 has been analyzed. The inadequate data format does not reflect the whole salary distribution. Fréchet distributions have been fitted to the data. This simple distribution has similar accuracy in relation to the data when compared to other distributions (Log-Normal, Gamma, Dagum, GB2). Analysis of the data through the fitted Fréchet distributions reveals a tendency towards more balanced (i.e., less skewed) salary distributions from 2002 to 2014 in Spain. Keywords: Spanish economy; salary distribution; parametric modelling; Fréchet distribution; minimum wage JEL Classification: C22; J31 1. Introduction In November 2015, the salary distribution data in Spain was updated in the statistics database of the Spanish Tax Agency.1 This data is organized by taking into account several aspects of the Spanish society (gender, age, economic sectors, etc.). According to the best-selling newspaper in Spain,2 the most significant information was the salaries earned in relation to the salary brackets (see in Tables1 and2 the number of salaried people and its weight in terms of total amount of paid euros, in relation to the salary, expressed in times the minimum wage), which demonstrates that the average annual salary in Spain fell in 2014 to the levels of 2007.