Educational systems, intergenerational mobility and social segmentation.

• Author: Chusseau, Nathalie
• Position: Report

1. Introduction (3)

   In the economic literature, the impact of human capital acquisition upon social segmentation has been analysed through the emergence of under education traps, i.e., situations in which a proportion of the population remains unskilled from generation to generation.

   In the early approach of Becker and Tomes (1979) with a perfectly competitive credit market, all the dynasties converge towards the same human capital in the long term. Assuming credit market imperfections, Loury (1981) and Becker and Tomes (1986) show that this convergence still holds but it is slowed down, thereby creating a 'low mobility trap' (Piketty, 2000).

   These rather optimistic diagnoses were subsequently questioned by a number of works that analysed the emergence of under education traps. Several determinants can cause the emergence of such traps: a credit constraint with a fixed cost of education (Galor and Zeira, 1993, Barham et al., 1995), an S-shaped education function (Galor and Tsiddon, 1997), a neighbourhood effect resulting from local externalities (Benabou, 1993, 1996a, 1996b; Durlauf 1994, 1996), limited parental altruism (Das, 2007) etc. In most of these works, the trap results from non convexities that make certain individuals select low education. However, these approaches typically suppose that the institutional access to education is equally guaranteed. Financial constraints, family and social characteristics and limited abilities are then the main factors that explain the differences in educational choices and the related social segmentation.

   However, since Weber (1906), the sociological literature has drawn attention to the fact that the educational system itself can create social segmentation (Bidwell and Friedkin, 1988, for an early review). It has been underlined that the type of knowledge that is promoted corresponds to the cultural backgrounds of the children from the upper and middle classes (Sorokin, 1959; Bourdieu and Passeron, 1970; Baudelot and Establet, 1971) and that families from the lower classes overestimate the cost of and underestimate the return from education (Boudon, 1973, 1974). In addition, because of better information and network effects, the children from higher classes select better educational strategies, and they have access to better positions than children from lower classes even when they possess the same degree (Anderson, 1961; Boudon, 1973, 1974; Thelot, 1982). Finally, a number of analysts have emphasised the influence of the selection pattern, i.e. the very structure of the educational system, on the formation and the persistence of social segmentation (Bourdieu and Passeron, 1970; Bowles and Gintis, 1976). Several recent empirical studies confirm the impact of the educational system upon social stratification. Using data from an international survey, Shavit and Muller (2000) find that the institutional characteristics of the school systems partly explain the differences in educational and occupational attainment across countries. Similarly, by comparing the transition from school to work in France, Germany, the UK and the US, Kerckhoff (2000) concludes that the differences across these countries are partially due to the differences in their educational systems.

   If sociologists have studied for a long time the impact of hierarchical educational systems upon social stratification, this has only recently been investigated by the economic theory. Driskill and Horowitz (2002) and Su (2004) analyse hierarchical educational systems by focusing on the allocation of public funding between basic and advanced education. They study the impacts upon growth, welfare and income distribution, but not on social stratification. Bertocchi and Spagat (2004) model a three-level educational system (basic education and secondary education divided between vocational and general studies) so as to analyse social stratification during the different stages of economic development. However, their approach does not generate lasting under education trap because workers without secondary education disappear with the vanishing of the traditional sector.

   Our objective is to analyse the impact of the structure of the educational system, i.e., the way the courses of study are organised with their different stages, divisions, selection procedures and funding, upon the formation and the intergenerational persistence of social segmentation.

   The starting point of the analysis consists in a simplified stylised picture of the education systems that exist in most of the countries. These educational patterns exhibit rather similar structures, with however significant differences in the weight and funding devoted to each stage and in the severity of the selection procedures (see Tavares, 1995, for a description of the European systems in the mid-nineties). Compulsory schooling is enforced until the age of 15-18 in advanced countries, and until 12-15 years old in most of the developing countries. After compulsory schooling, young adults can either join the labour market, or pursue their studies. In the latter case, they typically face two courses of study. They can firstly select vocational studies. If such studies do exist in all countries, their shape and entry conditions significantly differ between as well as within countries. Usually, the access to vocational study does not require the obtainment of a final degree that sanctions secondary schooling (A-Level, Abitur, Baccalaureat etc.), even if this is the case for certain technical studies. In addition, vocational studies typically begin at upper secondary school level and can be part of an apprenticeship system. A second course of study consists in going to university, i.e., the tertiary educational system. Entering a university typically requires the obtainment of a degree that sanctions secondary school, and additional selection procedures are often enforced.

   We firstly construct a simple stylised model that can describe this general educational framework, and that can be declined into various configurations. From this general model, we derive several possible social segmentations depending on the characteristics of the educational system. We finally implement a series of simulations that illustrate different social segmentations resulting from different educational systems.

   The article is original in several respects. It firstly develops an intergenerational theoretical framework that allows modelling the impact of the structure of the educational system upon social segmentation. Secondly, the model generates social segmentations that depend on both the educational system and the initial distribution of human capital between households. Finally, different educational systems result in different segmentations for the same initial distribution of human capital.

   The main features of the educational general framework are presented in section 2. The educational choices of individuals are analysed in section 3. The characteristics of the educational systems and the related social segmentations are determined in section 4. Section 5 analyses the human capital dynamics and the resulting segmentation. A series of simulations are implemented in section 6. We conclude in section 7.

2. The model general framework

   2.1. Production

   The economy produces one good with technology Y = [omega]H, H = [[summation].sub.j] [t.sub.j][h.sub.j], [h.sub.j] being the human capital of individual j and [t.sub.j] her/his time spent in the production activity. By assuming perfect competition on the market for goods, the profit is nil at equilibrium and [omega] is the before tax wage per unit of human capital x time. As a consequence, individual j earns the pre-tax income [[omega].sub.j] = [omega][h.sub.j][t.sub.j] .

   2.2. Individuals and Education

   We consider a succession of generations with the same number M of individuals. The successive generations linked by a parent-child relationship form a dynasty.

   An individual's life comprises two periods. Being young, s/he receives a basic education. Being adult, s/he lives one period of length 1 that s/he can divide between higher education and work.

   The government provides individuals with both basic and higher education. Public education is funded by a tax on the parents' income at rate [tau]. The after tax wage per unit of human capital x time is thus w = (1 - [tau]) [omega].

   Basic education is compulsory and this provides individuals with the human capital necessary to get access to the labour market. In contrast, pursuing higher education is a choice of the individual who takes her/his decision by comparing the related income benefit and cost. Albeit spending the same time in basic education, individuals differ in their human capital at the end of this time. This is because intra- family externalities make children from more educated families more able to acquire the provided education. In addition, it is assumed that the market for credit is perfect and that the interest rate is nil (4). These assumptions are tailored so as to place individuals in the most favourable situation in their choice for higher education, and thereby to focus on the sole impacts (i) of the uneven distribution of human capital across parents and (ii) of the educational structure, on the emergence of social stratifications.

   At the end of basic education, an individual can choose, either to join directly the labour market, or to pursue further education. In the latter case, two courses of study are open that are exclusive of each other. The individual can firstly choose vocational studies (denoted V) without any constraint in terms of human capital attainment at the end of basic education. S/He can also go to university (denoted U) if her/his human capital at the end of basic education is at least [[bar.[lambda]].sub.U] .

   2.3. Education functions

   Basic education produces individual j's human capital according to the following function:

   [[lambda].sub.j]...