### Coordonat de Gabriella FALCICCHIO & Viorella MANOLACHE

**Volum IV, Nr. 3 (13), Serie nouă, iunie-august 2016**

**Vizualizari articol **

** (31)**

**The inequality effect on family composition [1]**

**Maria Carmela MICCOLI**

**Antonella BISCIONE**

**Abstract: ***The aim of this paper is to analyse the inequality in Italy by using Dagum’s decomposition of Gini index (Dagum, 1997). Dagum’s decomposition has solved many problems related to the decomposability of the Gini index. The paper is divided in three sections. In the first section is analysed the family context in Italy. The second part presents the explanation of Dagum’s decomposition is explained. Then, in the last part is analysed the inequality in Italy by using the data collected by the Bank of Italy “Survey on Household’s Income and Wealth 2012”.*

**Keywords: ***family composition, inequality, Gini index, Dagum’s decomposition.*

**Introduction**

The Italian family has always played the role of a social safety net; role almost exclusive in the past and still relevant despite the gradual emergence of public institutions competitors. However, the Italian family is in deep structural transformation both for the progressive fall in the birth rate and for the increased geographical mobility.

These factors have led to a rapid growth of single-person households with consequent increase in the degree of exposure to the risk of social exclusion. The idea of this paper is to analyse how the change in family structure is closely linked to the dynamics of inequality in our country.

This paper is split into four sections. The main characteristics of the evolution of the Italian families structure will be outlined in the first one. The second section is devoted to analyzing the structure and size of households, the analysis of the differences positioned in the family and to the analysis of the spatial distribution in the three Italian macro-areas, the different types of families. In the third section is exposed the methodology developed by Dagum (1997a, 1997b) to decompose the Gini index in three components. In the fourth and final part of the paper shows the results obtained using the Dagum’s method, the data used to perform this decomposition are those made available by the Bank of Italy that every two years carried out a Survey “*Indagine sui Bilanci delle famiglie italiane*“.

**The recent growth of the instability of the Italian family structure**

The family has played and plays an important role as a social safety net, by being systematically load of difficult situations even when there are public institutions that work in this direction.

For this reason it is considered that any analysis concerning the inequalities existing in today’s Italian reality cannot be separated from an analysis of the major structural changes in families.

Many of the changes are associated with variation over time in the role of women, which reached a better position in the labour market (due to both a rise in the level of education and specialization is the promulgation of rules that guarantee gender equality not only in the field economic, but also in the family), she heard decrease the „necessity” of a husband, resulting in lower propensity to marriage and motherhood (often postponed or completely removed from life projects). In fact, today the condition of single woman (with or without children) is not an anomalous and outstanding event. Obviously, these changes (e.g. the progressive fall of birth, the strengthening of the rate of aging, to a lesser inclination towards marriage and the opposing higher frequency alternatives to unions) are not exclusively an Italian peculiarity, but it is possible to find these features, with different intensities, in the whole of Europe.

Considering the latest data published by ISTAT and EUROSTAT, we focus our attention on families, their birth, disintegration, composition, and their changes taking place, it appears, with regard to marriage that the Italian context has remained essentially stable over time, in fact the propensity to get marriage is among the lowest in the EU-27 with a rate of 3.5 per thousand (the average for the EU-27 is equal to 4.4 per thousand, with a peak of 7.3 per thousand for Cyprus and with a minimum result of 2.9 per thousand for Bulgaria).

The low propensity Italian to get marriage has strong internal regional differences. The highest values are in the South (4.1% o), with a maximum in Calabria (or 4.4%), while the minimum value is in the North-West (or 3.0%).

The choice of rite for the celebration (religious or civil) follows a trend related to the territory, in fact, the civil unions are most in the North (53.3% of marriages), the Centre follows it and between them there is a short distance (49.4%), southern culture makes that only 24.5% is celebrated with civil celebration, with a minimum in the Basilicata region (13.4%)^{2}.

In the territory, is not homogeneous the level of marital instability, which growth throughout the country. Although the rate of divorce in Italy is not particularly high compared with other European countries, such as Latvia and Lithuania (respectively 3.6 and 3.5 per thousand in 2012).

Naturally, a comparison based only on the rates of divorce does not say anything about the instability of families.

An efficient comparison can be performed using the separation rate: laws and procedures to get a divorce in different states can’t be compared. In addition, more and more frequently, the separation is the first and often the only step, which formalizes the breakup of a marriage in Italy.

Considering this indicator, the instability passes from 0.9% (or one divorce rate) to 1,5% (total instability per thousand inhabitants).

Table 1 – *Number of marriages, separations, divorces and marriage rate, separation rate and divorce rate (thousand inhabitants) in Italy*.

1995 | 2001 | 2011 | |

Marriages | 290009 | 264026 | 204830 |

Separations | 52323 | 75890 | 88797 |

Divorces | 27038 | 40051 | 53806 |

Marriage rate | 5,1 | 4,6 | 3,4 |

Separation rate | 0,9 | 1,3 | 1,5 |

Divorce rate | 0,5 | 0,7 | 0,9 |

**Source: **our elaboration on ISTAT data

In order to better understand the Italian situation, it is important to consider other indicators. These indicators put in relation the number of separations and divorces of one year and own cohort.

The results show an increase of this indicator: it goes, in fact, by 158.3% or 79.7% or a thousand separations and divorces registered in 1995 to 242.6% and 123.8%, or separations or divorces in 2001, to reach 310.7% and 181.9%, or separations or divorces in 2011.

Finally, the increased marriage interruption of our country has produced, with other phenomena most mentioned in the literature concerning the family (up to age at marriage, motherhood delayed …), a substantial change in the family structure with regard to the number and the composition of households.

**The Italian family structure **

Observing the information of census since the Seventies (as is well known in this period, in Italy, is legalized the opportunity to put end to the civil effects of marriage), we can see interesting changes: even if the number of households is increased, this growth is counterbalanced by the systematic reduction in the average number of its members. In addition, we can find this situation in all the areas analysed (see table 2 and table 3).

Table 2 – *Number of families. Absolute and percentage values and average number of components *

1971-2011

1971 | 1981 | 1991 | 2001 | 2011 | |||||||||||

North-West | 4910610 | 30,7 | 3,00 | 5513511 | 29,8 | 2,74 | 5745700 | 28,9 | 2,58 | 6217200 | 28,5 | 2,38 | 6927969 | 28,2 | 2,26 |

North-East | 2970841 | 18,6 | 3,33 | 3379613 | 18,3 | 2,94 | 3772707 | 19,0 | 2,73 | 4238787 | 19,4 | 2,49 | 4878478 | 19,8 | 2,33 |

Centre | 3020589 | 18,9 | 3,36 | 3575539 | 19,3 | 2,99 | 3858046 | 19,4 | 2,80 | 4235422 | 19,4 | 2,55 | 4915726 | 20,0 | 2,35 |

South | 3369187 | 21,1 | 3,75 | 4029685 | 21,8 | 3,01 | 4358575 | 21,9 | 3,18 | 4748274 | 21,8 | 2,92 | 5249239 | 21,3 | 2,66 |

Isles | 1709950 | 10,7 | 3,56 | 2001671 | 10,8 | 3,35 | 2173975 | 10,9 | 3,03 | 2370993 | 10,9 | 2,77 | 2640354 | 10,7 | 2,51 |

Italy | 15981177 | 100,0 | 3,35 | 18500019 | 100,0 | 3,23 | 19909003 | 100,0 | 2,83 | 21810676 | 100,0 | 2,59 | 24611766 | 100,0 | 2,40 |

The close relationship that exists between the economic and demographic phenomena is evident in some of the data that are present in Table 3. Emblematic is the substantial contraction, in the range of 91/81, of the growth rate of the number of households viewed in the north-west (signal of crisis and stop the attractiveness of the car industries), while the Italian transformation of a immigrant land has produced a significant increase in the number of families registered in the North East and Central especially in the last decade.

Considering the classic Italian territorial subdivisions, it is possible to analyze the evolution in the time of the weight of two familiar forms: the single-person households and those formed by 5 and more members respect to the total families of the same areas (see table 4).

Table 4 –*Percentage weight of families with 1 or 5+ components respect to the total families*

Area | 1971 | 1981 | 1991 | 2001 | 2011 | |||||

1/Tot | 5+/Tot | 1/Tot | 5+/Tot | 1/To. | 5+/To. | 1/To. | 5+/To. | 1/To. | 5+/To. | |

North-West | 16,1 | 13,9 | 21,3 | 9,2 | 24,3 | 6,2 | 28,4 | 4,1 | 33,7 | 4,0 |

North-East | 12,3 | 20,7 | 18,4 | 13,5 | 21,2 | 8,9 | 26,4 | 5,8 | 32,5 | 5,1 |

Centre | 10,9 | 20,7 | 16,3 | 13,3 | 20,3 | 10,0 | 25,0 | 6,4 | 32,8 | 5,1 |

South | 10,9 | 31,2 | 15,2 | 23,2 | 16,4 | 19,0 | 19,8 | 13,1 | 25,9 | 8,8 |

Isles | 12,4 | 27,3 | 16,5 | 20,4 | 18,9 | 15,7 | 22,8 | 10,4 | 29,3 | 6,7 |

Italy | 12,9 | 21,5 | 18,0 | 15,0 | 20,6 | 11,3 | 24,9 | 7,5 | 31,2 | 5,7 |

**Source:** Our elaboration on ISTAT data

Table 5 – *Percentage weight of families with 1 or 5+ components respect to the total families*, 1971-2011

Area | 1971 | 1981 | 1991 | 2001 | 2011 | ||||||||||

1/Tot. | 5+/Tot. | 1+5+ | 1/Tot. | 5+/Tot. | 1+5+ | 1/Tot. | 5+/Tot. | 1+5+ | 1/Tot. | 5+/Tot. | 1+5+ | 1/Tot. | 5+/Tot. | 1+5+ | |

North-West | 4,9 | 4,3 | 9,2 | 6,4 | 2,7 | 9,1 | 7,0 | 1,8 | 8,8 | 8,1 | 1,2 | 9,3 | 9,5 | 1,1 | 10,6 |

North-East | 2,3 | 3,9 | 6,2 | 3,4 | 2,5 | 5,8 | 4,0 | 1,7 | 5,7 | 5,1 | 1,1 | 6,3 | 6,5 | 1,0 | 7,5 |

Centre | 2,1 | 3,9 | 6,0 | 3,2 | 2,6 | 5,7 | 3,9 | 1,9 | 5,9 | 4,9 | 1,2 | 6,1 | 6,5 | 1,0 | 7,6 |

South | 2,3 | 6,6 | 8,9 | 3,3 | 5,1 | 8,4 | 3,6 | 4,2 | 7,8 | 4,3 | 2,9 | 7,2 | 5,5 | 1,9 | 7,4 |

Isles | 1,3 | 2,9 | 4,2 | 1,8 | 2,2 | 4,0 | 2,1 | 1,7 | 3,8 | 2,5 | 1,1 | 3,6 | 3,2 | 0,7 | 3,9 |

Italy | 12,9 | 21,5 | 34,4 | 18,0 | 15,0 | 33,0 | 20,6 | 11,3 | 31,9 | 24,9 | 7,5 | 32,4 | 31,2 | 5,7 | 36,9 |

**Source:** Our elaboration on ISTAT data

It is evident that the structural change occurred in our country: all the areas considered shown an increase of single-person households and a loss of importance of numerous families.

It also appears a gradual reduction with regard to the relative distances between the North and South of the country.

The information presents in Table 5 is also significant: these two kinds of families are compared with the total number of households; in addition it has been also considered the total weight of these two familiar forms.

Observing the data, we may notice that the single person households play an important role, on the contrary, the role played by the other kind of familiar form has faded; this situation also concerns those areas that have always had a strong reluctance to change.

The overview of the Italian situation is a useful starting point for the analysis of structural inequality, believing that the two extremes of the distribution (single-person households and numerous families) represent the features points of system crisis.

**The theoretical framework **

The Gini index is certainly one of the tools most used for the analysis of economic inequality and it is recognized for its many advantages. These advantages are, however, strongly limited because the Gini index cannot be decomposed in an additive manner in within and between groups.

This happens because the inequality of income can be measured correctly only if we consider the non-income characteristics of families: two families who have the same income, they may differ in their composition, gender, age and many other features. Only some of these characteristics can be explained by resorting to the use of equivalence scales that, in any case, are arbitrary and objectionable. Therefore, a key feature of an index of inequality is its decomposition within component „groups” and „between groups”.

For a long time, the most well-known decomposition of the Gini index has been that proposed by Mookherjee and Shorrocks (1982), which allowed decomposing the index into three components: the component within the groups, the between-group component and finally a residual term. By Mookherjee and Shorrocks (1982) defined the residual term such as the interaction effect between groups. Since then, numerous papers have been devoted to the decomposition of the Gini index. In this paper is used an alternative formulation of the decomposition of the Gini index, in particular the residual term, which is based on the concept of transvariation (Gini, 1996; Deutsch and Silber, 1997; Dagum, 1997).

In particular, Dagum (1997a, 1997b) suggested a decomposition of the Gini index into three components: the inequality within each subgroup, the inequality between subgroups and the inequality of transvariation between subgroups. This method presents some advantages: it allows the analysis of income differences on a wide range of distributions; shows how each subgroup contributes to the value of the Gini index, and the third component (the transvariation) is derived from the overlap of income distributions that belong to various subgroups.

The methodology postulated by Dagum presupposes the existence of a population Q composed by *n* households who have an income *y _{i}* and characterized by an average income μ. The population is divided into k subgroups

*Q*(j = 1, 2, 3,….k). Each subgroup

_{j}*j*is characterized by nj households and an average income μ

_{J}. The Gini index, for the total population, can be calculated in the following way:

The Gini coefficient that measures the inequality income of the Q_{j} subgroups (within-group) is:

The Gini coefficient has got values between 0 and 1, if the value is equal to zero, the income existing inside the group are equally distributed among its members, on the contrary, if the value is equal to 1 an individual from the group owns has the entirety of the existing income.

The coefficient that derives from the Gini index within group doesn’t allow measuring the inequality level between the groups. The Gini index between groups quantifies the difference of hope for income between an individual aleatorily chosen from group *j *and another one aleatorily chosen from group *h*. The Gini index between presents the following formulation:

When this index presents a value different from zero, the income distribution between the groups is not equal, if the index tends to 0, the income distribution tends to be equal.

The mean differences between the groups *j* and *h* is a generalization of Gini mean difference and it represents the mean differences of income of *n*_{j}x*n _{h}* binary combination of the individuals that belong to the group

*j*and

*h.*

The Gini mean difference allows calculating the Gini coefficient between two groups and it can be expressed through the following formulation:

The measure used to quantify the inequality contribution between the groups j and k (*gross affluence*) can be expressed through the mean differences between the incomes of the individuals Î j that present an income higher than the individuals Î h

The measure used to observe the ** transvariation** between the group j e k is expressed by the mean differences between the income of individuals Î h that have an income higher than individuals Î j.

Therefore, it is possible to define the net affluence, as a measure of greater wealth of the group j compared to the group h and to net of transvariation, the net affluence can be expressed by the difference between two components:

Moreover, we can define the relative economic affluence as the ratio between the net affluence and its maximum value:

The REA quantifies the proportion of G* _{jh }*(Gini index between

*j*and

*h*) through which the groups

*j*and

*h*contribute to inequality between groups, appropriately weighted for the numerosity and the amount of income. The difference between 1 and the value of the relative economic affluence (1-REA) allow estimating the portion of G

_{jh}that depends by the transvariation between groups.

Finally, weighting the products (G_{j}^{*}D_{jh}) e [G_{jh} *(1-D_{jh})] it is possible to decompose the general Gini Index into three components:

If *G _{w}* is equal to zero there is no inequality inside the subgroup and the incomes are equally distributed among the individuals; if

*G*presents a value equal to zero the mean incomes of all subgroups are equal and the total inequality equals:

_{nb }*G = G*; if the average of the intergroup incomes is different, then Gt = 0 and the economical distance equals 1.

_{w}+G_{t}**Data and empirical results **

In order to observe the inequality among Italian families, you used the Survey “Indagine sui Bilancidelle Famiglie Italiane carried out by the Bank of Italy in 2012. In order to apply the decomposition developed by Dagum, the 8140 households were divided into five subgroups with regard to the number of components. The fifth and final group collects the households composed by five or more components. The results obtained by using the methodology proposed by Dagum are presented in Table 6.

Tab. 6 – *Gini index families decomposition *(*Disposable net income*), 2012

Families by number of components | ||||||

Families | 1 | 2 | 3 | 4 | 5 e + | |

Total inequality (G) | 0.351889 | 0.295409 | 0.310124 | 0.328015 | 0.324721 | 0.367545 |

Contribution to the within-group inequality (Gw) | 0.071651 | 0.012983 | 0.030911 | 0.015168 | 0.010938 | 0.001650 |

Contribution to the gross between-group inequality (Gnb+Gt) | 0.280238 | – | – | – | – | – |

Contribution to the net between-group inequality (Gnb) | 0.134140 | – | – | – | – | – |

Transvariation | 0.146098 | – | – | – | – | – |

**Source:** Our elaboration on Bank of Italy data

Looking at the values in the table it is possible to note that in general a higher level of inequality characterizes the households composed by five or more components while the single-person households have the lowest value.

The decomposition of the Gini index within groups does not support this difference because the households formed by three members are those that are characterized by an higher value. In addition, the inequality within groups explained only 20% of total inequality. With regard to the total contribution of inequality between groups, this is also supported by the intensity of transvariation. The net contribution of inequality between groups has a value similar to that of transvariation, this means that there are substantial differences between the various Italian families. This type of inequality contributes 38% to the total inequality while the intensity of transvariation between the various groups is equal to 0.146098 and contributes 41% to the total inequality.

Finally, with regard to the two forms of inequality (between groups and within groups) these contribute differently to the total inequality.

**Final Remark**

There seems, in general, to have shown that the recent Italian population dynamics distinguished by an accelerated increase in the relative importance of single-person households has contributed to increasing exposure to the risk of poverty (both absolute and relative) for the progressive disappearance constraints of internal solidarity that characterized for a long time the Italian social structure.

This structural element seems to have interacted in the recent past, with the negative effects of the present growth trends in the functional distribution of income in Italy (revenue growth and decrease in the share wages) in both the short-term effects resulting from the financial crisis.

The decomposition of the Gini index developed by Dagum (1997a, 1997b) suggests that the degree of exposure to the risk of impoverishment grows as the number of family members, but also highlights that higher level of internal inequalities to each group I appear instead in the families of small size.

**Note.**

**[1]** Though the paper is the joint production of the authors, M.C. Miccoli has written paragraphs 2 and 3 and A. Biscione paragraphs 5-7. Introduction and Conclusions are entirely shared.

**[2]** ISTAT, *Noi Italia*, 2014.

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