metadata: authors: 0: author: Bussolo,Maurizio
1: author: Checchi,Daniele
2: author: Peragine,Vito
count: France,Germany,United Kingdom,Italy,Switzerland
docna: 0: docna: Long-Term Evolution of Inequality of Opportunity
docty: Policy Research Working Paper
subtopic: Educational Sciences,Gender and Development,Rural Labor Markets,Labor Markets,Tertiary Education,Poverty Reduction Strategies
teratopic: Gender,Rural Development,Education,Poverty Reduction,Social Protections and Labor
abstracts: cdata!: The main goal of this paper is to
            document and analyze the long-term evolution of inequality
            of opportunity and thus extend the recent empirical
            literature, which is mainly concerned with its measurement
            at a specific point in time. Using repeated cross-section
            surveys for five European countries (France, Germany, Great
            Britain, Italy, and Switzerland), the evolution of
            inequality of opportunity is measured for a period of about
            two decades for the whole populations, as well as for
            different birth cohorts. Relative inequality of opportunity
            represents an important portion of total income inequality,
            with values ranging from 30 to 50 percent according to the
            standard deviation of logs (and reaching a lower share in
            case of mean log deviation) and, for all the countries, it
            shows a stable or declining time trend. When the birth
            cohorts are followed across time, inequality of opportunity
            decreases with age: the effect of circumstances seems to
            weaken over the life cycle. This is a quite different age
            profile from that of inequality of outcomes (income or
            consumption), which generally increases with age. A
            decomposition of the relative inequality of opportunity
            allows highlighting some key drivers of its time evolution.
            In all the countries, there has been a clear enhancement of
            equality of educational opportunity (as captured by a
            downward trending intergenerational education persistence)
            and a reduction of the returns to education. However, for
            some countries, notably Italy, these trends have failed to
            translate into decreasing inequality of opportunity in the
            income distribution because of the increasing role of
            parental networking (an additional channel through which
            parental background affects the incomes of offspring).
geo_reg_key: 517190,517191
repnme: repnme: Long-Term Evolution of Inequality of Opportunity
display_title: Long-Term Evolution of Inequality of Opportunity
listing_relative_url: /research/2019/01/30760748/long-term-evolution-inequality-opportunity
topicv3: Tertiary Education m1326349 482,Labor Markets m1326488 855,Education m1327048 470,Gender m1327621 615,Income Inequality m1503891 2668
publishtoextweb_dt: 2019-01-15T00:00:00Z
historic_topic: Gender,Rural Development,Education,Poverty Reduction,Social Protections and Labor
no_of_pages: 28
author_keys: 0: author_key: 669228
1: author_key: 1184032
2: author_key: 1153876
model_extractions: WPS8700 Policy Research Working Paper 8700 Long-Term Evolution of Inequality of Opportunity _Maurizio Bussolo Daniele Checchi Vito Peragine_ Europe and Central Asia Region Office of the Chief Economist January 2019
Policy Research Working Paper 8700

# **Abstract**

The main goal of this paper is to document and analyze the long-term evolution of inequality of opportunity and thus extend the recent empirical literature, which is mainly concerned with its measurement at a specific point in time. Using repeated cross-section surveys for five European countries (France, Germany, Great Britain, Italy, and Switzerland), the evolution of inequality of opportunity is measured for a period of about two decades for the whole populations, as well as for different birth cohorts. Relative inequality of opportunity represents an important portion of total income inequality, with values ranging from 30 to 50 percent according to the standard deviation of logs (and reaching a lower share in case of mean log deviation) and, for all the countries, it shows a stable or declining time trend. When the birth cohorts are followed across time, inequality of opportunity decreases with age: the effect of circumstances seems to weaken over the life cycle. This is a quite different age profile from that of inequality of outcomes (income or consumption), which generally increases with age. A decomposition of the relative inequality of opportunity allows highlighting some key drivers of its time evolution. In all the countries, there has been a clear enhancement of equality of educational opportunity (as captured by a downward trending intergenerational education persistence) and a reduction of the returns to education. However, for some countries, notably Italy, these trends have failed to translate into decreasing inequality of opportunity in the income distribution because of the increasing role of parental networking (an additional channel through which parental background affects the incomes of offspring).

This paper is a product of the Office of the Chief Economist, Europe and Central Asia Region. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The authors may be contacted at mbussolo@worldbank.org, daniele.checchi@gmail.com, peragine.vito@gmail.com.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Long-Term Evolution of Inequality of Opportunity**<sup></sup>

Maurizio Bussolo (World Bank), Daniele Checchi (University of Milan) and Vito Peragine (University of Bari)

**Keywords:** Inequality of Opportunity, Decomposition methods, Education mobility, Returns to Education, Family Networking, Cohort Analysis.

**JEL codes:** D31, D63, E24, I24, J62

>  This paper was started as background paper for the World Bank regional flagship report on “Towards a new social contract: Taking on distributional tensions in Europe and Central Asia”. We thank Jorg Neugschwender (Luxemburg Income project) and Teresa Randazzo (University of Bari) for technical assistance in building the dataset, and Tullio Jappelli (University of Naples, Italy) for extensive discussions. All errors are our own responsibility.
# **1. Introduction**

The recent empirical literature on equality of opportunity (EOp) has provided a significant body of evidence on the extent of inequality of opportunity in different countries. See Brunori et al. (2015) for a first assessment of the existing evidence and Ferreira and Peragine (2016), Ramos and Van de Gaer (2016) and Roemer and Trannoy (2015) for methodological and conceptual issues related to the measurement of EOp.

A common feature of the existing literature is the static approach. Almost all empirical analyses use income distribution at a given point in time as the relevant distribution of individual advantages and are limited to computation of inequality of opportunity as a snapshot for a given country or set of countries.<sup>1</sup> This paper instead is concerned with the evolution of inequality of opportunity, i.e. with a dynamic approach. In addition, the time variation of EOp allows to study its main determinants. By so doing, we move the research on EOp a step forward and propose and test a (simple) empirical model that can explain the generation of inequality of opportunity in a given economy.

There are three different ways to analyze the evolution of inequality of opportunity, which correspond to three different concepts of inequality dynamics: (i) inequality measured across repeated snapshots of the population (repeated cross-sectional analysis); (ii) inequality measured along life courses (longitudinal analysis); (iii) inequality measured across generations (cohort analysis).

While analysis (ii) requires the availability of a rich longitudinal data set containing information of individual incomes and circumstances over the entire life cycle of the individuals, the analyses (i) and (iii) can be potentially carried out by using repeated cross-section surveys, hence are much less data intensive. This is the reason why in the present paper we focus on analyses (i) and (iii). See Aaberge et al. (2011) for an analysis of long-term inequality of opportunity along the lines of concept (ii).

# **2. The model**

# **2.1 Canonical models of inequality of opportunity**

The conceptual basis for the definition of inequality of opportunity is provided by the distinction, among the factors influencing the individual achievements, between individual efforts and predetermined circumstances – defined as those which lie outside the realm of individual responsibility. The EOp approach considers that inequality due to the former is not ethically offensive, whereas it suggests that differences in individual outcomes due to the latter represent a violation of the principle of equality of opportunity and should be removed. In what follows we will follow the simple framework introduced by Checchi and Peragine (2010) to measure inequality of opportunity.

Consider a distribution of income Y in a given population. Suppose that all determinants of Y, including the different forms of luck, can be classified into either a set of circumstances C that lie beyond individual responsibility, belonging to a finite set Ω, or as responsibility characteristics, summarized by a variable e, denoting effort,<sup>2</sup> belonging to the set Θ. The outcome of interest is generated by a function g: Ω �Θ →R such that:

> 1 Also the cross-country comparability is a relevant issue, given the potentially different definitions of outcome and circumstances involved in the analysis.

> 2 Effort could also be treated as a vector. However, we follow the literature and treat it as a scalar.

2
This can be seen as a reduced-form model in which income is exclusively determined by circumstances and effort, such that all individuals having the same circumstances and the same effort obtain the same income. Roughly speaking, the source of unfairness in this model is given by the effect that circumstance variables (which lie beyond individual responsibility) have on individual outcomes.

A parametric implementation of the model above,<sup>3</sup> which has been extensively used in the literature (see Bourguignon et al. 2007), considers estimating by OLS the following equation and computes inequality of opportunity as the value of a given inequality measure I�∙� applied to the distribution of the predicted values Y<sup>�</sup> �, where Y<sup>�</sup> � � a��b<sup>�</sup> C�. Hence the value of absolute inequality of opportunity is given by I�Y<sup>�</sup> � while the value of relative inequality of opportunity is given by I�Y<sup>�</sup> �/I�Y�.

A dynamic version of the model can be obtained by introducing the time dimension in alternative ways. We could consider a first expression, in which income is assumed to vary with time, while circumstances are assumed to be time invariant: Model (3) assumes that circumstances impact income in an identical way over the entire life. A variant of the same model considers the possibility of time-varying effects, possibly distinguishing between fixed and time-varying circumstances: Both models (3) or (4) are highly demanding in terms of data, because their longitudinal structure requires repeated observations of the same individual, possibly under alternative sets of circumstances which are independent from her will. In addition, implementing models (3) or (4) would provide a picture of the evolution of EOp over the life cycle of the specific birth cohorts that are present at the start of the analysis.

A less demanding approach in terms of data exploits the availability of repeated cross sections from the same population. If one is interested in understanding whether a society is experiencing changes in the EOp of its citizens, the relevant model considers where Y�� is the income of individual i sampled in survey t. The data generating process is allowed to change over time among random draws from the (same country) population. The implicit assumption is the over-time stability of the population, such that changes in EOp can be attributed to changes in the relevant parameters a and b. Model (5) is specular to cross-country analysis, once t is interpreted as a country indicator, but has the advantage of greater comparability of the underlying populations, originating from the same country.

> 3 In this paper we follow the ex ante approach. See Fleurbaey and Peragine (2013) for a comparison between the ex ante and ex post approaches to equality of opportunity.

3
If the number of cross-sections available for the same country is large enough, and their time span covers a sufficient number of years, one could interpret them as a pseudo-panel, in order to get as close as possible to model (3). In such a case the relevant model becomes where Y��� is the income of individual i born in year τ and sampled in survey t. In such a case, EOp can be repeatedly measured along three dimensions: in a specific year of survey t, repeated observations refer to different birth cohorts τ’s; for a specific birth cohort τ, repeated observations refer to different dates of survey t’s; for a specific age cohort �t�τ�, repeated observations refer to different life cycles. Section 2.2 initially adopts the approach described by model (5). It uses repeated cross-section surveys of the population of a specific country and estimates, for each year, the relevant parameters of the model. An extension which uses the cohort structure of model (6) is also considered. Both these _dynamic_ approaches provide interesting and distinct insights on the evolution of EOp.

# **2.2 Our empirical model**

This section presents a decomposition of measured inequality of opportunity into its constituting components in the same vein as what Solon (2004) did for intergenerational mobility of incomes. In the empirical literature (Ferreira and Peragine 2015), circumstances have included gender, age, ethnicity, region of birth, parental background (in terms of educational attainment and occupational status). For simplicity of exposition, let us consider circumstances as consisting of a single variable, parental education, indicated with E��� where θ denote generations.<sup>4</sup> We assume that parental background affects the income opportunity of the child through two main channels: _educational investment_ and _family networking_ .<sup>5</sup> The first channel can be simply described by the intergenerational persistence of educational attainment (Black and Devereux 2011) where E�� is the education of the child, E���� is the education of the parents, η is a measure of intergenerational persistence and ε captures any unobservable component (like ability as well as effort). This intergenerational correlation can be justified on various grounds: _cultural dependency_ (more educated parents value education more and press their children to follow in their footsteps), _financial resources_ (more educated parents hold better jobs and earn higher salaries which allow larger resources to be invested in education); _teaching practices_ (more educated parents are capable to support their children during their schooling career).

Education is valued in the labor market. Following the _Mincerian_ approach, we assume that individuals choose optimally the amount of schooling by balancing costs (foregone incomes) and benefits (higher wages expected in the future – see Heckman et al 2005). As a consequence, the earnings of people with different educational attainments will differ by an amount that will be proportional to the years of schooling, as in the following equation (where we abstract from the usual demographic information):

> 4 One could easily add additional circumstances (like gender, age and foreign citizenship, as we do in the empirical section) but the line of argument would remain unaffected.

> 5 Since parental background includes many other dimensions beyond education (like parental income, access to educational resources, family wealth, neighborhood), our model is observationally equivalent to many other models of intertemporal transmission of social status. See for example DeFraja (2002),

4
i log(Yie) = a + BEig + VEjg_1 + Wi9 log(Yig) = vie = [a + 66) + [y + NB JEig-1 + [wig + BEie] I(’) I(ye) = I([a + 66] + [y + NB] Eg-1 + [we + Bee) sd(yg) = Jvar(y,) = Vv + nB)*var(Eg_1) + var(we) + B2var(eg) + 2Bcov(we 4) Jig =(@ +8) +(F + AB) Es
1OpP== ~~<u>Veer)</u>~~ — ~~+B)Varga)~~ Vvar(y) <u>|r aa?</u> ~~2~~ <u>m2</u> ~~a~~ (7+7B) var (E9-1)+6i),+ B62, +2Bcov(Hg,eg) _ ~~<u>(7+78)</u>~~ a2 242 A aA (749B) + ~~arEga)~~

4 A) (7 +98) io = Of; + NEjg-1 + Ein log(Yig) = a; + BEig + VEig-1 + Wi9 i var(~) = A(1 — A) 10 ~~Jvar(9) (@+5B) |(AG-A))+(7+9B) var(Eg-1)~~ Pp ~~le ......~~ var) I (@48B)" (aaa) +(7+ 9B) var (Eo_1)+63,, +8202, +2Bcov(@g.ée)
Existing sources of publicly available data are rather limited with respect to these three criteria. We resorted to the LIS Cross-National Data Center in Luxembourg (http://www.lisdatacenter.org/), which allowed us to process data from four countries (Italy, Germany, France and Switzerland), while a fifth country was obtained from accessing the original provider (United Kingdom – <u>https://www.understandingsociety.ac.uk/).</u> The surveys we have used are therefore the following:

- **Italy:** Survey on Household Incomes and Wealth (SHIW), collected by the Bank of Italy – 11 surveys, covering the period 1993-2014 (information on parental background is not available before the starting date – originally consisting of 112,690 individuals, which reduces to 107,846 when considering non-missing information.

- **Germany:** German Socio-economic Panel (SOEP) – 11 surveys, covering the period 1984-2013 – originally including 156,338 individuals, then reduced to 133,467 in case of non-missing information.

- **France:** Household Budget Survey (HBS), conducted by the Banque de France) – 6 surveys, covering the period 1978-2005 – originally consisting of 97,306 individuals, declining to 89,119 when missing information is excluded.

- **Switzerland:** Swiss Household Panel (SHP) – 6 surveys, covering the period 1999-2014 – originally consisting of 43,102 individuals, which then decline to 31,273 valid observations.

- **United Kingdom:** starts as British Household Panel (BHPS), replaced after 2009 by the Understanding Society-Household Longitudinal Survey (UKHLS) – considers 24 waves over the period 1991-2014 – originally consisting of 434,253 individuals, which then decline to 308,625 valid observations.

Our selection rules include individuals aged 25-80 with a positive disposable income, harmonized according to the LIS procedure (variable DPI).<sup>7</sup> Incomes are converted to constant prices using the national consumer price index. Parental education is typically a categorical variable recording the highest educational attainment in the parental couple. In order to estimate a unique coefficient associated to the intergenerational transmission of education, we have converted them into years of education.<sup>8</sup> Descriptive statistics at survey/country disaggregation are reported in tables 1 to 5 in the Appendix.

Using these data, total inequality, absolute inequality of opportunity (namely inequality computed over incomes predicted according to circumstances) and relative inequality of opportunity (see equation (13)) have been estimated for each country and for each survey/year. These measures are reported in tables 6 to 10, including two indicators of inequality (standard deviation of logs and mean

> 7 To avoid negative values associated to logs, we have excluded all individuals with yearly incomes below 10. Data for the United Kingdom were rather volatile with respect to top incomes: in order to avoid confounding factors associated to differences in sampling procedures, we have trimmed them excluding incomes exceeding the 99.5 centile.

> 8 In the Italian file, recoding implies the following conversion: [1] illiterate=0 years; [2] primary=5 years; [3] lower secondary=8 years; [4] upper secondary=13; [5] tertiary=18. In the German file, recoding implies the following conversion: [1] school not attended =0 years; [2] no school degree =4; [3] Secondary General School ( _Hauptschule_ )=9 years; [4] Intermediate School ( _Realschule_ )=10 years; [5] Technical High School ( _Fachoberschule_ )=12 years; [6] Upper Secondary School ( _Abitur_ )=13 years. In the Swiss file, recoding implies the following conversion: [1]1: Primary or first stage of basic education=6 years; [2] 2: Lower secondary or Second stage of basic education=9 years; [3] 3A&B Upper secondary education (preparation for tertiary education & voc.educ)=12 years; [4] 3C: Upper secondary education (entrance into the labor market)=11 years; [5] 4A: Post-secondary education non-tertiary (preparation for an institution for higher education)=13 years; [6] 5B: First stage of tertiary education (professional education)=15 years; [7] 5A/6 tertiary education (general education)=16 years. In the UK file recoding implies the following conversion: [1] no qualification =8 years; [2] some qualification=10 years; [3] post school qualification=12 years; [4] university degree=18 years. Eventually, in the case of France there is no information on parental education, but only on parental occupation. In order to retain the country, we have created a dummy variable corresponding to either [5] intermediate profession (foreman, nurse, etc.) or [6] executive, liberal profession. We interpret this variable as the (likely) completion of secondary or tertiary education.

7
log deviation), which behave in very similar ways. In addition, to apply the decomposition of relative inequality of opportunity as shown in equation (13), equations (7) (which captures intergenerational persistence in education) and (9) (Mincerian wage equation) have been estimated. Estimations were conducted at the country and year/survey level. For illustrative purposes, the results of these estimations at the country level and for the full sample (i.e. for all the surveys pooled together) are reported in table 11.

One can notice that country samples are rather consistent, according to the impact exerted by the regressors. Education is adequately rewarded in all countries, with an estimated yearly return rate ranging between 5.4% in France and 13.2% in Great Britain. The intergenerational persistence in education is highest in Italy and Germany and lowest in Great Britain. There is also general evidence that parental education exerts an impact beyond favoring educational attainment of the next generation, as the coefficient γ� in equation (9) is estimated positive and statistically significant in all countries (its magnitude being highest for continental countries). In all countries, women are on average penalized in terms of both schooling and incomes, while age exhibits an opposite trend: the younger age cohorts are better educated than the older ones, but incomes increase with age, the net effect being ambiguous. Finally, being born in less developed regions (South of Italy, East Germany) or holding a foreign citizenship is associated to lower incomes (but not necessarily lower schooling).

To study the evolution of inequality of opportunity – the main objective of this paper – the estimation of the models reported in table 11 is performed for year survey/year and the results are graphically reported in figures 1, 3, 5, 7, and 9, and discussed in detail in section 4 below.

Given that the sample sizes are large enough, it is possible to carry out the estimations at a more disaggregated level. By disaggregating the population in birth cohorts, we can estimate inequality of opportunity for each cohort and investigate whether the cohort-specific evolution of inequality of opportunity differs from that of the full population. More in detail, we have partitioned birth years and ages in 5-year intervals, and we have retained only cells gathering at least 400 individuals. In each population subgroup, we have estimated inequality, inequality of opportunity and other structural parameters. This procedure is exemplified in table 12 and figure 11 for the Italian case. Despite having the population distributed over 66 cells (the potential number of cells depending on dates of initial and final surveys – top part of the table), only 53 satisfy a sufficient numerousness and are therefore retained for estimation of (relative) inequality of opportunity (bottom part of table 12). Once we have obtained these measures, if we ask ourselves what the time pattern of IOp is, we can plot these measures by birth cohort, as we have done in figure 11. Looking at the graph, one would be tempted to conclude that during the life course IOp exhibits an inverted U-shaped profile, at least in Italy. However, we would be confusing two different dimensions, namely age and cohort: some birth cohorts (for example the one born around the second world war) have experienced higher IOp at any age, compared to neighboring birth cohorts. Thus, we need a more rigorous method to summarize the information contained in the cells, possibly distinguishing between age and cohort effects.

We have then followed Deaton (1997), and we have regressed the obtained measures onto age, cohort and survey dummies, imposing restrictions on the estimated coefficients for dummies. Results are reported in table 13, and then plotted using a smoothing procedure in figure 12 using the LOWESS command in Stata. Simple inspection of the coefficients indicates that the time profiles of the constrained and unconstrained estimates are rather similar, though the time trend may be different. The same procedure is also applied to the estimated structural parameters, weighting the observations by the inverse of their standard errors.

8
# **4. The results**

Having clarified our statistical procedure, it is now time to review our main results, which are fully summarized by figures 1 to 10. For each country, we report two sets of estimates: a) The first set contains the analysis by year/survey and reports the estimated values of four different variables: relative inequality of opportunity, return to education (β<sup>�</sup> ), parental network (γ�) and the intergenerational persistence in education (η̂) (see figures 1, 3, 5, 7, and 9); b) The second set contains the same variables calculated at different ages and for different birth cohorts. Hence, it reports respectively the age and the cohort profiles of each of the four estimates mentioned above (see figures 2, 4, 6, 8, and 10).

Instead of reviewing the results twice, first by surveys and second by decomposing age and birth cohorts, we have preferred a thorough discussion by country.

# _4.1 Italy_

Starting with relative IOp, the analysis by survey shows a clear reduction in relative IOp at the beginning of the 2000s and then an increase at the beginning of the 2010s. In sum a rather constant time trend: the value of IOp is the same at the start and at the end of the period, also confirmed by the mean log deviation (MLD). As for the magnitude, it varies between 45% and 50% according to the standard deviation of logs and between 30% and 40% according to MLD (see figure 1).

What is behind this high and rather constant time evolution of inequality of opportunity? The decomposition approach of this paper – and in particular considering the trends of intergenerational persistence of education, returns to education, and parental networking – can help answering this question. The intergenerational persistence of education shows a clear declining trend. This trend is well known and explained by the expansion in education that took place in Italy following the compulsory education reform at the beginning of the 1960s, with some signals of trend reversal in recent years. However, this declining trend has not translated into a declining inequality of opportunity in income. Furthermore, the return to education displays a downward trend, which should also help in reducing inequality of opportunity. Apparently, this reduction is not materializing because of the counterbalancing increasing trend of parental networking. Our suggested interpretation is that the increased equality of educational opportunity (associated to the decrease in intergenerational education persistence) and the reduced “value” of education in the labor market have failed to translate into a decrease of opportunity inequality in income because of the increasing role of parental networking.

This interpretation is substantially confirmed when looking at both the age and the cohort analyses, which however shows some additional interesting facts (see figure 2). As for the age profile, the results show a clear declining pattern in relative inequality of opportunity, which is associated with a consistent declining trend in the return to education and a clear increasing trend in both intergenerational persistence and parental networking. The cohort profile follows a similar path in inequality of opportunity, return to education and parental network, while the intergenerational persistence shows a clear declining pattern, which is explained by the expansion in education level that took place in Italy during the last decades. Thus, the general declining pattern of intergenerational education observed in the analysis by survey seems to be mainly driven by the cohort effect.

# _4.2 Germany_

The analysis by survey shows a clear declining pattern in relative IOp, which takes values between 40% and 55% in the case of standard deviation of logs (between 20% and 50% in case of MLD). This is complemented by a fairly constant pattern of intergenerational education persistence and a weakly increasing trend of parental networking (which however is not statistically significant for most of the 9
sample period), while the return to education shows a declining trend in the 1980s and then a fairly stable pattern (see figure 3).

As for the age profiles, the results show a clear declining pattern in the value of relative inequality of opportunity, which is associated with an inverted U-shaped trend of the return to education and a flat pattern of both intergenerational persistence of education and parental networking. The cohort profile follows a similar path in the values of inequality of opportunity, parental network, and intergenerational persistence of education, while the return to education is rather stationary across cohorts (see figure 4).

# _4.3 France_

The analysis by survey clearly shows a declining pattern in relative IOp, which takes values between 30% and 45% in the case of standard deviation of logs (between 20% and 30% in case of MLD). This is complemented by a decreasing trend in intergenerational education persistence. On the other hand, parental networking shows a pretty flat picture and the return to education a constant pattern with a decline in the last period (the first half of the 2000s). Hence, the declining trend of IOp might be mainly driven by the reduction in intergenerational educational persistence (see figure 5).

As for the age profiles, our results show a clear declining pattern in the value of relative inequality of opportunity, which is associated with a consistent declining trend in the return to education and a clear increasing trend in both intergenerational persistence and parental networking. The cohort profile follows a similar path in the values of inequality of opportunity, although the pattern shows an increase in the very first period, and in the return to education and parental network, while the intergenerational persistence shows a clear declining pattern, which is explained by the expansion in education level that has taken place during the last decades (see figure 6).

# _4.4 United Kingdom_

The analysis by survey (see figure 7) shows a declining pattern in relative IOp, which takes values between 30% and 50% in the case of standard deviation of log incomes (between 10% and 35% in case of MLD). On the other hand, it is observed a stable pattern in parental networking and a weakly declining trend in both intergenerational education persistence and return to education. Hence the declining trend of IOp might be mainly driven by the reduction in intergenerational educational persistence.

As for the age profiles, the results show a clear declining pattern in the value of relative inequality of opportunity, which is associated with a declining pattern in the return to education. On the other hand, both parental network and intergenerational persistence of education show an increasing trend. The cohort profile follows a similar path, except for the intergenerational persistence of education, which is more stable, while the return to education shows a more stable path (see figure 8).

# _4.5 Switzerland_

The analysis by survey shows a clear declining pattern in relative IOp, which takes values between 30% and 40% in the case of standard deviation of logs (between 15% and 25% in case of MLD). This is complemented by a fairly increasing pattern of both intergenerational education persistence and parental networking, while the return to education shows a decreasing trend (see figure 9).

As for the age profiles, the results show a clear declining pattern in the value of relative inequality of opportunity, which is associated with an inverted U-shape of the return to education, a fairly stable trend of parental networking and an increasing pattern of intergenerational persistence of education. The cohort profile follows a fairly similar path, except for the return to education that, after an increase for the first cohorts, then remains stable (see figure 10).

10
_4.6 Summing up_ In general, our empirical results are consistent with theoretical expectations. More precisely, the relationships between the trends of inequality of opportunity in the income space, intergenerational persistence in education, return to education and parental networking are consistent with the conjectures based on equation (13).

In addition, it is possible to highlight the following stylized facts: _i_ ) in all the countries and the period considered, inequality of opportunity represents an important portion of total income inequality, with values ranging from 30% to 50% according to standard deviation of logs (and reaching a lower share in the case of mean log deviation); _ii_ ) in general, inequality of opportunity shows a stable or declining pattern over the period considered in all countries; _iii_ ) on the other hand, in all countries considered, there has been a clear enhancement of equality of educational opportunity (as captured by the intergenerational education persistence); _iv_ ) in some countries the egalitarian process taking place in the education system has failed to translate into decreasing opportunity inequality in the space of income because of the increasing role of parental networking and the reduced “value” of education in the labor market. This mechanism seems to be at work notably in Italy; _v_ ) in some other countries (France, Germany and Great Britain), where both returns to education and the family networking followed a more constant pattern, inequality of opportunity seems to decrease both in the education and in the income space.

The decomposing of inequality of opportunity trends according to the age and cohort effects allow to identify the following additional facts: _vi_ ) in all the countries considered, inequality of opportunity decreases with age: the effect of the circumstances at birth seems to weaken over the life cycle. This pattern is quite different from the age profile of the inequality of outcomes (income or consumption), which generally increases with age; _vii_ ) the decreasing pattern of relative inequality of opportunity in France and Italy is associated with a consistent declining trend in the return to education and a clear increasing trend in both intergenerational persistence and parental networking. Great Britain shows an increase in intergenerational education persistence, while Germany is characterized by a stable trend of intergenerational education persistence; _viii_ ) the cohort effect, on the other hand, shows a more mixed picture: while for Great Britain and Germany the data show a declining path in the values of inequality of opportunity, with the younger generation experiencing lower IOp levels, both Italy and France are characterized by an inverted U- shape pattern; _ix_ ) these trends are associated, in Germany and Great Britain, with a stable or weakly increasing trend of the intergenerational educational persistence, while in Italy and France with a clear declining trend in the intergenerational persistence of education, which is explained by the expansion in education level that has taken place during the last decades.

# **5. Concluding remarks**

This paper contributes to the analysis of inequality of opportunity in three respects. First, by using extended samples, it is capable to detect time trends, showing that the role of circumstances (parental background, gender, age, and place of birth) in shaping income distribution has declined over the last two decades in all the countries considered in the present analysis. Depending on the inequality index we choose, inequality of opportunity accounts for between one-third (MLD) and half (standard deviation of logs) of total inequality in personal disposable incomes, at least for the four largest economies in the European Union.

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Second, we exploit the large sample sizes to obtain inequality measures by age group and birth cohorts, thus being able to decompose observed trends in age profiles and birth cohort changes. For the five countries under analysis, the observed inequality of opportunity exhibits an inverted U- shaped pattern over the life cycle. Moreover, the most recent age cohorts have experienced a lower IOp, thus appearing as the main beneficiaries of the overall decline in inequality.

Third, the paper proposes a theoretical framework identifying the variables that affect (positively or negatively) inequality of opportunity. The framework is then estimated, and the data confirm the predicted signs. The analysis has focused on the role of three variables: the intergenerational persistence in educational attainment, the return of education, and the networking activity of parents. While the first two variables exhibit a declining trend, which other things constant should produce a decline in IOp, the third one appears to be rising in many countries, thus counteracting the effects of the first two. Consequently, the fair optimism that descriptive statistics suggest with respect to income inequality should be mitigated by paying attention to educational persistence and labor market segmentation.

# **References**

Aaberge, R., M. Mogstad, & Peragine, V. (2011). Measuring Long-term Inequality of Opportunity, _Journal of Public Economics_ , 95(3-4), 193-204.

Black, S., and P. Devereux. (2011). “Recent Developments in Intergenerational Mobility.” _Handbook of Labor Economics_ , 4(B), Ch-16, pages 1487- 1541 Bourguignon F., Ferreira F.H.G., Menéndez, M. (2007). Inequality Of Opportunity In Brazil, _Review of Income and Wealth_ , 53(4), 585-618.

Checchi, D., Peragine, V. (2010). Inequality of opportunity in Italy, _Journal of Economic Inequality_ , 8(4), 429-450.

Deaton, A. (1997). “ _The analysis of household survey. A microeconometric approach to development policy_ ” Johns Hopkins University Press (Baltimore and London) DeFraja, G. (2002). "The Design of Optimal Education Policies," _Review of Economic Studies_ , vol. 69(2), pages 437-466.

Ferreira, F.H.G., Peragine, V. (2016). Individual responsibility and equality of opportunity, in M. Adler and M. Fleurbaey (eds.), _Handbook of Well Being and Public Policy_ , Oxford: Oxford University Press.

Fleurbaey M., Peragine, V. (2011). Ex ante versus ex post equality of opportunity, _Economica,_ vol. 80(317), pages 118-130.

Heckman, James J., Lochner, Lance J. and Todd, Petra E., 2006. “Earnings Functions, Rates of Return and Treatment Effects: The Mincer Equation and Beyond” in Erik Hanushek and F. Welch (ed.), _Handbook of the Economics of Education_ . Elsevier, vol.1 Kramarz, Francis and Oskar Nordström Skans, 2014. "When Strong Ties are Strong: Networks and Youth Labour Market Entry," _Review of Economic Studies_ , Oxford University Press, vol. 81(3), pages 1164-1200.

Ramos, X., Van de Gaer, D. (2016). Approaches to inequality of opportunity: Principles, measures and evidence, _Journal of Economic Surveys_ , 30(5), 855-883.

Roemer, J.E., A. Trannoy (2015). Equality of opportunity, in A.B. Atkinson and F. Bourguignon (eds). _Handbook of Income Distribution_ , vol.2B, Amsterdam: North Holland.

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Solon, G. (2004). “A Model of Intergenerational Mobility Variation over Time and Place.” Chapter 2 in Miles Corak (ed.), _Generational Income Mobility in North America and Europe_ Cambridge, UK: Cambridge University Press 13
Figure 1 – Italy, by survey <!-- Start of picture text --> Italy<br>Relative inequality of opportunity Return to education<br>1995 2000 2005 2010 2015<br>year of survey<br>st.deviation logs mean log dev. 1995 2000 year of survey2005 2010 2015<br>Parental networking Intergenerational persistence in education<br>1995 2000 2005 2010 2015 1995 2000 2005 2010 2015<br>year of survey year of survey<br>Regressors include gender, age, age2, born in South Italy and foreign citizenship<br>.5 .09<br>.4<br>.49<br>.38 .08<br>.48<br>.36<br>st.deviation logs .47 .34 mean log dev. .07<br>.46 .32<br>.06<br>.45 .3<br>.05<br>.04<br>.5<br>.03<br>.45<br>.02<br>.01<br>.4<br><!-- End of picture text --> Figure 2 – Italy, age-cohort decomposition <!-- Start of picture text --> Italy<br>Inequality of opportunity - Standard deviation of logs personal incomes Return to education<br>30 40 50 60 70 80 30 40 50 60 70 80<br>Age Age<br>. .<br>1920 1940 1960 1980 1920 1940 1960 1980<br>Born in... Born in...<br>. .<br>Parental networking Intergenerational persistence in education<br>30 40 50 60 70 80 30 40 50 60 70 80<br>Age Age<br>. .<br>1920 1940 1960 1980 1920 1940 1960 1980<br>Born in... Born in...<br>. .<br>Regressors include gender, age, age2, born in South Italy and foreign citizenship - Age and cohort effects obtained from Deaton's decomposition<br>.1 .08<br>.06<br>.08<br>beta1 beta1 .04<br>.06 .02<br>.04 0<br>.15 .05<br>.04<br>beta1 .1.05 beta1 .03.02<br>.01<br>0 0<br>0 -.02<br>-.04<br>-.01 -.06<br>beta1 beta1<br>-.08<br>-.02<br>-.1<br>-.03 -.12<br>0 .3<br>-.02 .2<br>beta1 beta1 .1<br>-.04<br>0<br>-.06<br>-.1<br><!-- End of picture text --> 14
Figure 3 – Germany, by survey <!-- Start of picture text --> Germany<br>Relative inequality of opportunity Return to education<br>1980 1990 2000 2010 2020<br>year of survey<br>st.deviation logs mean log dev. 1980 1990 year of survey2000 2010 2020<br>Parental networking Intergenerational persistence in education<br>1980 1990 2000 2010 2020 1980 1990 2000 2010 2020<br>year of survey year of survey<br>Regressors include gender, age, age2, born in East Germany and foreign citizenship<br>.55 .5 .09<br>st.deviation logs .45.5 .3.4 mean log dev. .08<br>.07<br>.4 .2<br>.06<br>.03<br>.75<br>.02<br>.01 .7<br>0<br>.65<br>-.01<br>-.02 .6<br><!-- End of picture text --> Figure 4 – Germany, age-cohort decomposition <!-- Start of picture text --> Germany<br>Inequality of opportunity - Standard deviation of logs personal incomes Return to education<br>30 40 50 60 70 80 30 40 50 60 70 80<br>Age Age<br>. .<br>1920 1940 1960 1980 2000 1920 1940 1960 1980 2000<br>Born in... Born in...<br>. .<br>Parental networking Intergenerational persistence in education<br>30 40 50 60 70 80 30 40 50 60 70 80<br>Age Age<br>. .<br>1920 1940 1960 1980 2000 1920 1940 1960 1980 2000<br>Born in... Born in...<br>. .<br>Regressors include gender, age, age2, born in East Germany and foreign citizenship - Age and cohort effects obtained from Deaton's decomposition<br>.4 .04<br>.3 .03<br>beta1 .2 beta1 .02<br>.1 .01<br>0 0<br>.5 .03<br>.4 .02<br>.01<br>beta1 .3 beta1 0<br>.2 -.01<br>.1 -.02<br>.02 0<br>0 -.05<br>beta1 -.02 beta1 -.1<br>-.04 -.15<br>-.06 -.2<br>.05 .2<br>0 0<br>beta1 -.05 beta1 -.2<br>-.1 -.4<br><!-- End of picture text --> 15
Figure 5 – France, by survey <!-- Start of picture text --> France<br>Relative inequality of opportunity Return to education<br>1980 1985 1990 1995 2000 2005<br>year of survey<br>st.deviation logs mean log dev. 1980 1985 1990year of survey 1995 2000 2005<br>Parental networking Intergenerational persistence in education<br>1980 1985 1990 1995 2000 2005 1980 1985 1990 1995 2000 2005<br>year of survey year of survey<br>Regressors include gender, age, age2 and foreign citizenship<br>Parental education is absent and is replaced by dummy indicating middle-high parental occupations<br>.46 .3 .065<br>.44 .28<br>.06<br>.42 .26<br>st.deviation logs .4 .24 mean log dev. .055<br>.38 .22<br>.05<br>.36 .2<br>.045<br>5<br>.2<br>.15 4.5<br>.1 4<br>.05<br>3.5<br><!-- End of picture text --> Figure 6 – France, age-cohort decomposition <!-- Start of picture text --> France<br>Inequality of opportunity - Standard deviation of logs personal incomes Return to education<br>30 40 50 60 70 80 30 40 50 60 70 80<br>Age Age<br>. .<br>1920 1940 1960 1980 2000 1920 1940 1960 1980 2000<br>Born in... Born in...<br>. .<br>Parental networking Intergenerational persistence in education<br>30 40 50 60 70 80 30 40 50 60 70 80<br>Age Age<br>. .<br>1920 1940 1960 1980 2000 1920 1940 1960 1980 2000<br>Born in... Born in...<br>. .<br>Regressors include gender, age, age2 and foreign citizenship - Age and cohort effects obtained from Deaton's decomposition<br>Parental education is absent and is replaced by dummy indicating middle-high parental occupations<br>.1 .04<br>.03<br>.05<br>beta1 beta1 .02<br>0 .01<br>-.05 0<br>.2 .06<br>.04<br>.15<br>beta1 beta1 .02<br>.1<br>0<br>.05 -.02<br>.1 -.2<br>.05 -.4<br>0<br>beta1 -.05 beta1 -.6<br>-.1 -.8<br>-.15 -1<br>.2 2<br>.1 1.5<br>beta1 0 beta1 1<br>-.1 .5<br>-.2 0<br><!-- End of picture text --> 16
Figure 7 – Great Britain, by survey <!-- Start of picture text --> GreatBritain<br>Relative inequality of opportunity Return to education<br>1990 1995 2000 2005 2010 2015<br>survey<br>st.deviation logs mean log dev. 1990 1995 2000 survey 2005 2010 2015<br>Parental networking Intergenerational persistence in education<br>1990 1995 2000 2005 2010 2015 1990 1995 2000 2005 2010 2015<br>survey survey<br>.5 .35 .25<br>.3<br>.45<br>.25 .2<br>.4<br>.2<br>st.deviation logs mean log dev.<br>.35 .15<br>.15<br>.3 .1<br>.1<br>.025 .15<br>.02 .14<br>.015<br>.13<br>.01<br>.12<br>.005<br>0 .11<br><!-- End of picture text --> Regressors include gender, age, age2, born in England and foreign citizenship Data trimmed at 99.5th centile - vertical dashed line indicates change of survey Figure 8 – Great Britain, age-cohort decomposition <!-- Start of picture text --> GreatBritain<br>Inequality of opportunity - Standard deviation of logs personal incomes Return to education<br>30 40 50 60 70 80 30 40 50 60 70 80<br>Age Age<br>. .<br>1920 1940 1960 1980 2000 1920 1940 1960 1980 2000<br>Born in... Born in...<br>. .<br>Parental networking Intergenerational persistence in education<br>30 40 50 Age 60 70 80 30 40 50 Age 60 70 80<br>. .<br>1920 1940 Born in...1960 1980 2000 1920 1940 Born in...1960 1980 2000<br>. .<br>Regressors include gender, age, age2, born in England and foreign citizenship - Age and cohort effects obtained from Deaton's decomposition<br>.4 .15<br>.3<br>.1<br>beta1 .2 beta1<br>.1 .05<br>0 0<br>.8 .25<br>.6 .2<br>beta1 .4 beta1 .15<br>.2 .1<br>0 .05<br>.005 .03<br>0 .02<br>beta1 -.005 beta1<br>.01<br>-.01<br>-.015 0<br>0 .15<br>-.01 .1<br>-.02<br>beta1 beta1 .05<br>-.03<br>-.04 0<br>-.05 -.05<br><!-- End of picture text --> 17
Figure 9 – Switzerland, by survey <!-- Start of picture text --> Switzerland<br>Relative inequality of opportunity Return to education<br>2000 2005 2010 2015<br>year of survey<br>st.deviation logs mean log dev. 2000 2005 year of survey 2010 2015<br>Parental networking Intergenerational persistence in education<br>2000 2005 2010 2015 2000 2005 2010 2015<br>year of survey year of survey<br>Regressors include gender, age, age2 and foreign citizenship<br>.38 .24 .12<br>.22<br>.36 .11<br>.2<br>.34 .1<br>st.deviation logs .18 mean log dev.<br>.32<br>.16 .09<br>.3 .14<br>.08<br>.05 .38<br>.04 .36<br>.34<br>.03<br>.32<br>.02<br>.3<br>.01<br>.28<br><!-- End of picture text --> Figure 10 – Switzerland, age-cohort decomposition <!-- Start of picture text --> Switzerland<br>Inequality of opportunity - Standard deviation of logs personal incomes Return to education<br>30 40 50 60 70 80 30 40 50 60 70 80<br>Age Age<br>. .<br>1920 1930 1940 1950 1960 1920 1930 1940 1950 1960<br>Born in... Born in...<br>. .<br>Parental networking Intergenerational persistence in education<br>30 40 50 60 70 80 30 40 50 60 70 80<br>Age Age<br>. .<br>1920 1930 1940 1950 1960 1920 1930 1940 1950 1960<br>Born in... Born in...<br>. .<br>Regressors include gender, age, age2 and foreign citizenship - Age and cohort effects obtained from Deaton's decomposition<br>.3 .05<br>.2 .04<br>.03<br>beta1 .1 beta1 .02<br>0 .01<br>-.1 0<br>.25 .04<br>.2 .02<br>beta1 .15.1 beta1 0-.02<br>.05 -.04<br>0 -.06<br>.02 0<br>0 -.1<br>beta1 beta1<br>-.02 -.2<br>-.04 -.3<br>.02 .05<br>0<br>0<br>beta1 beta1 -.05<br>-.02 -.1<br>-.04 -.15<br><!-- End of picture text --> 18