Measuring Educational Poverty in Italy under a Small Area Estimation approach

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Preface

In the following pages of this work the reader will nd an exposition that seeks to expand our horizons in thinking about government and society, this will be carried out through the discussion of the Italian scenario under a Small Area Estimation approach. The role of government in this fast-pacing society has become the main subject in nowadays political debates and determined the rise of new political movements and the fall of longevous political realities. From the direct estimation of Educational Poverty to the debate about the introduction of new tech-niques to aggregate the multidimensional phenomenon into a more comprehensive synthesis we will analyze both theoretically and empirically some of these questions.

In a rst part the theme of educational poverty will be addressed through small area estimates. The objective of this topic is represented by the desire to enhance the knowledge of estimation techniques for small areas to meet a deeper understanding of socioeconomic phenomena concerning development and poverty. This topic was developed through the internship at the national statistics institute (ISTAT) with the precious collaboration of Professor Monica Pratesi and the support of Luciana Quattrociocchi and Gaia Bertarelli.

In a second part a debate around various dimensional reduction techniques is carried out, with the spirit of discussing the techniques currently present in the literature, highlighting strengths and weaknesses and illustrating some innovative paths to understand the phenomenon.

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Introduction

Domain1 _{estimation of poverty has been studied by several authors}2_{as being one of the ve headline targets of the}

Europe 2020 strategy of the European Union. The key objectives of the Europe 2020 strategy are represented by the following headline targets at the EU level:3

• Increasing the employment rate of the population aged 20-64 at least 75% • Increasing combined public and private investment in R&D to 3% of GDP • Climate change and energy targets

• Reducing school drop-out rates to less than 10 % and increasing the share of the population aged 30-34 having completed tertiary education to at least 40 %.

• Lifting at least 20 million people out of the risk of poverty and social exclusion.

Most of these indicators are monitored through statistics. The monitoring of poverty requires a set of statistics systematically generated for a particular study domain on a regular basis. These statistics, usually developed on an annual basis to meet the particular needs of the policy maker, are characterized by a small domain for the policy maker to be able to properly tailor their policies to the precise area and to target the right group of people. The role of the scholar thus becomes that of producing local, meaningful, ash data and indicators on poverty and vulnerabilities, which are understandable and useful to policy making. These estimates often rely on available data and some underlying model that helps to provide estimates in all areas, even in those that were not sampled. In this framework, Small Area Estimation methods tackle the problem of providing feasible estimates of the variable of interest in areas where data available is not large enough to provide direct estimates of adequate precision.

The indicators used in this framework are typically nonlinear and are based on non-smooth functions such as medians and quantiles, which makes the estimation a non-trivial task, but on the other side possibly accounts more

1_{In the drafting of this work, especially as regards the writing of its introductory and historical revision parts, numerous materials}

have been consulted both in Italian and in English. Where not acknowledged, the work was written by hand by the candidate, however, also in consideration of the great quantity of materials consulted and of the presence of dierent languages among the materials used, a complete certainty that both the structure and the bibliographic elements to be cited are completely innovative is complicated to reconstruct. The candidate therefore felt it necessary to compare what was written with the free online Plagiarism Checker, a satisfactory state-of-the-art tool for assessing Plagiarism, passing all the tests for plagiarism as no signicant plagiarism was detected as of 26/04/2016.

2_{The reader can see Elbers et al (2003), Molina and Rao (2010) and more recently Pratesi (2016).}

3_{The reader can see the eurostat website for more information.}

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CHAPTER 1. INTRODUCTION 2 accurately for heterogeneity in the data than a simple linear framework. This particularly holds when performing estimation of indicators for domains and small areas.

Although there is a mountain of literature on the subject of the denition of wellbeing, no single denition has emerged that has satised the whole academic community. This complexity revolves around the denition of well-being has soon been reduced to the simple monetary evaluation of this concept, reducing itself to seeking a description only through numerical measures such as income, the amount of consumer spending or personal wealth. The GDP, so far used massively to describe the dynamics of collective well-being must be overcome, not denying it's importance, in favor of a multidimensional approach. Recognizing its potential fallacy means understanding the inability of this measure to account for the possibility of heterogeneity in either the local communities that make up a state and the people. Going beyond GDP - expression much in vogue today - means that relying solely on this variable leads to obtain a partial and potentially misleading picture of both the current situation of Italian standards of living and their evolution over time.

In what follows, both Design-based and Model-based estimators are investigated for the estimation of the selected poverty indicators for domains and small areas. Whenever dealing with Design-based estimation for nite population parameters we refer to a bunch of estimation techniques in which randomness is introduced through the sampling design. In this framework it is crucial to design consistent and possibly unbiased estimators4_{. Generalized regression}

(GREG) type estimators and calibration type estimators are examples of nearly design unbiased estimators. Model-assisted GREG estimators are constructed such that they are robust against model misspecication. Design-based estimators for domains and small areas are usually constructed so that the complexities of the sampling design, such as stratication and unequal inclusion probabilities, are accounted for. In GREG and model calibration we often employ estimators that use nonlinear assisting models involving random eects in addition to the xed eects. For example, it is customary that design weights are incorporated in a design-based estimation procedure. This does not necessarily hold for model-based or model-dependent methods. In this respect, a conceptual separation of model-based and model-dependent methods can be helpful. In strict model-dependent methods, the estimation is considered to rely exclusively on the statistical model adopted. For example, design weights do not play any role in a model-dependent estimation procedure. For design consistency, variables that capture (at least some) of the sampling complexities, such as stratication variables and PPS size variable, can be included in the underlying model. In model-based methods, design weights can be incorporated in the estimation procedure to account for unequal probability sampling, leading to design consistent pseudo synthetic, pseudo EBLUP (empirical best linear unbiased predictor) and pseudo EBP (empirical best predictor) type approaches. The methods coincide under equal probability sampling. Model-based estimators can have desirable properties under the model but their design bias does not necessarily tend to zero with increasing domain sample size. The monograph by J.N.K. Rao (2003) provides a comprehensive treatment of model-based small area estimation (SAE) which the reader can nd very useful.

4_{As pointed out by Estevao and Särndal (2004) an estimator is nearly design unbiased if its bias ratio approaches zero with order}

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CHAPTER 1. INTRODUCTION 3

1.1 History of Education in Italy

According5 _{to the estimates developed by Barro and Lee in 2013 Italian adults have completed 9.6 years of the}

educational process on average. After completing primary school and the lower part of secondary school, the average Italian enters the world of work at about the age of 16. This model of schooling leads Italy to be in fact half a century behind the world leaders in terms of education, especially the United States, which had reached the average value of 9.6 already in the 1960s and broke the 13.0 threshold in 2010. In particular, if compared with the educational level of other 24 advanced economies, the level of education possessed by Italy surpasses only that of two other realities, that of Portugal and that of Turkey. A technique commonly used to assess the educational level of a state is to look at the prole over the years of the average number of years of schooling. Based on the 2009 Morrison Murtin estimates, we can look at these values in a comparative perspective to better analyze their behavior, especially in relation to that of other states. From these estimates it emerges that Italy is chronically lagged compared to the more developed economies. Italy is about half a century behind the United States and several decades behind the most relevant economic players in the European Union.

On the eve of unication, the Italian Peninsula was home to seven separate states. With literacy rates above 40 percent - and above 50 percent in some regions - the former kingdoms of Sardinia and Lombardy-Venetia were not far behind France or the Habsburg Empire. In the provinces of the former Kingdom of the Two Sicilies, by contrast, hardly more than one person in ten could read, with the literacy rate failing to reach 20 percent even in the most educated of the southern regions, Campania. The north and south of Italy were two dierent worlds. Literacy rates in 1861 were the product of schooling in the pre-unication states. In relatively literate Lombardy and Veneto municipalities had been required to set up and maintain elementary schools, and parents obliged to send children aged 6-12 to school. In the Kingdom of Sardinia, schooling had not been compulsory, but education had been rmly in the hands of the state, which by 1848 had imposed a centralized system with detailed regulations covering everything from nursery schools to technical schools and universities, from the training of teachers to their salaries, from curricula to examinations. At the other extreme, in both the Papal State and the Kingdom of the Two Sicilies there had been no obligations of any kind regarding school provision or attendance, nor a recognizable, planned school system. Time would reveal how resistant these regions remained to implementing Italian laws on compulsory schooling.

Having made Italy, we must now make the Italians - D'.Azeglio is said to have said - A rst step would be to teach them Italian. In a population of over twenty ve million, De Mauro's (1963) estimate is that only 600,000 might have been able to read and write Italian. The remainder were either illiterate or had basic literacy in a language too far removed from Italian for easy comprehension (true of dialects everywhere outside Tuscany and Rome) . The new Kingdom's government moved quickly on the legislative front. Piedmont's Casati Law of 1859, which continued the system of detailed and comprehensive regulation of education, was extended to each of the formerly independent states of Italy as there were annexed. The law made basic primary education both free and compulsory. Article 317 stated: "Elementary education is provided free of charge in all municipalities. The latter must provide it in proportion to their capabilities and according to the needs of their inhabitants." Meanwhile, Article 326 declared that parents of both boys and girls who failed to ensure their children received two years of elementary education were punishable by law.

But the diculty of actually enforcing the Casati Law in the absence of either stick (eective sanctions) or carrot

5_{In the exposition of this historical bird eye's view on the themes of education we acknowledge Vecchi 2017 as being the inspiration}

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CHAPTER 1. INTRODUCTION 4 (nancial support) soon became clear. In 1911, fty years and two generations on from unication, youth literacy barely reached 50 percent in the south and islands. The 45-point gap relative to the northwest had not diminished at all since 1861. Southern regions closed the gap signicantly only from the 1930s, progressing at a plodding pace while the north ran up against the ceiling of 100 percent literacy. Regional convergence was more by mathematical necessity than by virtue.

1.2 Education and Human Capital

The original commitments of Schultz (1963) and Becker (1993) set up education as a key determinant of individual prot, regardless of whether this is ascribed to its job in building human capital, as they proposed, or to its capacity as a agging or screening device, as Spence (1978) and others have kept up. On a macroeconomic dimension, various later hypothetical commitments since the powerful works of Romer (1986) and Lucas (1988) have underlined the job of human capital as a propelling of development. These both incorporate endogenous development models, following Romer and Lucas, which ascribe long-run development to expanding total aggregate returns to education, just as exogenous development models that broaden the standard Solow (1957) model to incorporate human capital (e.g., Mankiw et al., 1992). The two methodologies decipher the regularly seen positive relationship between national pay and instruction as proof of its protable commitment. This view is bolstered by recorded investigations, which show how the democratizing impact of rising salaries prompted the general extension of government funded training, as a component of the modem welfare state (Lindert, 1994; Justman and Gradstein, 1999). Obviously, the two perspectives are not fundamentally unrelated, and there is space to contend that expanded dimensions of education are both the circumstances and logical results of rising salaries.

The dispersion of salary additionally enters in this nexus of macroeconomic impacts among development and instruction. Early commitments following Kuznets' (1966) fundamental work concentrated to a great extent on the eect of salary levels on the dispersion of income, arguing that it is an experimental normality that imbalance pursues a backwards U-formed example the Kuznets bend over the span of development. At rst, disparity increments as salary levels rise, topping at some middle of the road dimension of pay and afterward falling with further increments in pay levels.

This would appear to infer a trade-o among disparity and development at the beginning times of advancement, however the dierentiation between the quick industrialization of populist economies in East Asia and the a lot imsier exhibition of Latin American economies with an a lot higher level of imbalance unequivocally shows that this exchange o can be maintained a strategic distance from (Chenery et al., 1974). This has prompted observational and hypothetical work went for recognizing the channels through which development inuences and is inuenced by the distribution of salary. Addressing the role of education in this unique situation, Galer and Zeira (1993) present a model in which the eciency of training relies upon accomplishing some minimum amount, which suggests that at low dimensions of pay some proportion of disparity is important to accomplish development yet at more elevated amounts more noteworthy balance is advantageous, as it enables a bigger proprietor of families to achieve the limit dimension of education. Political economy approaches the eect of pay dispersion on the designation of open assets for education, from one viewpoint, and on the tax collection of private pay, then again (Meltzer and Richard, 1981). These dierent methodologies contend that the dimension of normal pay as well as its dispersion inuence the total dimension and appropriation of current education venture, which shapes, in tum, the dimension and dissemination of pay later on.

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CHAPTER 1. INTRODUCTION 5 The social separation between an individual and dierent individuals from her neighborhood inuences the protability of her instrumental human capital. While some level of social heterogeneity obviously oers monetary advantages, empirical proof from a range of sources shows the mischief that can emerge out of profound social partitions. Mauro's (1995) cross-country investigation nds that social polarization unfavorably inuences the nature of administrations given by the focal government and produces political shakiness. Easterly and Levine's (1997) examination of a cross-area of nations likewise nds that it advances debasement and lease chasing and causes wasteful approaches bringing about poor foundation, an absence of monetary establishments and low instructive accomplishment driving them to presume that ethnic heterogeneity is the primary wellspring of backwardness in Africa. Di Pasquale and Glaeser (1998), utilizing both U.S. furthermore, universal information, demonstrate that ethnic decent variety is a huge determinant of urban contest.

Through an early work on the connection among instruction and pay imbalance in the U.S. local setting, Becker and Chiswick (1966) demonstrate that disparity is emphatically associated with imbalance in schooling and contrarily related with the normal dimension of schooling. Ensuing examinations, for example, the cross-country investigations of Adelman and Morris (1973) and Chenery and Syrquin (1975), armed these discoveries, all around, despite the fact that Ram's (1987) marginally extraordinary particular neglected to identify a noteworthy connection between mean schooling and schooling imbalance from one perspective and salary disparity on the other hand. All the more as of late, Teulings and van Rens (2003) contend that in light of the fact that skilled and unskilled are imperfect substitutes underway, an expansion in normal training levels packs the appropriation of peripheral protability, which should prompt an increasingly equivalent conveyance of work salary. The authors test this speculation on the impact of instruction on income distribution in OECD nations and discover support for it in their board information. More work done here analyzes the switch impact of disparity on instruction. However, the exact channel that oers ascend with this impact isn't totally clear, and Perotti (1996) oers two modify local clarications: one keeps up that the benecial outcome of imbalance by and large fruitfulness lessens normal interest in human capital on account of the amount quality exchange o; alternate sees disparity working through credit limitations, which infer that in less equivalent social orders more families are precluded the open door from claiming understanding their ideal dimension of interest in human capital. While Perotti's proof can't recognize these two clarications, the negative impact of in equity on human capital speculation is unmistakably distinguished and is powerful. Ensuing work by Flug et al. (1998) and DeGregorio and Lee (2002), among others, gives further supporting proof of this negative impact, accentuating the importance of credit requirements. These discoveries accord well with the proof in Psacharopoulos (1994) that returns to schooling are most noteworthy at the essential dimension and lessening with the dimension of schooling: richness is higher and credit requirements are all the more intensely felt among low-pay, ineectively instructed families. Sylwester (2000) centers all the more explicitly around interest in government funded instruction, nding that more elevated amounts of beginning salary disparity are related with higher open consumption on education. This forties past discoveries of Easterly and Rebelo (1993), who correspondingly report that salary imbalance raises open consumption on education. He likewise nds that democracies spend more than non democracies on education, as a level of GDP, recommending that it is the political economy of education account that drives support for state funded education in unequal social orders.

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CHAPTER 1. INTRODUCTION 6

1.3 Education, child, poverty

In Italy more than one million minors live in conditions of absolute poverty. They are born and raised in contexts of economic and material deprivation, on which often educational poverty represents an occult handicap. This phenomenon is often largely underestimated as it is not fully understood in its implications on girls and boys personal growth, combined with this, its diculty in being discovered makes precise interventions dicult to implement. This phenomenon is dened as the inability accomplish some classical personal developments goals as to learn, make and discovery the own talent and let personal aspirations ourish freely. Educational poverty is particularly insidious because it aects children in the rst years of life, a vulnerable period in their existence trajectory, causing an irreversible delay and triggering a cascade of long-term domino eects from generation to generation. These disadvantage are largely inherited and inuenced by the socioeconomic situation of the family and other material penalizing factors such as the geographical place where the boys and girls grew up. This particular mechanism just described makes it almost impossible for a young individual to determine her own existence and to separate herself from a destiny that seems already written in a trajectory similar to her parents' trajectory thus leading to become the excluded of tomorrow. A country that does not guarantee rights, duties and equal opportunities for all those fumbling in the suburbs, suocating in the bud the aspirations of children and the ourishing of their talents, it is not just an unjust country, but it is a country without a future.

In a complex, fast pacing and rapidly changing economic environment, the strategic use of human capital is crucial as it represents one of the fundamental resources to foster the process of growth and development of the economies. Through the transmission of the stock of knowledge inherited from previous generations, education is one of the main channels through which knowledge is both created and shared. Therefore the public intervention is not only justied on the basis of the economic eciency, but also from the pursuit of equity. It seems necessary to guarantee, among other things, that the lack of nancial means does not prevent access to the world of education and its full fruition. This hinge principle is enshrined in the constitution of the Italian Republic in Article 34, Title 2, Part One where the text quote:

La scuola è aperta a tutti. [...] I capaci e meritevoli, anche se privi di mezzi, hanno diritto di raggiungere i gradi più alti degli studi. La Repubblica rende eettivo questo diritto con borse di studio, assegni alle famiglie ed altre provvidenze, che devono essere attribuite per concorso.

The education is open to everyone. [...] Those who talented and deserving, even if without means, have the right to reach the highest levels of studies. The Republic makes this right eective through scholarships, family allowances and other provisions, which must be awarded by means of a public competition.

In the famous lm Trading Places of 1983, the director John Landis told the story of an upper-class commodities broker and a homeless street hustler. Are people predisposed from birth to delinquency and success? Or is it the environment in which they live to determine the positive or negative behavior of an individual? On this question Randolph and Mortimer Duke, two nancial brothers, were betting. Cavy of this experiments were the two antithetical protagonists. The theme dealt with this story-line is how the life of each boy is conditioned by the environment and the family in which he comes into world. This Christmas eve classic, being broadcast by Italian television every year in the past 20 years, is considered to be the modern version of the Prince and the Pauper novel by Mark Twain. It is the family, the curiosity, the dream, the tenacity in pursuing the objective, the precious help of a teacher to represent those factors that most likely determine the trajectory and the discovery of an individual.

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CHAPTER 1. INTRODUCTION 7 Boys and girls are not isolated plant that grows autonomously on the slopes of a volcano or in the driest of deserts; on the contrary, they are the fruits of a combination of characteristics, a phenomenon of synergies within a context. Children are formed by imitating, sharing, emulating, competing with others. The place where everything starts is fundamental, it will oer a starting advantage that is dicult to recover later, it will create networks of relationships that last a lifetime, will create that personal endowment that will then make the adult capable of facing and solving the world.

The training and development of talents is today a social, economic and political issue, not just for the family and for educational agencies. It is much more: it is the recognition by the company and institutions that our society and economy have become a society and economy of knowledge and that the creation of value has the primary source in the talents of people. The well-being of an evolved society is based on the ability to nurture and exploit at the highest possible level the talents of people, in all contexts. In this, our country can no longer wait to address a concrete and eective commitment to the development of a cultural context full of opportunities in every corner of the peninsula, to nally give a dusting to our constitutional paper and make sure that no more boys and girls are born as fragile plants in an arid desert.

1.4 Educational Poverty

The subject of educational opportunity so far developed in this work has been interpreted in a nuance of a bygone era. The idea of educational opportunity as training of human capital aimed at work and productivity needs, in a globalized world governed by the economy of innovation and knowledge from brain power, can nowadays be overcome. This reductive but predominant idea of education considered as an individual and collective eco-nomic instrument comparable to the traditional material capital has also developed through two analytical projects promoted by the OECD in the recent past.

OCSE-PISA The OCSE-PISA is an international investigation promoted by the Organization for Cooperation and Economic Development which involves 80 countries. This surveys covers as subject of investigation the fteen-year-old students of the analyzed countries to assess their preparation and likelihood to face a successful path for an adult life. By detecting students' skills in mathematics, science, reading and nance and by collecting background information on educational practices in the participating countries, it oers a reliable method to compare students across countries and to evaluate dierent learning environments. Through the assessment of students' abilities to develop their knowledge, their potential and their likelihood to play an active role in society, this strategy allows schools, education systems and the governments of the 80 adherent countries to identify aspects of their systems to improve.

Reliable indicators of student competences serve to guide public decisions in education and those of companies on the labor market. The most advantageous measure is the school grades. This could potentially represent a method of valuation which is both characterized by an high resolution (we could potentially have data for each student in Italy) at a considerably low cost (thanks to the introduction on a national scale of the electronic register of grades, nowadays it is potentially easy to integrate each student's scholastic performances in a single national database). However, although this strategy has potentially the most eective method for obtaining high resolution, aordable and frequent data, Italy just not seems to be the right place. Here teachers seem to replicate a "relative" voting criterion within classes rather than confronting a national meter.

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CHAPTER 1. INTRODUCTION 8 In their work on Grading in Heterogeneous Schools Dardanoni et al. (2007) present a theoretical model and empirical evidence relating to ve countries (Australia, Germany, Italy, the Netherlands and the United States in the 2003 OECD survey) on the informational value of school grades as indicators of the level of preparation of students in dierent institutional contexts. National school systems are identied in which, with the same level of competence, the marks are homogeneous and independent of the school attended by the student, and systems in which, on the other hand, the criteria for assigning grades are uneven among schools. In this case there is a more or less strong information distortion in the territory and, typically, in the weaker schools higher grades are assigned with the same level of competence. In Italy this is more marked for students with lower levels of competence, but to a much lesser extent for students with higher levels of competence. In other words, in their model (assuming that the distribution of votes is decided substantially at the level of the single school and that two schools that have a similar distribution of competences will tend to use similar evaluation criteria) it results that in Italy a student with high grades he is good even if he comes from an unfavorable context. On the other hand, the tendency not to reject too many students per school leads to a substantial correction of low grades in the worst schools, predominantly located in the South.

Figure 1.1: Italy - left diagram - and Germany - right diagram - PISA Scores needed for valuation corresponding to thresholds between Math Levels 1-2 and 5-6.

The gure above, borrowed from Dardanoni et al. (2007), represents - for Germany and Italy - the relationship between the Pisa scores estimated at the national level and the evaluation given by the school, for students attending an average "good" school (below) and an average "poor" (line above). It is noted that in Germany (right diagram) there is a large dierence in score between schools both for students who obtained low marks from their teachers and for those who received high marks, while in Italy (left) the dierence is much more marked for students with poor grades.

In the Italian environment the absence of centralized examinations, particularly in the lower middle schools, and the delay in the construction of a national evaluation system have contributed to the impoverishment of the references available to teachers and schools. Thus learning standards or essential levels of performance for the school have not yet been dened, even though they are provided for by the constitutional provision.

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CHAPTER 1. INTRODUCTION 9 OCSE-PIACC The PIACC program for the International Assessment of Adult Competencies is a program devised by the OECD which has so far involved 24 countries including Italy. The survey was held between the autumn of 2011 and the spring 2012 and involved around 12,000 people. Respondents of the PIACC survey were identied among the members of families surveyed from the registry lists of Italian Municipalities.

The survey aims to learn through a questionnaire and specic cognitive tests the fundamental abilities of the adult population between 16 and 65 years, or those skills deemed indispensable to participate actively in today's fast-pacing social and economic life. The data provided by PIAAC are of great importance to understand what strategies to adopt in the future, both to improve education and training trajectories and to understand how to enhance adult skills. The PIAAC international survey is repeated over time to get information and updated data on the evolution of the skills of the adult population.

1.5 La Lampada di aladino

The educational poverty concept tackled as a multi-dimensional topic raised subsequent to the seminar work of Sen A. and the exposition of the theory of capabilities. The title of this chapter is inspired to a seminal report6 _by

save the children which analyzed the Italian context with a renewed eye, paying attention to the various aspects of educational poverty by discussing data and introducing new indicators. The authors take up what represents one of the most famous tales of the Book of One Thousand and One Nights to discuss how poverty is not an inevitable destiny. The almost inevitable trajectory towards poverty of the young Aladdin was interrupted by the discovery of a magical instrument capable of opening up new worlds of possibilities. That young kid was able to turn his life upside down from being a poor teenager to being able to feed his mother and marry the princes by the use of a lamp to activate the good oces of a Genius.

Today the new tools to set in motion the genius of the little ones and free their future are the dierent educational opportunities, starting with the school, which should be available to everyone and which instead are often, in whole or in part, denied to the more.

The development process which is at the very basis of composite indexes is inserted in the international aim to overcome the GDP. Abandoning the GDP as a measure of well-being it is based on the conviction that the parameters on which to evaluate the progress of a society do not have to be strictly economical but should desirably belong to the social and environmental sphere, thus the presence of inequality and sustainability measures it is not only of strategical importance but also essential to adequately map the social phenomenon we are observing. It is of common knowledge that numerous socioeconomic phenomena can no longer be measured by a single descriptive indicator and that, instead, they must be represented on several dimensions. Phenomena such as development, progress, poverty, social inequality, well-being, quality of life, infrastructural endowment - they all require to be measured by the combination of dierent dimensions which aggregated are considered as proxies for the phenomenon. This combination can be obtained through synthesis methods known in literature as synthetic indices. Having for each geographical area of interest a one-dimensional quantication that collects in itself all the information has the desideratum advantage of providing an immediately visible and interpretable statistic that does not make the interpretation and the analysis of the phenomenon burdensome and complicated. On the other and the observation of the system of elementary indicators would nevertheless provide complete and exhaustive information about the phenomenon we are observing. Furthermore, a single measurement can be a valid aid for the policy maker who,

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CHAPTER 1. INTRODUCTION 10 having to transform information into decisions, can be particularly favored by the immediate usability of such indexes.

The emerging popularity of synthetic index, in fact, owes its success to the combination of statistical rigor and high level of communicability. It is no coincidence that among the most well-known synthetic indexes there are the Human Development Index (HDI) and the Human Poverty Index (HPI) which are based on a small number of non-replaceable indicators, aggregated together through power averages.

This multidimensional index therefore consider the Educational Poverty as a combination of relational, cultural and material problems which are likely to obstacle a proper development of personal capabilities essential for having a complete and purposeful life in this modern-days complex environment.

Many indicators show an alarming situation. In terms of cognitive results, 17 percent of young people do not obtain a high school diploma and leave each training course prematurely. The PISA test results for 15-year-olds are also among the lowest in the OECD countries, despite some recent improvements. Beyond the cognitive results, there are other indicators that show a weak or non-existent relationship with culture and sport. Nearly 90 percent of young people between the ages of three and seventeen watch TV every day, but only one in two has read a book and one in four has never done physical activity, while about 60 percent of children have never visited a museum.

To give a picture of this situation and to show its territorial distribution, the Educational Poverty Index was constructed by ISTAT in a way that through its 4 dimension would be able to trace a map of the risk for young people of not being able to take possession of the tools necessary to have a better quality of life once adults and develop an active citizenship in the social context. The rst dimension is represented by the participation to the social life and to formation; the second dimension is represented by the develop of an attitude of trusting oneself and one's abilities - its the attitude to resilience; the third dimension is represented by the ability to lead an inclusive, healthy and safe life providing an adequate standard of living; the fourth and last dimension is represented by the ability to weave relationships with others and to achieve those skills needed to succeed in such a fast-pacing world.

1.6 Research question

Starting from the consideration that the phenomenon of Educational Poverty requires an approach capable of ap-preciating all its facets, not limiting itself to analyzing a single value, but exploiting a combination of several factors and dimensions, the aim of this work is to analyze the current available techniques and take a few steps forward. Currently the issue of dimensionality has not an univocal solution approach, the debate between aggregating all the indicators in a single step using a single index or exploiting the dimensional structure by performing a 2 steps aggregation still remains an open question. In both cases the aggregation process has been streamlined in dierent ways through the literature ranging from clustering techniques to variance-based dimension reduction techniques, a process highly dependent on the technique used.

Numerous techniques have been proposed in the literature, all having peculiar characteristics and capable of rewarding some aspects rather than others within the aggregation process, among these ISTAT has chosen the Mazziotta-Pareto index. The choice of the composite index to be used as well as the relative weights to be assigned to the various characteristics of the data in the aggregation process remain a strand of research in continuous evolution and which is outside the scope of the present work in which therefore we will concentrate on the application of current techniques available rather than on their evaluation and on the search for dierent congurations of the parameters that characterize them.

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CHAPTER 1. INTRODUCTION 11 Currently the estimates produced by ISTAT are characterized by a resolution addressed to the regions or to macro-regions, this comprises a solid constraining factor for the policy maker. Faced with the obvious diculty of expanding the level of detail of the estimates available to us due to the design of the survey which gather the information to be utilized just at the regional level and due to the fact that the variances would otherwise be too high to be released, The introduction of new techniques therefore becomes of crucial importance. Abandoning the idea of extending the sampling domain of the survey to be able to obtain reliable estimates with a better resolution than the regions, the utilization of estimation procedures for small areas becomes crucial. The combination of these two elements has therefore led us to take a step forward in the frontier of the techniques used, by discussing a routine aimed at producing estimates of Educational Poverty on a new domain - region by degurba. The use of Fay-Herriot estimates solves the problems related to the inaccuracy of direct estimates allowing us to be able to release and discuss the results obtained.

A deeper understanding of the phenomenon within each region will therefore be able to allow policymakers more punctual and eective interventions aimed at improving circumscribed situations and avoiding the indiscriminate distribution of funds aimed at combating Educational Poverty throughout the region. This also responds to the need to adapt the current set of available tools to a literature that now describes the phenomenon as increasingly diverse across Italy and jagged within the same region.

In what follows the reader will nd Chapter 2 dedicated to the exposition of the various techniques used, Chapter 3 devoted to the description of the dataset used, Chapter 4 describing the obtained results and Chapter 5 providing some concluding remarks.

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Chapter 2

Methods

Development, poverty and unemployment are three nancially vital ideas that have been signicantly viewed as uni-dimensional, particularly by the market analysts, for quite a while: development has more often than not been estimated by close to personal income or per-capita product though the poverty has been estimated by absence of income or low expenditure. The move from a unique measurement to multidimensional measurements by broadening and enhancing the extent of the investigation, speaks to an imperative hypothetical advancement and has some applicable points of interest as far as arrangement. Be that as it may, despite those advantages, multidimensionality makes the estimation and assessment of advancement and neediness progressively troublesome. While estimating and surveying a given single measurement should be possible with a single indicator, numerous measurements require a lot of various indicators. This variety includes various theoretical and factual issues particularly when we have to make examinations across time as well as over space.

The Educational Poverty as a multidimensional phenomenon has recently been analyzed by ISTAT as a combi-nation of 4 dimension. These 4 dimensions together represents a state of the art solution to describe all the faces of Educational Poverty which, however, shall be condensed into a single-dimensional measure to provide the policy maker with a scorecard for evaluating dierent policies and decide in which way to distribute critical resources for the development of dierent areas. It is for this main reason that also an overcome of the actual techniques possessed by ISTAT shall be completed to provide the policy maker with a deeper resolution that goes beyond the region. In what follows we rst provide a description of indicators that make up each dimension while leaving for the next sections a discussion on dimension aggregation and small area issues.

2.1 The dimensions of Educational Poverty

The rst dimension is represented by the participation to the social life and to formation, in terms of AVQ it aggregates three direct estimates:1

• Political Activity - percentage of people that not carry out political activity

• Internet - percentage of people that do not use the internet or they do not use it every day

1_{Due do data availability we restricted this process only on AVQ as for the other data sources (INAPP and EU-SILC) we were not}

able to retrieve the variance of direct estimates.

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CHAPTER 2. METHODS 13

• Volunteer - percentage of people that do not volunteer freely

The second dimension is represented by the develop of an attitude of trusting oneself and one's abilities - its the attitude to resilience and is represented by six direct estimates from AVQ:

• Free time satisfaction - percentage of people that are not satised with their free time • rely on - percentage of people that do not have people to rely on

• cultural activities - percentage of people that perform less than 4 cultural activities • books - percentage of people that do not read books or read less than four a year • trust - percentage of people that do not trust others

• internet and PA - percentage of people that do not use internet to interact with the PA

The third dimension is represented by the ability to lead an inclusive, healthy and safe life providing an adequate standard of living and is represented by three direct estimates from AVQ:

• sport - percentage of people that do not practice sports

• deterioration - percentage of people who live in presence of elements of deterioration in the area in which they live

• green spaces - percentage of people who do not have public parks where they live

The fourth and last dimension is represented by the ability to weave relationships with others and to achieve those skills needed to succeed in such a fast-pacing world - these are represented by two direct estimates from AVQ:

• friends - percentage of people that do not have friends or if they have rarely frequent them

• digital skills - percentage of people with low digital skills, represented by a combination of software skills, problem solving ability, communication and information skills.

2.2 Aggregation of indicators

The extensive debate in the literature concerning the validity and reliability of synthetic indexes should lead all the experts, rst and foremost the policy maker, to the utmost caution. It is therefore appropriate to underline the considerable limitations of these measures: on the one hand the numerous components of arbitrariness that necessarily are introduced stand out, in particular as regards the selection of elementary indicators, on the other hand criteria of data normalization, standardization and synthesis raised important questions to be addressed (Brunini et al., 2002). In essence, the trajectory towards the implementation of a synthetic index moves through numerous obstacles, the overcoming of which can require dicult and even arbitrary decisions. As ocial statistics, the possible synthesis methods must comply with the following requirements:

• spatial comparability - the possibility of comparing summary statistics between territorial units • temporal comparability - the possibility of comparing summary statistics overtime

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• non-substitutability of elementary indicators - each elementary indicator should have the same weight in the aggregation process and the impossibility of compensating the value of one indicator with that of another

• _{simplicity and transparency of calculation}

• immediate availability and interpretation of output results • robustness of the results obtained

In the implementation of the Educational Poverty Index by ISTAT a synthetic indicator emerged among all the families of indicators populating the literature as the one satisfying all the requisites streamlined above, the Adjusted Mazziotta-Pareto index.

2.2.1 Mazziotta Pareto

The basic formulation of the Mazziotta-Pareto index (MPI) is dened in a case of negative polarity of the indicator (as in case of educational poverty) following this formulation:

zij = 100 −

(xij− Mxj)

Sxj

10

where X = {xij} is an n-row (number of statistical units) x m-columns (number of indicators) matrix of input

data. Mxjrepresents the mean of indicator j while Sxj represents its' mean square deviation. The synthetic MPI

formulation then is provided by:

M P I_i− = Mzi− Szicvi

The routine for the adjusted version of the Mazziotta Pareto Index is slightly dierent. Its' purpose is to dene a benchmark value equal to 100 and forcing the values in the range [70, 130]. In this way the index aims at solving the main issue of the basic formulation, by providing with the possibility of introducing a benchmark value, the inter-temporal comparability of results can be achieved.

First step in the analytical formulation of the Adjusted MPI is represented by a range data forcing through the following expression:

rij=

(M axxj − xij)

M axxj − M inxj

60 + 70 The formulation of the Adjusted Mazziotta Pareto Index is then given by:

adjM P I_i−= Mri− Sricvi

Both MPI and adjMPI where presented in the specic case of a negative polarity indicator and without men-tioning the inter-temporal corrections the reader might want to adopt when moving from a static framework - the one in which we are located - to a more dynamical outlook. The reader can see Mazziotta and Pareto work of 2016 for a more detailed exposition.

Worth mentioning is the fact that in the MPI (not adjusted) the rst normalization step should be based upon indicators' means and variances which can be easily recollected when aggregating direct or Fay Herriot estimates but can be problematic in the case of a two step procedure whenever aggregating the results of a rst Mazziotta-Pareto

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CHAPTER 2. METHODS 15 step. The Adjusted MPI does not suer from this major issue during the normalization process as it is not based on variances so it can be successfully applied to rst step results of an Adjusted Mazziotta-Pareto routine.

The above considerations highlighted one of the major shortfalls of the actual routine used by ISTAT, a formu-lation of the variance for the Mazziotta-Pareto results is not available. This lead us to consider only the Adjusted Mazziotta-Pareto as a possible routine for aggregating the results as otherwise we would be unable to perform both stages required by the two step aggregation for the computation of EPI. This however remains an open problem that will need to be adequately analyzed in further future work in order to provide the researcher with eective tools to assess the accuracy of the estimates obtained.

2.2.2 Two possible routines

So far we have dealt in a rather abstract way with the issue of dimensional reduction without making specic reference to the input or output elements of the process. It is therefore necessary to set some additional specications and draw the two possible aggregation techniques that will be used in the continuation of the present work. The rst routine we introduce, to which we will refer as 1-step, 1-stage or direct aggregation does not exploit the information regarding the dimension and foresees a direct aggregation of all indicators. Through a single step of the Mazziotta-Pareto algorithm we therefore condensed the 14 indicators into a single dimensional value of EPI for all small areas of Italy. An outline of the procedure is given by the following table 2.1 which in a graphical way depicts an aggregation procedure characterized by a Mazziotta-Pareto way of summing all the dimension which is stylized by the square block with the plus symbol.

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CHAPTER 2. METHODS 16 Political Activity Internet Volunteer Free Time Rely on Cultural Activities Books Trust Internet and PA Sport Deterioration Green Spaces Friends Digital Skills

EPI

1-step aggregation

Table 2.1: Graphical representation of the 1-stage aggregation routine.

The second routine we introduce, to which we will refer as 2-steps or 2-stages exploits the information regard-ing the dimension and proceeds with two consecutive aggregation. Through a rst step of the Mazziotta-Pareto algorithm we therefore obtained a single dimensional value for each dimension, aggregating each group of indicators together to create 4 single-dimensional vectors, one for each dimension. A second step of aggregation is now per-formed to aggregate the obtained single-dimensional expression for each dimension into a nal single dimensional value for each of the small areas of Italy. The obtained result is again a synthesis of the starting 14 indicators but provides a dierent look at the EPI hedging the impact of each dimension on the overall value of the index. An outline of the procedure is given by the following table 2.2 which in a graphical way depicts an aggregation procedure characterized by 2 steps. First aggregation takes place in the four squares labeled with an orange tag, referring to each dimension, thus a second stage aggregates these results into a nal single-dimension value of EPI.

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CHAPTER 2. METHODS 17 Political Activity Internet Volunteer Free Time Rely on Cultural Activities Books Trust Internet and PA Sport Deterioration Green Spaces Friends Digital Skills

EPI

2-step aggregation

Participation Standard of living

Friends and skills

Resilience

Table 2.2: Graphical representation of the 2-stages aggregation routine.

The reader shall notice that the two proposed routines do not rely on any particular formulation for the aggre-gating algorithm which can either be a Mazziotta-Pareto like or based upon clustering or other dimension reduction techniques. Additionally in each of the two stages presented above a dierent aggregation algorithm may be used and even the four dimensions can potentially be the result of dierent aggregating techniques, shall the single dimensional output being the only common argument.

2.3 Fay Herriot

In what we have described so far we discussed the procedure for aggregate the multidimensional nature of the Educational Poverty Index into a single dimensional index highlighting the procedures and possible problems that arises when utilizing one routine in favor of another one. All these routines start from a same common building block, namely the input direct estimates matrix. By the use of small area estimation methods and in particular by the exploitation of the Area Level EBLUP we can improve the estimation of our indicators by ensuring their

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CHAPTER 2. METHODS 18 reliability introducing a linear relationship between the direct estimates and known area level auxiliary variables.

Estimation of indicators through the simple totals or means cannot be considered reliable enough since their variance is too high to be released, this is due to the fact that our survey, as most of the surveys produced by the National Statistical Oce, are designed to be applied to an higher level than the region x degree of urbanization hence, the sample size may be not large enough to guarantee release of direct estimates.

The EBLUP area level is a small area estimation method based on a linear mixed model formulating the relationship between the parameter of interest and auxiliary area level information, introduced by Fay and Herriot (1979) to obtain small area estimators of median income in U.S. small places. The model is dened in two consecutive stages.2

Given ˆδDIR

d the direct estimator of δd, the rst stag assumes ˆδDIRd being an unbiased estimator of δd, i.e.

ˆ

δ_dDIR= δd+ ed, ed ind

∼ N (0, φd) (2.1)

where φd is the sampling variance of the direct estimator ˆδDIRd given δd assumed to be known for all small areas d.

The second stage assumes that the area parameters δd are linearly related with some area level auxiliary

covari-ates as in the equation below:

δd= XdTβ + ud (2.2)

where XT

d represents a set of covariates whose values are known for each domain of interest and the ud are domain

specic random eects assumed to be distributed with mean zero and variance σ2 uand ud

ind

∼ N (o, σ2

u), additionally

ud and ej are independent for all pairs (d, j).

Equation 2.1 is called sampling model as it represents the uncertainty due to the fact that δd is unobservable,

instead of δdwe observe its direct estimator ˆδdDIR, equation 2.2 is called linking model as it relates all areas through

the common regression coecients β, allowing us to borrow strength from all areas. The combination of these two gives the linear mixed model:

ˆ δDIR_d = xT_dβ + ud+ ed, ed ind ∼ N (0, φd) and ud ind ∼ N (0, σ2 u)

An important consideration is streamlined by Prasad and Rao (1990) and it is represented by the fact that the requirement of Normality is not needed for point estimation but it is required for the estimation of the mean squared error.

The derivation of the best linear unbiased predictor (BLUP) of a combination of the xed and random eects β and u was developed by Henderson (1975) and is given by:

˜

δdBLU P = xTdβ(A) + ˜˜ ud(A)

where ˜ud(A) = γd(A)(ˆδdDIR− x T

dβ(A))˜ represents the predicted random eect, γd(A) = A/(A + φd) ∈ (0, 1) and

˜

β(A) =P

d(A + φd)−1xdxTd

−1P

d(A + φd)−1xdδˆdDIR represent the weighted least squares estimator of β. In this

framework, the BLUP routine assumes that A is known, an overcoming of any problems in this sense is given by the empirical BLUP (EBLUP) in which A is replaced by a consistent estimator ˆA.

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CHAPTER 2. METHODS 19 EBLUP can be expressed as a combination of direct and regression-synthetic estimators in a way that whenever the direct estimator is reliable the EBLUP would be closer to the direct estimator, when otherwise the direct estimator is unreliable then the EBLUP gets closer to the regression-synthetic estimator. This intuition is translated into the following model conguration:

ˆ

δ_dEBLU P = ˆγdˆδdDIR+ (1 − ˆγd)xTdβˆ

where

ˆ

γd= γd( Â) = Â/( Â + φd) and ˆβ = ˜β( Â)

In this way the EBLUP makes use of the regression assumption only for those areas where borrowing strength is needed, i.e. when φd is large as compared with ˆA.

In addition we assume that φ is unknown but the Dj's are known.

Across the literature and supporting the package provided on cran for small area estimation and in particular for the Fay-Herriot model, four popular ways of estimating the variance components are introduced:

• Prasad Rao estimator

denote ˆφP R it can be written as y

T_{(I−P x)y−tr((I−P x)D)}

m−p where P x = X(X

T_X)−1_XT _{is the projection}

matrix onto the column space of X • Fay Herriot estimator

denote ˆφF H it can be found as the solution of the equation

yT_Q(φ)y

m − p = 1 where the numerator yT_Q(φ)y_{is given by}

yTQ(φ)y =X

d

(yd− xTdβ) 2

φ + Dd

• Maximum likelihood estimator

denote ˆφM L it is obtained by maximizing the likelihood function of the model.

• REML

denote ˆφREM Lit is obtained through the Residual Maximum Likelihood routine involving an adjustment

for the degrees of freedom involved in estimating the xed eects to encompass the main drawback of the likelihood approach. For further details, the reader can see pakage's supporting materials on Cran and Searle et al (2009).

Covariates selection To support the Fay Herriot model, we selected among the covariates available through the website "A misura di comune" provided by ISTAT some percentages ratios that could describe the composition of the population and the territory of each of the areas subject to analysis. This online repository presents only a

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CHAPTER 2. METHODS 20 few of indicators for all the municipalities of Italy while suering from missing data problems for some of them and presenting numerous issues in the identication of municipalities subject to merge in the past ve years. In some of these cases we managed to recover the jagged information while in other cases, since we were not sure if the data reconstruction has led to a correct result we chose to not include those data in the covariates list and leave them for qualitative analysis. A set of covariates that we consider important for the description of the territory of each area is represented by its production mix, which however, as being the result of numerous compositions of datasets, suers from the joint inadequacy of these and therefore it was not possible to include it in this work. We are convinced that if in the future these problems will be resolved or if the harmonization of data by ISTAT will be successfully concluded, the inclusion of this set of covariates will bring signicant improvements to Fay Herriot estimates and to the whole routine.

Symbol Description Symbol Description

X1 Ratio of Male in Population X12 Ratio of people aged 18-19 in Population X2 Ratio of Female in Population X13 Ratio of people aged 20-29 in Population X3 Ratio of Foreign Male in Foreign Population X14 Ratio of people aged 30-59 in Population X4 Ratio of Foreign Female in Foreign Population X15 Ratio of people aged 60-64 in Population X5 Ratio of Foreign people in Population X16 Ratio of people aged 65-84 in Population X6 Ratio of cultural asset in Population X17 Ratio of people aged 85+ in Population X7 Ratio of people aged 0-3 in Population X18 Average population per municipality X8 Ratio of people aged 4-5 in Population X19 Number of municipalities X9 Ratio of people aged 6-10 in Population X20 Ratio of people aged 18+ in Population X10 Ratio of people aged 11-14 in Population X21 Ratio of people aged 15-29 in Population X11 Ratio of people aged 15-17 in Population X22 Euro spent by people aged 18+ in gambling

Table 2.3: List of covariates with with a brief description

Considerations This method can be successfully applied even when few or even no sample data are available for one or more domains of interest eventually by the use of synthetic estimators. This method provides a useful improvement of direct estimates whenever a set of covariates with a strong relationship with the variable of interest is available, it is for that reason that later in this work, whenever applying the Fay-Herriot model we rst search for the best supporting set of regressors among all the possiblen

k

= _k!(n−k)!n! combinations.3 We xed the number

of regressors to 5 to avoid risk of over-tting. Variance of the small area direct estimates has to be known, it is for this reason that a smoothed model for variance estimation is usually applied in the literature, thus leading to some problems with the MSE which can be circumvented by recovering the variances through the described ReGenesees procedure.

Two possible drawbacks characterize this model, the rst being the normality assumption, which might be untenable at small sample sizes, the second being the fact that when adding up small domains estimates to a larger domain, in general, a consistency between the two quantities is not ensured.

Following table concludes this Fay Herriot section by providing the list of best models for each direct estimator with their respective r-squared.

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Short Name Model r-squared Short Name Model r-squared

pol X6+X7+X8+X10+X11 0.390519 digsk X1+X5+X10+X11+X21 0.3181282 soddtl X5+X8+X12+X16+X21 0.2346632 lib3 X7+X9+X11+X13+X21 0.4822744 conta X5+X12+X13+X15+X21 0.3096271 int X1+X5+X10+X11+X14 0.3805379 sport X1+X10+X14+X17+X19 0.4950567 verde X8+X9+X11+X15+X21 0.7994131 cult X5+X6+X8+X11+X20 0.3667134 fiduc X5+X16+X17+X19+X22 0.1958112 amici X5+X9+X10+X14+X17 0.3187807 attvol X7+X11+X19+X20+X21 0.5659426 degrado X2+X5+X11+X12+X17 0.5730836 paweb X6+X9+X20+X21+X22 0.298454

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Chapter 3

Data set description

3.1 AVQ

The AVQ analysis on the aspects of everyday life survey represents an annually analysis over a sample of 20,000 families and 50,000 individual revealing fundamental aspects of the daily life. The thematic areas covered by this survey are many and varied, shall the reader being interested in exploring this aspect, she can consult the ISTAT websited to gather additional information. Starting from the data provided by the 2016 survey we dened the following 14 indicators, each constituting the building blocks of the 4 dimensions of Educational Poverty streamlined above:1

1. Do not carry out political activity

Nopol<−(15<=eta ) ∗ ( eta <=29)∗(comiz==1)∗( c o r t e i ==3)∗( volpa ==7)∗( f i n p a==7) INDICATORS$X1<−1∗Nopol

Table 3.1: Political activity - r code

(a) eta represents the age of each statistical unit

(b) comiz represents a dichotomous variable which is equal to 2 if the individual attended a political rally at least once in the past 12 moths, 1 otherwise

(c) cortei represents a dichotomous variable which is equal to 4 if the individual participated in a political procession at least once in the past 12 months, 3 otherwise

(d) volpa represents a dichotomous variable which is equal to 6 if the individual has carried out free activity for a party at least once in the past 12 months, 5 otherwise

(e) finpa represents a dichotomous variable which is equal to 8 if the individual has given money to a party either for subscription or for support at least once in the past 12 months, 7 otherwise

1_{Each of the following variables' missing values is replaced with either 99 or −99 according to the convenience of the specic operation.}

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CHAPTER 3. DATA SET DESCRIPTION 23 2. Not satised with your free time

Nosodd_TL<−(15<=eta ) ∗ ( eta <=29)∗((( temlib==1)+(temlib==2)+(temlib==0))==0) INDICATORS$X2<−1∗Nosodd_TL

Table 3.2: Free time - r code

(a) where temlib is equal to 3 or 4 if the individual is very satised or quite satised with his free time 3. Do not have people to rely on

No_conta<−(15<=eta ) ∗ ( eta <=29)∗(( Parent !=2)+( Amici2 !=2)+( V i c i n i !=2)) No_conta<−1∗(No_conta>=1)

INDICATORS$X3<−1∗No_conta

Table 3.3: People to rely on - r code

(a) parent represents a dichotomous variable which is equal to 2 if the individual has at least a parent to rely on outside of rst-degree relatives and grandparents

(b) amici2 represents a dichotomous variable which is equal to 2 if the individual has at least a friend to rely on

(c) vicini represents a dichotomous variable which is equal to 2 if the individual has at least a neighbor to rely on

4. Do not practice sports pratica <−1∗(spocon==2) pratica <−p r a t i c a +2∗( s p o s a l ==2)∗( spocon !=2) pratica <−p r a t i c a +3∗( a t t f i s >1)∗( spocon !=2)∗( s p o s a l !=2) pratica <−p r a t i c a +5∗( spocon ==99)∗( s p o s a l ==99)∗( a t t f i s ==−99) Nosport<−(15<=eta ) ∗ ( eta <=29)∗(( p r a t i c a ==3)+( p r a t i c a ==0)+( p r a t i c a ==5)) INDICATORS$X4<−1∗Nosport

Table 3.4: Sports - r code

(a) spocon represents a dichotomous variable which is equal to 2 if the individual practice a sport with continuity

(b) sposal represents a dichotomous variable which is equal to 2 if the individual practice a sport from time to time

(c) attfis represents a variable which is equal to 1 if the individual does not do physical activity in his spare time

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CHAPTER 3. DATA SET DESCRIPTION 24

arrat <−(15<=eta ) ∗ ( eta <=29)∗(( teatro >=4)+(cine >=4)+(museo>=4)+(monum>=4)+ ( music >=4)+(acmus>=4)+(spspo >=4))

No_cult<−(15<=eta ) ∗ ( eta <=29)∗( arrat <=3) INDICATORS$X5<−1∗No_cult

Table 3.5: Cultural activities - r code

(a) teatro is greater or equal to 4 if the individual went to a theater at least 7 times in the past 12 months (b) similarly cinema follows the same criteria as for teatro

(c) similarly museo follows the same criteria as for teatro w.r.t. attendance to museums

(d) similarly monum follows the same criteria as for teatro w.r.t. frequency of visits to archaeological sites and monuments

6. Do not have friends or if they have rarely frequent them no_amici<−(15<=eta ) ∗ ( eta <=29)∗( amici >=4) INDICATORS$X6<−1∗no_amici

Table 3.6: Friends - r code

(a) amici is greater or equal to 4 if the individual meet with friends less than 4 times a month 7. Presence of elements of deterioration in the area in which they live

degrado <−(15<=eta ) ∗ ( eta <=29)∗(( sporco <=2)+(sporco==99)+(inqar <=2)+(inqar==99)+ ( crim <=2)+(crim==99)+( i l l s t r <=2)+( i l l s t r ==99))

degrado <−(degrado >=1) INDICATORS$X7<−1∗degrado

Table 3.7: Deterioration - r code

(a) sporco is less or equal to 2 when the area where the individual lives has a lot or enough dirt on the streets

(b) inqar is less or equal to 2 when the area where the individual lives has a lot or enough pollution in the air

(c) crim is less or equal to 2 when the area where the individual lives has a lot or enough risk of crime (d) illstr is less or equal to 2 when the area where the individual lives has poor street lighting 8. Composite index on digital skills

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CHAPTER 3. DATA SET DESCRIPTION 25

Ipcope2a <−(inttempo <=2)∗(pcope2a==2) ICLOUDSAL<−(CLOUDSAL==2)

Iintuso1 <−(intuso1==2)+(intuso1==3) I i n t a t t 1 6 <−(i n t a t t 1 6 ==2)

I i n t a t t 1 4 <−(i n t a t t 1 4 ==8)

macro1si <−(Ipcope2a==1)+(ICLOUDSAL==1)+( I i n t u s o 1==1)+ ( I i n t a t t 1 6==1)+ ( I i n t a t t 1 4 ==1) DSK_I<−1∗(15<=eta ) ∗ ( eta <=29)∗(( inttempo <=2)∗( macro1si ==1))

DSK_I<−DSK_I+2∗(15<=eta ) ∗ ( eta <=29)∗(( inttempo <=2)∗( macro1si >1)) Table 3.8: Low information skills - r code

i. inttempo is equal to 1 if the individual used internet at least once in the past 3 months, it is equal to 2 if the individual used internet in the past year (but not in the past month), it is equal to 3 if the individual used internet more than 1 year ago, it is equal to 4 if the individual never used internet. ii. pcope2a is equal to 2 if the individual has le management skills on an operating system

iii. cloudsal is equal to 2 if the individual in the last 3 months used at least once a storage/sharing service on the internet

iv. intuso1 is equal to 2 if in the last 3 months the individual used internet to gather information on P.A. websites, it is equal to 3 if less recently than 3 months but within the last year.

v. intatt16 is equal to 2 if in the last 3 months the individual has searched for information on goods or services on the internet

vi. intatt14 is equal to 8 if in the last 3 months the individual has been seeking health information on the internet

(b) Low communication skills IINCOMU5<−(INCOMU5==2)

Iincomu6<−(incomu6==2) IINCOMU1B<−(INCOMU1B==4)

I i n t a t t 2 6 <−(i n t a t t 2 6 ==4)

macro2si <−(IINCOMU5==1)+( Iincomu6==1)+ (IINCOMU1B==1)+ ( I i n t a t t 2 6 ==1) DSK_C<−1∗(15<=eta ) ∗ ( eta <=29)∗(( inttempo ==1)∗( macro2si ==1))

DSK_C<−DSK_C+2∗(15<=eta ) ∗ ( eta <=29)∗(( inttempo ==1)∗( macro2si >1)) Table 3.9: Low communication skills - r code

i. incomu5 is equal to 2 if in the past 3 months the individual has either send or received at least one email

ii. incomu6 is equal to 2 if in the past 3 months the individual has participated in social networks iii. incomu1b is equal to 4 if in the past 3 months the individual has made phone calls via the internet

and or video-calls via webcam at least once

iv. intatt26 is equal to 4 if in the last 3 months the individual has uploaded contents of his own creation at least once

Measuring Educational Poverty in Italy under a Small Area Estimation approach

Preface

Contents