DOCUMENT DE TREBALL XREAP2017-11 EFFICIENCY IN THE TRANSFORMATION OF SCHOOLING INTO COMPETENCES: A CROSS-COUNTRY ANALYSIS USING PIAAC DATA Inés P. Murillo José L. Raymond (GEAP, XREAP) Jorge Calero (IEB, XREAP) Efficiency in the transformation of schooling into competences: A cross-country analysis using PIAAC data Inés P. Murillo (Universidad de Extremadura: ihuertas@unex.es), José L. Raymond (Universidad Autónoma de Barcelona & IEB: josep.raymond@uab.edu) and Jorge Calero (Universidad de Barcelona & IEB: jorge.calero@ub.edu) Abstract This study (i) compares the competence levels of the adult population in a set of OECD countries; (ii) assesses the comparative efficiency with which the education system in each country transforms schooling into competences, distinguishing by educational level, and (iii) tracks the evolution of this efficiency by birth cohorts. Using PIAAC data, the paper applies standard parametric frontier techniques under two alternative specifications. The results obtained under both specifications are similar and identify Finland, Sweden, Denmark and Japan as being the most efficient and Spain, the United Kingdom, Italy, Ireland and Poland as the least efficient. The evolution of the efficiency levels by age cohorts shows that higher education is more efficient for younger cohorts, while lower and upper secondary education present a stable trend over cohorts. Key words: adult population competences; efficiency; PIAAC; parametric frontier techniques. JEL codes: I21, C13. 1. Introduction The consideration of human capital as a key factor both in the economic growth of countries and in the labor outcomes of individuals represents a long-standing tradition in the literature. Similarly, the limitations researchers face as they seek to measure this human capital – typically by resorting to the number of years of schooling (or, alternatively, the level of education attained) on the basis of Mincer’s (1970; 1974) proposal – have been well documented. More recently, various studies have recommended considering the cognitive skills or competences acquired by individuals – as well as the number of years of schooling – when measuring human capital. Borghans et al. (2001) discuss the advantages of such an approach, stressing that the level of education achieved by an individual is an imperfect indicator of their human capital at any one point in time. Indeed, several studies provide empirical support for such arguments and show that cognitive competences can account for a large part of a country’s growth in productivity (Hanushek and Kimko 2000; Barro 2001; Hanushek and Woessmann 2008) and for a part of an individual’s labor achievements that 1 cannot be explained by their educational attainments (McIntosh and Vignoles 2001; Green, and Riddell 2003). If, therefore, we assume that an individual’s skills are defined not only by the quantity of education they have received (measured in terms of the number of years of schooling), but also by the quality of that education (measured in terms of the cognitive competences acquired), it is of great interest to researchers to (i) determine which factors account for the acquisition of competences throughout an individual’s life cycle and (ii) identify the greater performance that some individuals derive from their schooling in terms of competences than is obtained by others. The first of these issues has been broadly analyzed by estimating education production functions (Hanushek 1979; 1997). It has been concluded that not only the number of years of formal education received but other relevant variables, including an individual’s personal characteristics and his/her socio-economic environment, can determine the acquisition of cognitive competences (Björklund and Salvanes 2011; Mazzona 2014). When estimating education production functions, however, it is assumed that all the units included in the sample obtain the same benefit from each of the explanatory variables considered. In international comparisons, this means, for example, assuming that an additional year of schooling in two countries with different institutional environments – and, more specifically, with different education systems – is equally effective, on average, in translating higher levels of schooling into competences for their populations. In order to refine this assumption, we need to determine whether the efficiency in the transformation of the number of years of schooling received into competences varies by country. The estimation of production frontiers is useful for this purpose since it indicates, for a given reference unit, the distance from that unit to the frontier, estimated using the most efficient units in the sample. For a given set of countries, this technique would provide a sorting of countries as a function of their distance from the frontier, or what is the same, as a function of the efficiency with which their education systems transform an additional year of schooling into competences 1. The importance attached to the analysis of efficiency in education has grown notably in recent years (see De Witte and López-Torres 2015, for an exhaustive review of the literature). The bulk of the work in this regard has focused on estimating the efficiency of different units (districts, schools or students) operating within the same country, with far fewer studies comparing the efficiency of education systems across countries. However, among the latter, the most relevant draw on information provided by the OECD’s PISA program as they compare from different perspectives the efficiency with which the education systems of different countries operate. For example, Afonso and Aubyn (2005; 2006) and Sutherland et al. (2009) analyze the efficiency of public spending on education for a group of OECD countries, and emphasize the role played by the institutions of each country in accounting for the disparity in the results reported. The influential role played by a country’s institutions is similarly stressed by De Jorge and Santín (2010), who, like Deutsch et al. (2013), consider an analysis of efficiency at the student level as the best approach to optimize the use of available information. Agasisti and Zoido (2015) assess efficiency at both the national and school level for a broad set of OECD countries. They document a notable heterogeneity both 1 A review of papers using parametric boundary techniques to analyze various issues related to education can be found in Worthington (2001). 2 between and within countries in terms of the degree of efficiency achieved by their respective education systems and schools. Giambona et al. (2011), in contrast, focus on the role played by the students’ socio-economic characteristics in the determination of their competences. The authors assess the efficiency of the education systems of several EU countries with particular regard to their ability to help students from a poor family background achieve optimal development of their cognitive competences. The importance of the socio-economic environment is similarly stressed in Thieme et al. (2012). The authors compare the efficiency of a broad set of countries taking into account not only the results obtained by the students but also the degree of dispersion in the distribution of those results as an indicator of the equity of the system. Other studies use several waves of cross-sectional data in order to evaluate the evolution of a given output over time. This is the case of Agasisti (2014) when comparing the efficiency of public expenditure on education in twenty European countries between 2006 and 2009. In a similar vein, Giménez et al. (2017) examine student progress in terms of competences between 2003 and 2009, as they assess the extent to which their progress can be accounted for by the availability of better resources and/or the enhanced efficiency of their respective education systems. Other databases that have been used to evaluate the efficiency of education systems in an international setting include the Third International Mathematics and Science Study (TIMSS) – see Clements (2002) and Giménez et al. (2007); and the Progress in International Reading Literacy Study (PIRLS) – see Cordero et al. (2017). The aforementioned papers adopt different methodologies (mainly non-parametric, but also semi-parametric and parametric) to calculate the efficiency with which different inputs are combined (at the country, school and/or student levels) in the production of various outputs related to student competences. However, despite this multiplicity of tools and results, they share a common limitation derived from their use of cross-sectional data that refer to individuals belonging to the same birth cohort. This means that we can only evaluate the efficiency of the education system for a given academic year (as in the case of TIMSS or PIRLS) or for a specific age (as in the case of PISA). In contrast, to the best of our knowledge, this paper is among the first that seeks to undertake an efficiency analysis for the education system as a whole, distinguishing by country and by level of education 2. This is possible as we draw on data from the Program for the International Assessment of Adult Competencies (PIAAC), a survey conducted by the OECD among individuals aged 16-65 that have received a varied number of years of schooling. By estimating standard stochastic frontier functions, our objectives are as follows: (i) to compare the competence levels of the adult population in a set of OECD countries; (ii) to assess the comparative efficiency with which the education system in each country transforms schooling into competences, distinguishing by educational level, and (iii) to track the evolution of this efficiency by birth cohorts. 2 Gupta and Verhoeven (2001) use information on adult population competences to make international comparisons of efficiency indicators. However, the aim of their study is not to evaluate the efficiency with which schooling is translated into competences, as is the case in our paper, but rather to compare the efficiency with which public expenditure on education and health improve a series of social development indicators, for some thirty African countries. For the specific case of education, the outputs assessed are school attendance rates in primary and secondary education and adult population competences. 3 The rest of the paper is structured in four sections: sections 2 and 3 outline the methodology and the database used, section 4 reviews the main results obtained and, finally, section 5 presents the study’s main conclusions. 2. Methodology Here we propose an education production function and employ standard stochastic frontier techniques to calculate the distance from each country to the frontier. In this way, a classification of the countries is obtained as a function of the (in)efficiency with which they transform schooling into competences. The education production function can be expressed as follows: YiJ= β ′ X iJ + wiJ= β ′ X iJ + ( viJ − uiJ ) E [uiJ / wiJ = δ iJ= hi + θ J ] (1) in which the competences of individual “i” living in country “J” are accounted for by the variables included in “X iJ ” plus a term of inefficiency or of distance with respect to the frontier, “ uiJ ”. The expected value of this distance from the frontier, for individual “i”, is given by “ δ iJ ”, which is the result of the standard calculation of frontier distances when using stochastic frontiers. The distance to the frontier for individual “i” living in country “J” has two components: the individual component “ hi ”, which gathers the innate ability of individual “i”, and “ θ J ”, a component of the country that includes the average efficiency with which the country’s education system transforms schooling into competences. When calculating the average of the individuals living in country “J”, we obtain: M ∑δ M ∑h iJ = 1= 1 i i M = M i + θJ → θJ (2) In other words, for individuals from country “J”, insofar as the innate ability of the individuals within the same country tends to be compensated for, the average of the individual distances to the frontier will come closest to the average distance from the component country’s derived frontier, which may represent a way to approach the efficiency of that country’s education system. The functional specification for the education production function suggests that using a linear, as opposed to a semi-logarithmic model, provides the best fit for the available data. Moreover, it appears that age and experience – two of the explanatory variables included in the model – have a free effect on the competences when creating dummy specific variables for age (i.e. a dummy for each age in years) and experience (i.e. a dummy for each experience in 4 years), compared to a more standard specification that suggests a linear effect for age and a quadratic effect for experience. We estimate both options with the available data and conclude that the latter gives the better outcomes (see Annex 1). Standard stochastic frontier techniques are applied to Equation 1 under two different specifications. In the first, the influence of the explanatory variables is accounted for, which means the equation is estimated using the standard frontier function technique and that the estimated coefficients are common to all the countries considered. In the second, the frontier functions methodology is adapted so as to allow the coefficients (other than formal education) that affect the transformation of inputs into competences (including, for example, number of years of experience or type of occupation) to vary from country to country. This approach, which can be consulted in Annex 2, means we can isolate more precisely the (in)efficiency of the formal education system in transforming years of education received into competences. This said, both approaches in fact give very similar results. 3. Data The data used in the present paper are drawn from the first wave of the PIAAC (corresponding to 2012), an OECD initiative aimed at assessing the competences of the population aged 16-65. This database follows in the wake of others that have measured the competences of the adult population (including IALS and ALL), although the number of participating countries is in this case greater and the competences evaluated refer not only to language skills, but also to mathematical skills and the use of new technologies. All these competences are measured using specific tests, the results of which are presented in terms of plausible values (ten for each skill). These plausible values indicate the performance of each individual on a scale of 0 to 500 points and are grouped into six levels. The survey, designed to facilitate a comparative analysis of the participating countries, also offers harmonized information on the use of the competences assessed in the workplace and in daily life; on the socio-demographic characteristics of the individuals surveyed (e.g. gender, age, nationality, level of education of parents); and on their training and job characteristics (e.g. education level, work experience throughout their working life, work situation: employed, inactive, unemployed, salary and other characteristics of the job: type of contract and working day, performance of supervision tasks, and even variables that allow for the identification of eventual educational or skill mismatches). We have excluded from the sample those countries that give rise to any kind of concern regarding the reliability of the data they provide and those which fail to provide information on some of the variables considered in our study. Our model’s dependent variable is numeracy competences rescaled to 1000 so as to facilitate the interpretation of the results 3. The explanatory variables provide information about age, number of years of schooling, work experience (in quadratic terms), gender, first or second generation immigrant status, (the All of the study’s estimations have been replicated using literacy skills as the dependent variable. The results obtained (available upon request) are, to a large extent, quantitatively and qualitatively similar to those presented here for numeracy. 3 5 absence of) coincidence between the mother tongue and the language in which the survey is carried out, the level of studies of the parents, type of occupation and possible attendance on non-regulated training courses. Table 1 presents the descriptive statistics for the variables in the overall sample (excluding observations without information regarding any of the variables considered in the analysis, which limits the sample to around 79,000 observations). The average value of the numeracy competence is c. 542 points, with a marked standard deviation of around 96 points. The average number of years of schooling stands at 12.73 for individuals whose average age is 40 years old and who have an average work experience of 18.21 years. The proportion of first generation immigrants is 7.9% (falling to 1.7% for second generation immigrants), most individuals (92%) respond to the survey in their mother tongue and 38% (22%) have at least one ascendant with post-compulsory (higher) secondary education. Roughly two-thirds of the individuals in the sample work in a skilled occupation and, finally, around 40% reported participating on non-regulated training courses in the 12 months prior to the survey. Table 1. Descriptive statistics Variable Average Standard dev. Min Max Mathematics Comp. 542.0646 96.1126 49.6917 888.2642 Schooling 12.7323 3.0259 3.0000 22.0000 Age 39.9555 14.4749 16.0000 65.0000 Experience 18.2143 13.1439 0.0000 55.0000 Man 0.4783 0.4995 0.0000 1.0000 Immigrant 1st gen. 0.0796 0.2707 0.0000 1.0000 Immigrant 2nd gen. 0.0173 0.1304 0.0000 1.0000 Mother tongue 0.9233 0.2660 0.0000 1.0000 Parents higher secondary ed. 0.3815 0.4858 0.0000 1.0000 Parents higher ed. 0.2232 0.4164 0.0000 1.0000 Qualified occupation 0.6122 0.4873 0.0000 1.0000 Non-regulated training 0.3919 0.4882 0.0000 1.0000 Table 2 shows the average competences by country, with values ranging from 491 for Spain to 576 points for Japan. Table 3 ranks the countries by competences, with Japan and the Nordic countries heading the classification and Ireland, Spain and Italy finding themselves at the bottom of the ranking. 6 Table 2. Average competences by country Table 3. Ranking of countries by competences Average Competences Country Belgium 560.7724 Japan Czech. Rep 551.4677 Finland Denmark 556.5568 Belgium Estonia 546.239 Holland Finland 564.4532 Sweden Ireland 511.1808 Norway Italy 494.2578 Denmark Japan 576.3407 Slovak Rep. Korea 526.7724 Czech Rep. Holland 560.6922 Estonia Norway 556.5957 Korea Poland 519.5378 United Kingdom Slovak Rep. 551.6152 Poland Spain 491.6435 Ireland Sweden 558.1049 Italy United Kingdom 523.4517 Spain Country Finally, and given that throughout this study the efficiency indices are estimated distinguishing by level of education, Graph 1 presents average numeracy scores for each level of education contemplated. Note that the rankings of countries according to their average competences per level of study (see Table 4) present considerable similarities to those obtained as a function of the efficiency indices (see Graphs 2 and 3). 7 Graph 1. Average competences by country and level of studies Numeracy 600 550 500 450 400 Lower secondary Higher secondary Higher education Table 4. Classification of countries as a function of their competence level, by level of studies Lower Secondary Higher Secondary Higher education Finland Holland Belgium Japan Japan Holland Norway Sweden Sweden Czech Rep. Slovak Rep. Japan Holland Denmark Slovak Rep. Estonia Finland Finland Denmark Norway Norway Sweden Belgium Denmark Belgium Czech Rep. Estonia Slovak Republic Estonia Poland Poland Italia United Kingdom Korea Korea Korea Italia United Kingdom Ireland United Kingdom Spain Italy Ireland Ireland Spain Spain Poland Belgium 4. Results Graph set 2 shows the results of the estimation of the efficiency indices for specification 1 (see methodology, section 2), in which the influence of the explanatory variables is taken into account. Graph set 3 corresponds to specification 2, which also incorporates a frontier function but in which the coefficients (with the exception of formal education) that affect the transformation of inputs into outputs are allowed to vary from 8 country to country 4. In each case, the results are broken down into the three educational levels completed by the individuals: up to lower secondary; higher secondary, and higher education. Note that the results obtained from the two specifications are largely similar, with only minor differences. Focusing on Graph set 2, similar patterns are found for the three levels of education (Graphs 2a, 2b and 2c). The efficiency in the transformation of the number of years of schooling into competences is greatest in three of the Nordic countries analyzed (Finland, Sweden and Denmark), Japan and Belgium. In contrast, the lowest levels of efficiency are recorded in Spain, Italy, Ireland, Poland, Korea and the United Kingdom. This pattern is repeated with only minor differences across the three levels of education: the order of the countries is largely similar, with some notable differences, (for example, in the case of higher education Italy presents an especially low level of efficiency and Poland presents a slightly higher level of efficiency). Graph set 3 (Graphs 3a, 3b and 3c) presents the efficiency indices using specification 2 (in which the coefficients that affect the transformation of inputs into outputs vary from country to country). As in Graph set 2, the Nordic countries present the highest rates of efficiency, these indices being slightly higher than those reported for specification 1. Japan and Belgium present very similar levels of efficiency to those obtained with specification 1, but they fall in the overall ranking of countries by rates of efficiency. The United Kingdom and Italy present the lowest levels of efficiency, while Spain, Ireland and Poland present indices that are similarly low for both specifications. Here the differences in the efficiency indices between the three levels of education (which are small in the case of specification 1) are even smaller. All in all, the positions occupied by the countries in the rankings are very similar across the three levels of education. Graph set 4 tracks the evolution of the efficiency levels over the different age cohorts for the three levels of education considered. In the case of higher education, it can be seen that in most of the countries considered the levels of efficiency in generating competences are higher among the younger cohorts. This increase in the index is most significant in Spain and Italy, but is also appreciable in the Nordic countries (with the exception of Denmark), Belgium, Holland and Korea. In the cases of the United Kingdom and Ireland, the increase is less pronounced. However, there are hardly any changes in the levels of efficiency in the remaining countries: Japan, Denmark and the four Eastern European countries considered (i.e. Czech Republic, Estonia, Poland and the Slovak Republic). In the case of higher secondary education, the pattern presented is one of general stability across all the cohorts. The only deviations from this trend are recorded in the cases of Italy and the United Kingdom, where there has been a fall in efficiency among the youngest cohorts, and in that of Finland, where there has been an increase in efficiency. Likewise, in the case of lower secondary education, efficiency levels in most countries remain stable across all the cohorts. There are exceptions to this general pattern. For example, Table A.3.1 of Annex 3 gathers the numerical indices calculated according to specification 1, and Table A.3.2 the numerical indices according to specification 2. 4 9 in Spain and Korea efficiency levels have increased among younger cohorts, whereas in Italy and the United Kingdom there has been a fall in efficiency levels for these same cohorts. In the Eastern European countries, the pattern of stability is interrupted in the cohort aged between 46 and 55 (26-45 in Slovakia) with marked declines in efficiency, associated in all probability with the historic evolution of the education systems in these countries 5. Conclusions The aim of this study has been to compare the degree of efficiency with which the OECD countries produce competences from the schooling provided and from other inputs and, also, to monitor how this efficiency has evolved over different age cohorts. To do so, we have estimated standard stochastic frontier functions applied to OECD data from the PIAAC. In order to estimate this frontier we used two specifications so as to verify the robustness of our results. In the first specification, the influence of the explanatory variables has been taken into account and a function was estimated whose coefficients are common to all of the countries considered; in the second, the frontier functions methodology has been generalized to allow the coefficients (other than formal education) that affect the transformation of inputs into competences (including, years of experience and type of occupation) to vary from country to country. The levels of efficiency reported by the analyses were similar for both specifications. Furthermore, the results by level of education show that in most cases the efficiency indices are similar for all three levels of education. However, efficiency in the transformation of schooling into competences is greatest in Finland, Sweden, Denmark, Japan and Belgium, while the lowest levels of efficiency are to be found in Spain, the United Kingdom, Italy, Ireland and Poland. Finally, as regards the evolution in the levels of efficiency associated with different age cohorts, we found that in the case of higher education, levels are higher among younger cohorts, whereas in the cases of lower and upper secondary education, the general pattern, albeit with some exceptions, is one of stability for all the cohorts considered. 10 Graph set 2. Efficiency indices for competence in mathematics. Specification 1. Graph 2.a. Lower secondary 100 95 90 85 80 75 70 Graph 2.b. Higher secondary 100 95 90 85 80 75 70 Graph 2.c. Higher education 100 95 90 85 80 75 70 11 Graph set 3. Efficiency indices for competences in mathematics. Specification 2. Graph 3.a. Lower secondary 100 95 90 85 80 75 70 Graph 3.b. Higher secondary 100 95 90 85 80 75 70 Graph 3.c. Higher education 100 95 90 85 80 75 70 12 Graph set 4. Efficiency indices for competence in mathematics according to level of education and cohort Continental countries Belgium Holland 100 100 95 95 90 90 85 85 80 16-25 26-45 46-55 56-65 80 16-25 26-45 46-55 56-65 Mediterranean countries Italy Spain 100 100 95 95 90 90 85 85 80 16-25 26-45 46-55 56-65 80 16-25 26-45 46-55 56-65 13 Nordic countries Denmark Finland 100 100 95 95 90 90 85 85 80 16-25 26-45 46-55 56-65 80 16-25 26-45 46-55 56-65 46-55 56-65 Sweden Norway 100 100 95 95 90 90 85 85 80 16-25 26-45 46-55 56-65 80 16-25 26-45 14 Eastern European countries Estonia Poland 100 100 95 95 90 90 85 85 80 16-25 26-45 46-55 56-65 80 16-25 Czech Republic 26-45 46-55 56-65 Slovak Republic 100 100 95 95 90 90 85 85 80 80 16-25 26-45 46-55 56-65 16-25 26-45 46-55 56-65 15 Anglo-Saxon countries United Kingdom Ireland 100 100 95 95 90 90 85 85 80 16-25 26-45 46-55 56-65 80 16-25 26-45 46-55 56-65 46-55 56-65 Asian countries Corea Japan 100 100 95 95 90 90 85 85 80 16-25 26-45 46-55 56-65 80 16-25 26-45 16 References Afonso, A. and Aubyn, M. 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(1997): Assessing the effects of school resources on student performance: an update, Educational Evaluation and Policy Analysis, 19(2), 141-164. Hanushek, E.A. (1979): Conceptual and empirical issues in the estimation of educational production functions, Journal of Human Resources, 14 (3), 351-388. Hanushek, E. and Kimko, D. (2000): Schooling, Labor Force Quality, and Economic Growth, American Economic Review, 90: 1184-1208. Hanushek, E. and Woessmann, L. (2008): The Role of Cognitive Skills in Economic Development, Journal of Economic Literature, 46: 607-668. Mazzona, F. (2014): The long-lasting effects of family background: a European cross-country comparison, Economics of Education Review, 40, 25-42. McIntosh, S. and Vignoles, A. (2001): Measuring and Assessing the Impact of Basic Skills on Labour Market Outcomes, Oxford Economic Papers, 53: 453-481. Mincer, J. (1970): The distribution of labor incomes: A survey with special reference to the human capital approach, Journal of Economic Literature, 8 (1): 1-26. Mincer, J. (1974): Schooling, experience and earnings, Columbia University Press, New York. Sutherland, D., Price, R. and Gonand, F. (2009): Improving public spending efficiency in primary and secondary education, OECD Economic Studies, 4: 1-30. Thieme, C., Giménez, V. and Prior, D. (2012): A comparative analysis of the efficiency of national education systems, Asian Pacific Education Review, 13 (1): 1-15. Worthington, A.C. (2001): An empirical survey of frontier efficiency measurement techniques in education, Education Economics, 9(3): 245-268. 18 ANNEX 1. Selection of the functional form of age and experience in education production Table A.1.1. Free Effect of age and experience Variables Schooling Age dummies: see Graph 1.A Experience dummies: see Graph 2.A Woman Immigrant 1st gen. Immigrant 2nd gen. Mother tongue Parents basic ed. Parents secondary ed. Unqualified occupation Without non-regulated training Constant Schwarz Statistic Observations Estimated coefficients 9.93*** 87.65 -21.31*** -39.57 -33.73*** -23.93 -7.42*** -3.65 -19.92*** -13.64 -30.98*** -40.98 -15.13*** -22.42 -27.94*** -43.79 -12.84*** -22.56 585.52*** 155.09 907087.7 78,825 19 Graph 1.A. Effect of age 20 0 -20 -40 -60 -80 -100 1 3 5 7 9 1113151719212325272931333537394143454749 Age Graph 2.A. Effect of experience 40 30 20 10 0 -10 -20 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 Experience Table A.1.2. Linear effect of age and quadratic effect of experience Variables Schooling Age Experience Squared experience Estimated coefficients 9.70*** 87.39 -1.50*** -31.94 1.85*** 20.42 -0.02*** -11.88 Woman -21.23*** Immigrant 1st gen. -34.24*** Immigrant 2nd gen. -7.51*** Mother tongue -39.38 -24.25 -3.68 -20.05*** -13.69 20 Parents basic ed. -31.87*** Parents secondary ed. -15.82*** Unqualified occupation -28.31*** Without non-regulated training -12.33*** Constant 590.32*** Schwarz Statistic Observations -42.28 -23.44 -44.37 -21.78 275.42 906532.7 78,825 ANNEX 2. A proposal to generalize the frontier production function (Approach 2) The starting point is the competence production functions at the country level: ′ µ (1) YiJ =J + β J X iJ + α J SiJ + wiJ where “i” is the individual and “J” the country. X iJ are the characteristics of the individual and SiJ are the number of years of education. From this, we obtain: ′ (2) YiJ − β J X iJ =J + α J SiJ + wiJ µ µ (3) YiJ * =J + α J SiJ + wiJ If “ Yij * ” of equation (3) were directly observable, this equation could be estimated using the standard frontier function technique and assuming a common proposal is: α J . As this is not the case, the a) Estimate (1) by OLS for the different countries. This enables us to obtain a consistent estimation of the “ β ” coefficients. ˆ ˆ= b) From this consistent estimation of “ β ”, we obtain an estimation of Yij* Yij − β ′ X ij . j ˆ This variable “ Yij* ” is an estimation of the competences of individual “i” living in country “J” after excluding the effects of experience, age, sex, and all the other variables on the competences acquired. ˆ* c) Given that “ YiJ ” is the net of the contribution of the remaining variables of education, a frontier function can be estimated for this variable using the number of years of schooling as the only explanatory variable. Following this approach, the efficiency term estimated from this frontier will also refer uniquely to the years of schooling. 21 ANNEX 3. Efficiency indices calculated according to specifications 1 and 2 Table A.3.1. Efficiency indices by levels of study. Specification 1 Lower Secondary Higher Secondary Higher education Belgium 87.02281 88.66001 91.17441 Czech Republic 85.46297 88.39928 90.40039 Denmark 86.66442 89.10681 89.91032 Estonia 86.17697 88.31044 88.65252 Finland 88.54883 89.32155 90.65049 Ireland 82.19496 85.06034 86.77006 Italy 84.83895 87.80328 85.25765 Japan 86.71206 90.28149 90.83987 Korea 83.38552 87.29479 87.14777 Netherlands 86.68916 90.00864 90.84135 Norway 85.86949 88.17571 89.82951 Poland 83.86766 85.2742 87.23417 Slovak Republic 85.85493 89.64773 89.68038 Spain 82.65196 86.29001 86.30075 Sweden 86.9926 89.72025 91.01138 United Kingdom 83.01533 86.13918 87.20603 Table A.3.2. Efficiency indices by levels of study. Specification 2 Lower Secondary Higher Secondary Higher education 87.359 89.06649 91.17212 84.65757 88.20512 90.12897 87.862 90.36086 90.93721 Estonia 86.20949 88.62979 88.8939 Finland 90.68295 91.31189 92.48883 Ireland 81.61584 85.55253 86.69101 Italy 82.47282 86.56282 84.66655 Japan 85.05509 89.02824 89.74224 Korea 85.04414 88.91232 89.33719 Netherlands 87.77496 91.26699 91.95099 Norway 87.44143 89.83485 90.65718 Poland 83.49704 85.52269 87.78531 Belgium Czech Republic Denmark Slovak Republic 85.24813 89.32839 89.73741 Spain 82.47431 86.91864 87.1491 Sweden 88.99646 91.47664 92.45048 United Kingdom 82.14009 85.82652 86.2135 22 SÈRIE DE DOCUMENTS DE TREBALL DE LA XREAP 2006 CREAP2006-01 Matas, A. (GEAP); Raymond, J.Ll. (GEAP) "Economic development and changes in car ownership patterns" (Juny 2006) CREAP2006-02 Trillas, F. (IEB); Montolio, D. (IEB); Duch, N. 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(AQR-IREA) “Informality and overeducation in the labor market of a developing country” (Novembre 2012) XREAP2012-21 Di Paolo, A. (AQR-IREA) “(Endogenous) occupational choices and job satisfaction among recent PhD recipients: evidence from Catalonia” (Desembre 2012) 2013 XREAP2013-01 Segarra, A. (GRIT), García-Quevedo, J. (IEB), Teruel, M. (GRIT) “Financial constraints and the failure of innovation projects” (Març 2013) XREAP2013-02 Osorio, A. M. (RFA-IREA), Bolancé, C. (RFA-IREA), Madise, N., Rathmann, K. “Social Determinants of Child Health in Colombia: Can Community Education Moderate the Effect of Family Characteristics?” (Març 2013) XREAP2013-03 Teixidó-Figueras, J. (GRIT), Duró, J. A. (GRIT) “The building blocks of international ecological footprint inequality: a regression-based decomposition” (Abril 2013) XREAP2013-04 Salcedo-Sanz, S., Carro-Calvo, L., Claramunt, M. (CREB), Castañer, A. (CREB), Marmol, M. (CREB) “An Analysis of Black-box Optimization Problems in Reinsurance: Evolutionary-based Approaches” (Maig 2013) XREAP2013-05 Alcañiz, M. (RFA), Guillén, M. (RFA), Sánchez-Moscona, D. (RFA), Santolino, M. (RFA), Llatje, O., Ramon, Ll. “Prevalence of alcohol-impaired drivers based on random breath tests in a roadside survey” (Juliol 2013) XREAP2013-06 Matas, A. (GEAP & IEB), Raymond, J. Ll. (GEAP & IEB), Roig, J. L. (GEAP) “How market access shapes human capital investment in a peripheral country” (Octubre 2013) XREAP2013-07 Di Paolo, A. (AQR-IREA), Tansel, A. “Returns to Foreign Language Skills in a Developing Country: The Case of Turkey” (Novembre 2013) XREAP2013-08 Fernández Gual, V. (GRIT), Segarra, A. (GRIT) “The Impact of Cooperation on R&D, Innovation andProductivity: an Analysis of Spanish Manufacturing and Services Firms” (Novembre 2013) XREAP2013-09 Bahraoui, Z. (RFA); Bolancé, C. (RFA); Pérez-Marín. A. M. (RFA) “Testing extreme value copulas to estimate the quantile” (Novembre 2013) 2014 XREAP2014-01 Solé-Auró, A. (RFA), Alcañiz, M. (RFA) “Are we living longer but less healthy? Trends in mortality and morbidity in Catalonia (Spain), 1994-2011” (Gener 2014) XREAP2014-02 SÈRIE DE DOCUMENTS DE TREBALL DE LA XREAP Teixidó-Figueres, J. (GRIT), Duro, J. A. (GRIT) “Spatial Polarization of the Ecological Footprint distribution” (Febrer 2014) XREAP2014-03 Cristobal-Cebolla, A.; Gil Lafuente, A. M. (RFA), Merigó Lindhal, J. M. (RFA) “La importancia del control de los costes de la no-calidad en la empresa” (Febrer 2014) XREAP2014-04 Castañer, A. (CREB); Claramunt, M.M. (CREB) “Optimal stop-loss reinsurance: a dependence analysis” (Abril 2014) XREAP2014-05 Di Paolo, A. (AQR-IREA); Matas, A. (GEAP); Raymond, J. Ll. (GEAP) “Job accessibility, employment and job-education mismatch in the metropolitan area of Barcelona” (Maig 2014) XREAP2014-06 Di Paolo, A. (AQR-IREA); Mañé, F. “Are we wasting our talent? Overqualification and overskilling among PhD graduates” (Juny 2014) XREAP2014-07 Segarra, A. (GRIT); Teruel, M. (GRIT); Bové, M. A. (GRIT) “A territorial approach to R&D subsidies: Empirical evidence for Catalonian firms” (Setembre 2014) XREAP2014-08 Ramos, R. (AQR-IREA); Sanromá, E. (IEB); Simón, H. “Public-private sector wage differentials by type of contract: evidence from Spain” (Octubre 2014) XREAP2014-09 Bel, G. (GiM-IREA); Bolancé, C. (Riskcenter-IREA); Guillén, M. (Riskcenter-IREA); Rosell, J. (GiM-IREA) “The environmental effects of changing speed limits: a quantile regression approach” (Desembre 2014) 2015 XREAP2015-01 Bolance, C. (Riskcenter-IREA); Bahraoui, Z. (Riskcenter-IREA), Alemany, R. (Risckcenter-IREA) “Estimating extreme value cumulative distribution functions using bias-corrected kernel approaches” (Gener 2015) XREAP2015-02 Ramos, R. (AQR-IREA); Sanromá, E. (IEB), Simón, H. “An analysis of wage differentials between full- and part-time workers in Spain” (Agost 2015) XREAP2015-03 Cappellari, L.; Di Paolo, A. (AQR-IREA) “Bilingual Schooling and Earnings: Evidence from a Language-in-Education Reform” (Setembre 2015) XREAP2015-04 Álvarez-Albelo, C. D., Manresa, A. (CREB), Pigem-Vigo, M. (CREB) “Growing through trade: The role of foreign growth and domestic tariffs” (Novembre 2015) XREAP2015-05 Caminal, R., Di Paolo, A. (AQR-IREA) Your language or mine? (Novembre 2015) XREAP2015-06 Choi, H. (AQR-IREA), Choi, A. (IEB) When one door closes: the impact of the hagwon curfew on the consumption of private tutoring in the Republic of Korea SÈRIE DE DOCUMENTS DE TREBALL DE LA XREAP (Novembre 2015) 2016 XREAP2016-01 Castañer, A. (CREB, XREAP); Claramunt, M M. (CREB, XREAP), Tadeo, A., Varea, J. (CREB, XREAP) Modelización de la dependencia del número de siniestros. Aplicación a Solvencia II (Setembre 2016) XREAP2016-02 García-Quevedo, J. (IEB, XREAP); Segarra-Blasco, A. (GRIT, XREAP), Teruel, M. (GRIT, XREAP) Financial constraints and the failure of innovation projects (Setembre 2016) XREAP2016-03 Jové-Llopis, E. (GRIT, XREAP); Segarra-Blasco, A. (GRIT, XREAP) What is the role of innovation strategies? Evidence from Spanish firms (Setembre 2016) XREAP2016-04 Albalate, D. (GiM-IREA, XREAP); Rosell, J. (GiM-IREA, XREAP) Persistent and transient efficiency on the stochastic production and cost frontiers – an application to the motorway sector (Octubre 2016) XREAP2016-05 Jofre-Monseny, J. (IEB, XREAP), Silva, J. I., Vázquez-Grenno, J. (IEB, XREAP) Local labor market effects of public employment (Novembre 2016) XREAP2016-06 Garcia-López, M. A. (IEB, XREAP), Hemet, C., Viladecans-Marsal, E. (IEB, XREAP) Next train to the polycentric city: The effect of railroads on subcenter formation (Novembre 2016) XREAP2016-07 Vayá, E. (AQR-IREA, XREAP), García, J. R. (AQR-IREA, XREAP), Murillo, J. (AQR-IREA, XREAP), Romaní, J. (AQR-IREA, XREAP), Suriñach, J. (AQR-IREA, XREAP), Economic impact of cruise activity: the port of Barcelona (Desembre 2016) XREAP2016-08 Ayuso, M. (Riskcenter, XREAP), Guillen, M. (Riskcenter, XREAP), Nielsen, J. P. Improving automobile insurance ratemaking using telematics: incorporating mileage and driver behaviour data (Desembre 2016) XREAP2016-09 Ruíz, A. (GEAP, XREAP), Matas, A. (GEAP, XREAP), Raymond, J. Ll. How do road infrastructure investments affect the regional economy? Evidence from Spain (Desembre 2016) 2017 XREAP2017-01 Bernardo, V. (GiM-IREA, XREAP); Fageda, X. (GiM-IREA, XREAP) Globalization, long-haul flights and inter-city connections (Octubre 2017) XREAP2017-02 Di Paolo, A. (AQR-IREA, XREAP); Tansel, A. Analyzing Wage Differentials by Fields of Study: Evidence from Turkey (Octubre 2017) XREAP2017-03 Melguizo, C. (AQR-IREA, XREAP); Royuela, V. (AQR-IREA, XREAP) What drives migration moves across urban areas in Spain? Evidence from the great recession (Octubre 2017) SÈRIE DE DOCUMENTS DE TREBALL DE LA XREAP XREAP2017-04 Boonen, T.J., Guillén, M. (RISKCENTER, XREAP); Santolino, M. (RISKCENTER, XREAP) Forecasting compositional risk allocations (Octubre 2017) XREAP2017-05 Curto‐Grau, M. (IEB, XREAP), Solé‐Ollé, A. (IEB, XREAP), Sorribas‐Navarro, P. (IEB, XREAP) Does electoral competition curb party favoritism? (Novembre 2017) XREAP2017-06 Esteller, A. (IEB, XREAP), Piolatto, A. (IEB, XREAP), Rablen, M. D. Taxing high-income earners: tax avoidance and mobility (Novembre 2017) XREAP2017-07 Bolancé, C. (RISKCENTER, XREAP), Vernic, R Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution (Novembre 2017) XREAP2017-08 Albalate, D. (GiM-IREA, XREAP), Bel-Piñana, P. (GiM-IREA, XREAP) Public Private Partnership management effects on road safety outcomes (Novembre 2017) XREAP2017-09 Teruel, M. (GRIT, XREAP), Segarra, A. (GRIT, XREAP) Gender diversity, R&D teams and patents: An application to Spanish firms (Novembre 2017) XREAP2017-10 Cuberes, D., Teignier, M. (CREB, XREAP) How Costly Are Labor Gender Gaps? Estimates by Age Group for the Balkans and Turkey (Novembre 2017) XREAP2017-11 Murilló, I. P., Raymond, J. L. (GEAP, XREAP), Calero, J. (IEB, XREAP), Efficiency in the transformation of schooling into competences: A cross-country analysis using PIAAC data (Novembre 2017) xarxa.xreap@gmail.com