Mens sana in corpore sano: the effects of sport on children’s learning in Italy

This study analyses the impact of sports participation on both cognitive and non-cognitive skills using micro data from Italian fifth grade pupils’ test scores. The performance of students is investigated by estimating different frequencies of sports practice. Using sports facilities as an instrument for sports participation, we find that its effect on school performance is positive, but only for an intermediate level of training. Sports drills have a negative effect, especially on females, when the extremes come into play: both inactivity and full-week action. On the contrary, daily sports practice seems to be effective on non-cognitive skills, revealing positive contributions to some personality traits that represent a major component of human capital.


Introduction
The main focus of this paper is on how human capital can be increased through sports activity for children by incrementing the chances of immediate school performance and the likelihood of success later in life. The key research questions can be expressed as follows: if sport is conventionally believed to be good for general wellbeing, can it also help enhance both cognitive and non-cognitive skills? Can sports practice improve learning efficiency and contribute to building a stronger knowledge base for the following steps of educational development?
These seem relevant questions since considering them differently can produce relevant and deep implications for the educational system, the labour market and overall potential economic growth.
It is common knowledge that practising sports can be very important for children, not only because of the enjoyment it brings, but also because of its many physical, social and emotional benefits (American Academy of Pediatrics, 2001). In this paper, the impact of sporting activities on the learning process is analysed by focusing on late childhood, an essential phase in both cognitive and non-cognitive human growth (Heckman et. al, 2006).
In particular, our database gives information about Italian children aged 10, a crucial stage representing a cognitive transition between the end of early childhood and the beginning of pre-adolescence. Does sport bring only immediate satisfaction or does it contribute to creating skills that are crucial for children and their future development?
From the empirical point of view, the classical problem which arises in this kind of analysis is due to potential endogeneity and reverse causality. Unobservable factors linked to the skills and abilities of each student can influence both sports participation and its effects.
The strategy to approach this problem, as most literature suggests, has been instrumental variables (2SLS) estimation. The choice of the instrumental variable is quite challenging and it is discussed and verified in every research to show that a strong and valid instrument has been used.
This research includes a variable representing sports facilities/space availability which, apart from the required characteristics, is one of the more detailed and reliable quantitative references for indoor and outdoor sports facilities in Italy (CNEL, 2003).
The econometric model specification tries to control the impact of other important factors linked to family characteristics and the personal characteristics of each student. The model, on the one hand, estimates variables on the education and profession of parents and, on the other hand, a rich set of variables measuring biographical characteristics, educational path and study facilities.
The dependent variables are differentiated according to the kind of human capital considered: on the one hand, school grades, for estimating cognitive skills and, on the other hand, a synthesis of personality characteristics, for estimating non-cognitive skills. Each model is estimated for both boys and girls, since the latter have internationally achieved very different, and often better, results in the last few years.
The first positive impact of sports training on human capital performance confirms the literature. However, this positive influence seems effective up to a certain level of training intensity, apart from girls who can devote more time to sport without affecting excellence in school results.
The second set of results shows that non-cognitive skills seem to benefit from the most intense level of sports training, since more intense practice could contribute better to enhancing this human capital component.
The contribution of this study seems quite innovative because it crosses different dimensions-gender, intensity, type of human capital-working on national data. Economia Politica (2023) 40:703-729 The remainder of the paper is organised as follows: Sect. 2 presents a brief literature review, Sect. 3 describes the dataset, Sect. 4 shows the empirical method adopted for the econometric estimation, Sect. 5 discusses our results and, lastly, Sect. 6 concludes the study by offering some policy insights.

Literature review
In the last thirty years, the literature has investigated the impact of sports on human capital, measuring outcomes by using different variables, such as school attainment, educational grade and educational degree (Pfeifer & Cornelißen, 2010). The learning process involves both education and other pursuits, which can influence school outcomes directly, by increasing school productivity, and indirectly, by maximising the chances of occupational success and a high income. Among these pursuits, sport plays a crucial role, since it is the extracurricular activity most often practised by children (NCES-National Center for Education, 1995) and takes up a considerable portion of their free time. From a theoretical point of view, the literature has explored the relation between sport and human capital following two different approaches, which primarily interpret sport as an alternative choice of time allocation.
On the one hand, sport could be regarded as a profitable way of spending leisure time. This is because it not only promotes fruitful use of busy time, enabling children to study or do homework with more dedication, but it also limits the time spent on those leisure activities-such as drinking, smoking, or taking drugs-that might reduce human capital and future productivity. Sport could indeed be considered a good investment, as it provides immediate gratification and boosts the skills-knowledge, ability, self-discipline-that have the potential to increase future earnings. In a standard model, the positive effect of a further hour spent doing sports increases, with marginal benefits on human capital (Leeds, 2015). The contribution of cognitive and non-cognitive skills can marginally exceed the cost of human capital. If sport can contribute to an increase in human capital, the optimal amount of training should grow along with good results for students, either immediate or deferred.
On the other hand, sport could be described as time allocation that provides immediate gratification, but does not contribute to skill creation, because it reduces the time devoted to much more productive activities in terms of human capital, such as studying or reading. This way of spending leisure time does not enhance prospective earnings and future well-being. Since skills are not improved by physical activity, sports practice should be considered a sort of consumption good, without any durable contribution to human capital growth (Eide & Ronan, 2001).
Empirical studies focusing on the relation between sports practice and human capital at all school levels have produced heterogeneous results. The majority of them have detected a positive effect, which seems to suggest that sport both enhances efficient time allocation and reduces time spent in unproductive leisure activities. 1
Recent investigations have looked at the influence of sport on different kinds of human capital. The main idea is that positive spillovers deriving from sporting activities can generate benefits going far beyond any impact on school grades. Ample evidence has emerged on the effects of sports on non-cognitive skills, whatever definition is chosen for them.
Positive effects on non-cognitive skills have been confirmed by different studies, which have found that participation in sports can improve not only school grades, but overall student behaviour and relationships with peers (Felfe, et al., 2016). Pfeifer and Cornelißen (2010) point out that sporting activities can provide benefits to skills other than those measured by school performance. They equate these human capital components with three main factors: health, soft skills (taking orders, leadership, teamwork) and behavioural habits (perseverance, self-esteem).
Non-cognitive skills seem to have important interactions with cognitive skills. In some studies, the former have been recognised as having effects on school attainment that are as crucial as those of cognitive skills (Heckman et al., 2006), particularly in terms of future success on the labour market, because non-cognitive skills stimulate effort and foster productivity (Brunello & Schlotter, 2011). Other works underline that the importance of non-cognitive skills derives specifically from their complementarity with cognitive skills (Lechner & Downward, 2017).
A more controversial, yet fundamental, issue concerns how to define and measure non-cognitive skills, since different personality traits are used in empirical studies depending on data availability or specific research needs. 2 Non-cognitive skills have been interpreted by some researchers as productive human capital or as social capital acquired through interpersonal skills and through social adaptability learnt within sports teams (Persico et al., 2010).
Although the debate is still ongoing, a widely accepted approach is based on five main personality traits that are both strictly connected with productivity and specifically rewarded by the labour market: extraversion, agreeableness, conscientiousness, emotional stability and autonomy (Digman, 1990;Nyhus & Pons, 2005). In economic psychology and behavioural economics, the analytical method based on the so called Big Five is rather commonly adopted to refer to these five personality traits in order to measure non-cognitive skills (Borghans et al., 2008;Cabus & Napierala, 2021;Zhou, 2016). They have widely recognized stability and reliability, which can be found in their summary of the individual heterogeneities of soft skills (Humphries & Kosse, 2017). In addition, the literature underlines that these components of human capital only weakly correlate with standard measures of cleverness, such as IQ or school grades (Brunello & Schlotter, 2011). Hence, exploring the impact of sports practice might yield different results compared to a traditional analysis of cognitive skills.
Although it might be difficult to agree on a shared point of view regarding the nature of non-cognitive skills, the most reliable measure, i.e., the use of the Big Five, seems to be the best solution for at least two reasons. Firstly, it relies on the contribution of disciplines more suited to finely exploring personal characteristics, such as psychology or sociology; secondly, its metrics and results are strongly context-dependent (Hulten & Ramey, 2019).
Non-cognitive skills are particularly relevant during childhood, given their malleability through training and intervention (Hulten & Ramey, 2019;Zhou, 2016). As Heckman et al., (2006, p. 4) points out, they are shaped early in the lifecycle, and non-cognitive components can have a profound influence on working and social performance throughout a person's life. Recent developments of the human capital theory emphasise the importance of dynamic complementarities, meaning that capabilities deriving from non-cognitive skills at one stage in life increase the productivity of following investments in capabilities. This also means that greater investments in skills during childhood-both cognitive and non-cognitive-boost the productivity of human capital during adolescence and later on in life (Heckman, 2007(Heckman, , 2008. These effects have been confirmed by empirical analyses (Almond & Currie, 2011) that explain how personality traits can be predictive of socioeconomic success (Borghans et al., 2008).
Overall, positive results about the relation between sport and human capital prevail in the literature, both for cognitive and non-cognitive skills (Felfe, et al., 2016;Pfeifer & Cornelißen, 2010). However, the impact of sport on human capital crucially depends on certain factors, in particular on the gender of the students and on training frequency. Some studies suggest dealing with the effects of sports on men and women separately, since they practise sports in different ways. Considering children aged 6-10 in Italy, substantial differences in sports participation emerge between boys and girls, since 69.8% of the former and 60.3% of the latter play sports (ISTAT, 2012).
The literature has also examined gender differences in approaching competitive sports starting from the age of 3 or 4, when males are more willing to enter competitions and achieve better results in the short term (Gneezy & Rustichini, 2004;Sutter & Glätzle-Rützle, 2010). Some authors show that sport can effectively contribute to gender equality, being associated with better school performance (Felfe, et al., 2016;Pfeifer & Cornelißen, 2010). In some cases, sports practice can be a crucial way of entering male-dominated professions and portions of the labour market (Stevenson, 2010).
The impact of different levels of training intensity, and in particular of competitive disciplines, is another widely debated issue, with empirical analyses yielding different, and sometimes opposite, results. In some works, high-intensity training and competitive sports are even more beneficial for human capital (Lipscomb, 2007;Robst & Keil, 2000), whereas other studies underline the trade-off in terms of time allocation, when sport training becomes time consuming (Eide & Ronan, 2001;Maher et al., 2016). The direction of the effects deriving from participation in intense sporting activity, in particular, seems to be empirically and theoretically uncertain. For 10-year-old children, hard training might be double-edged since, on the one hand, it can be exhausting and decrease 1 3 well-being but, on the other hand, it might increase self-esteem, with positive spillovers in education as a whole.

Data and variables
This analysis uses microdata on students collected by the Italian National Institute for the Evaluation of Education and Training (INVALSI) in 2009/2010. Each year, INVALSI gathers data on student achievements at different grades, in both primary (ISCED 1) and secondary school (ISCED 2), by using standardised tests.
In school year 2009/2010, the questionnaires were finally made compulsory for all classes in Italy, so that the wealth of information available for that year offers a unique opportunity for a deeper investigation (INVALSI, 2012a, b, c).
In the fifth grade of primary school, which is the year this paper analyses, pupils must fill in three questionnaires regarding their two main school subjects (Italian and Mathematics) and a very informative student questionnaire. The latter contains biographical data and questions regarding the students' family/social background, their feelings about the test, and their degree of commitment to studying and participating in school activities. The analysis is conducted separately for boys and girls since, as widely demonstrated by the literature mentioned above, gender differences in this regard should be taken into account when studying the impact of sport on homogeneous students.
The INVALSI test results provide a relevant basis both for the assessment of students' achievements and for the evaluation and self-evaluation of schools and teachers. The international literature supports the implementation of education accountability approaches based on tests of educational achievements (Hanushek & Woessmann, 2011) and teachers' performance (Meroni & Abbiati, 2012). Criticism of INVALSI tests is worth mentioning too, even though this issue cannot be examined in depth within this analysis. There are many different objections to INVALSI, regarding both test administration and questions methodology, which are considered inadequate for the Italian learning system and school organisation (Trinchero, 2014). Nevertheless, the general informative power of these data is unique in Italy, as confirmed by different studies and cross comparisons with similar databases (Mullis et al., 2008;OECD, 2010;Petracco-Giudiciet al., 2010;Sirin, 2005).
The available dataset comprises 112,876 males and 105,932 females, about which we have complete data for our analysis. These numbers represent the population of fifth grade students in Italy with data available for all the variables investigated. Approximately 60% of the 10-year-old students considered here do not practise any sports, which may seem quite a high percentage when compared to other sample surveys, but it confirms the results of other investigations pointing to a worrisome increase in children's sedentariness (Istituto Superiore di Sanità, 2008). This is strictly connected to pupils' changing lifestyles, since more and more time is devoted to watching television and playing video games, at the expense of physical activity (Public Health England, 2013).
The INVALSI dataset makes it possible to split the data concerning sports activities into four groups (Table 1). A binary classification (1/0) is adopted for each group, measuring the frequency of sports activities practised by each 10-year-old student according to the following four intensity levels: no sport, one or two times per week, three or four times per week and five times or more per week. The INVALSI test evaluates Italian and Maths knowledge using grades from 1 to 10; the higher the mark, the better. Table 1 shows that Italian and Maths grades are regarded as measures of the cognitive component of human capital.
The other component of human capital, the one related to non-cognitive skills, is assessed following the results obtained by economic psychology research on those personality traits that have greater importance, as mentioned in the previous section (Nyhus & Pons, 2005). These factors are usually uncorrelated with IQ (Brunello & Schlotter, 2011) and this is confirmed by the data analysed in this paper, since the correlation between measures of cognitive and non-cognitive skills is less than 10%. Table 2 presents the list of cognitive traits used for generating non-cognitive variables, with a very short description of each of them. The last column displays the real items of the INVALSI questionnaire used to evaluate each trait (2005).
All answers are dichotomised in 1 (yes) and 0 (no) to exclusively detect the presence of each trait. The final variable related to non-cognitive skills is obtained as a factor analysis result of the five traits in order to represent, by means of a single variable, a proxy for non-cognitive skills, as suggested by the literature mentioned above. 3 The first factor accounts for significant shares of the total variance both for boys (70.8%) and for girls (62.5%). Agreeableness explains a great part of the common variance of both factors.
The instrumental variable is the amount of spaces and facilities for sports in each macro-region and municipality size (CNEL, 2003). Data on sports facilities came from a deep and detailed survey of the National Council for Economics and Labour carried out in 2022 with the aim of knowing the real conditions of sports facilities. Different types of sources-data, financing documents, miscellaneous documentshave been connected and checked by local authorities to achieve the best possible picture of sports facilities.
For 10-year-old children, non-cognitive skills might be generally considered more malleable than at older ages (Brunello and Schlotter, 2011;Carneiro et al., 2007;Coneus et al., 2012). However, some authors consider a high degree of stability linked to non-cognitive skills ascribable to personal characters (Kautz et al., 2014). Most of all, malleability of non-cognitive skills in children seems to derive from the higher adaptability of this kind of skill to learning processes and from personal efforts to increase this kind of skill (Delavande et al., 2019;Mühlenweg et al., 2012).
The sport facilities index causally affects the amount of sport activities but is independent of cognitive and non-cognitive abilities (Brechot et al., 2017;Leeds, 2015).
Following the empirical literature on human capital, we estimate two groups of control variables. A first cluster regards family characteristics: level of education and professional condition of the father (Father's educational attainment i , Father's professional level i ) and the mother (Mother's educational attainment i, Mother's professional level i ). A second cluster concerns some of the childrens' characteristics: school path regularity (Education regularity i ), nursery school attendance (Nursery School i ), nationality (Italian nationality i ) and studying facilities (Facilities i ). This last variable is a factor that represents the best linear combination of some facilities that might support studying: availability of a quiet place for studying, a computer, encyclopaedias, Internet access, a personal desk and bedroom. 4 As in other studies (Pfeifer & Cornelißen, 2010;Rees & Sabia, 2010) the inclusion of these batteries of control variables captures some general determinants of human capital which cannot be neglected and helps focus better on the individual effect of sports activity.

Endogeneity and model specification
Estimating the impact of sport on human capital may pose a considerable risk of endogeneity, since causation could be in the opposite direction to that considered or in both ways simultaneously (Leeds, 2015). Pupils who are keen on studying are more likely to practise sports; obviously, in these cases, good school grades are not due to sports. Some authors detect a potential problem of reverse causality, good school grades may be the effect of more intense sports participation, causing endogeneity and biased results.
Some other studies provide evidence of the fact that the effect of sport on educational attainment and on wages is for the most part due to inherent capabilities of more able or industrious individuals (Barron, et al., 2000, 409). Other researches underline that the problem has mainly to do with selection factors affecting both school participation and learning performance, which can cause some degree of bias (Lipscomb, 2007).
For the sake of simplicity, the very core of the problem might be self-selection, which can be expressed by a basic research question: is it sports practice that contributes to achieving better school performance or the other way round?
Endogeneity raises the crucial issue of finding a proper instrumental variable (IV) that could be, at the same time, able to predict sports participation, but uncorrelated with school performance.
The literature shows that different kinds of instrumental variables have been adopted in order to predict students' participation, such as height (Eide & Ronan, 2001), sports participation intensity (Stevenson, 2010), and income and family characteristics (Barron, et al, 2000). In other cases, researchers have simply adopted a measure of municipality size as IV, since opportunities to do sports are linked to reaching the place of training in a short time (Felfe, et al., 2016;Pfeifer & Cornelißen, 2010;Steinmayr et al., 2011). The choice of instrumental variables often depends primarily on the actual availability of suitable data.
In this paper, the instrumental variable used is based on sports facilities/space availability (CNEL, 2003). 5 The underlying idea is that the availability of training grounds or swimming pools increases the chances of practising sports independently of school grades or non-cognitive skills. There is wide evidence in the international literature that a strong link exists between sports facilities in a city and participation in sports (Hallmann et al., 2012;Lechner and Downward, 2017;Ruseski et al., 2014;Wicker et al., 2013).
This instrumental variable responds positively to the most relevant conditions, since it displays a stronger correlation with sports practice dummies than with school performance. Its relevance has also been tested with the rule of thumb of the F-statistic, applied in the first stage and being always greater than 10. 6 Exclusion restriction applies to the facilities/space availability instrumental variable, since it seems to be implausible that facilities for sports could be directly related to school grades for different reasons. Firstly, sports facilities/space for 10-year-old children is constrained to a limited area close to their residence, in particular open spaces. Following this approach, sport is a physical activity open to all children without any pre-selection based on capacity or performance levels. This implies that the density of facilities/space could directly influence sports participation, but not school grades (Pfeifer & Cornelißen, 2010). Secondly, sports facilities in Italy are quite old on average since 62% date back to before 1981 and 30% before 1991 (CNEL, 2003). Given the age of the sports facilities, they cannot be correlated with families' location preferences nor with the children's capabilities (Felfe et al., 2016). Thirdly, some studies demonstrate that the availability of sports facilities can lead to greater sports participation and increase general results, particularly in developing countries (Majid Khan, et al., 2021). Lastly, indicators on the density of sports facilities have been widely adopted as an IV for estimating the impact of sports participation on different personal dimensions such as happiness or health. The starting hypothesis that sports facilities are uncorrelated to an unobservable factor is a shared consideration on exclusion restriction (Brechot et al., 2017;Ruseski et al., 2014).
The econometric approach adopted in order to control for any potential source of endogeneity is a two-stage IV applied to a nonlinear model (Terza, et al., 2008;Woolridge, 2010) using a probit-two-stage least square method (Cerulli, 2014). The predicted probabilities of the treatment variable estimated in the first stageprobit model-are used as instruments in the second stage. The original idea, which is in Woolridge (2002, 623) is based on the key assumption on the instruments, which goes far beyond the zero correlation assumption between the error term and elements of x in IV-2SLS. This concerns the zero conditional mean assumption, which is a strong exogeneity assumption since it means that ε is uncorrelated with any function both of the explanatory variables and of instruments (Musolesi & Huiban, 2010, 69). It follows that the function is correctly specified.
The model specification of the two-stage model considers in the first stage the estimation of the instrument of sports participation-sports facilities availabilityand in the second stage the IV estimator is used with other independent variables.
As clearly explained in Musolesi and Huiban (2010) this two-step approach displays some characteristics that ensure efficiency. The instrumental variables 2SLS estimator used in the second step does not need to be correctly specified, since it is asymptotically the most efficient and it remains valid. This estimator is consistent because requirements for consistency are not as strong as in 2SLS (White, 1982), even in the case that the probit model in the first equation is misspecified. 7 For the purpose of our analytical objectives, the model specification of the first stage is estimated for each of the four levels of training intensity described above. Each level of sports participation is regressed separately from the others in order to isolate and evaluate the real impact of each intensity level of sports practice individually and independently from the effect of other grades of training frequency.
Model specification based on instrumental variables 2SLS estimation is common to a great majority of studies about the effect of sports participation (Eide & Ronan, 2001;Pfeifer & Cornelißen, 2010;Rees & Sabia, 2010).
Apart from the general advantages mentioned above, this model allows deriving a consistent estimate of the effect of sports participation controlling for unobserved factors.
Studying the specific contribution of each level of sports activity by means of a dichotomous variable can focus on the estimation of each level while keeping the others fixed.
The first stage is a probit model of sports activity, where the variable related to sports facilities (Sportfacil) acts as the instrument for each individual (i). Control variables are those estimated also at the second stage.
First Stage In the second stage, two estimation methods are adopted for the three dependent variables, regressed following two models: in the first model (2) the Maths and Italian grades are regressed with an ordered logit model because of the nature of class grades; in the second estimation (3), the non-cognitive skills variable is regressed with an OLS model since the discrete number representing non cognitive skills represents five factors of difference characters. The battery of dependent variables was presented above.
In the last part of both equations, 2 and 3, the predicted residual of the first stage is u i and that of the second stage is e.
Second Stage (1) As far as concerns regression (2), it represents a treatment random coefficient model (Wooldridge, 2002), which is the best way to estimate the average treatment effect of sports intensity for each individual since, as mentioned above, the probability of doing sports (i.e., being treated) estimated in the first equation generates the smallest projection error. 8 Equation 3 represents a linear regression estimating Non-cognitive skill i for each individual i, which is a continuous variable obtained in the way explained in the previous section. Table 3 shows the results of the first stage, in which the IV appears to be fairly well correlated with sports activity, confirming its adaptability as an instrumental variable.

Estimation results
The small coefficients depend primarily on the sample size. Estimating the first stage-sports facilities on sports practice-of 2SLS with OLS we obtained the control of the F-statistics > 10, as literature suggests for the single endogenous regressor and R2 for the explanatory power. 9 The estimation results about the effects of sports practice on Italian and Maths grades are presented in Table 4 for males and Table 5 for females, using the instrumented variable for sports training. The results for males are very similar in terms of both sign and coefficient magnitude, and a single interpretation of the main results is exhaustive, except for a few specific cases.
The Sport instrumental variable indicates that a negative sign prevails only for two levels of training intensity, i.e., 1-2 times per week and no sports activity at all. The case of 1-2 training sessions displays the worst result in terms of coefficient magnitude (− 8.07). This suggests that, in case of limited weekly frequency, sport can interfere with study time and reduce school performance, while health benefits are also limited. Not being involved in sports can have a detrimental effect on grades, since it takes time away from learning activities. At least in some cases, this might mean that children who do not have the chance to practise sports only have worse alternatives as for how to spend their time.
On the other hand, the strongest positive effects are concentrated at the intermediate level of sports training: 3-4 times per week (13.33). The biggest influence of sport on school grades seems to be reached at this level of involvement, which (3) Non − cognitive skill i = Sport instrumental variable i + Father � s educational attainment i 2 + Mother � s educational attainment i 3 + Father � s professional level i 4 + Mother � s professional level i 5 + Education regularity i 6 + Nursery school i 7 + Italian nationality i 8 + Facilities i 9 + e 8 The Stata command ivtreatreg is used for the Probit-2SLSL estimation (Cerulli, 2014). 9 Results are available upon request.

Table 3
First step of estimation   represents optimal time allocation between doing sports and studying, as confirmed by the estimation results about a full week of training. In this case, even though the effect on school records remains positive (2.92), the magnitude is dramatically lower than in the intermediate case.
The above confirms that sport can have a very limited effect on school grades because, over a certain threshold of involvement, it can make it difficult for students to meet school requirements (Rees & Sabia, 2010). In other words, our evidence suggests that, when sport becomes a daily commitment, it can be hard to combine it with the study time needed to achieve high school grades. 10 As some studies point out, doing sports and studying are both very time-consuming activities (Pfeifer and Cornelißen, 2010), and parents should help their children in balancing both pursuits. Hence, sport becomes a major investment good, with deferred benefits in terms of human capital over an individual's lifetime.
The prevalent sign of the overall set of control variables is positive, as widely expected given the literature contributions on the role of both pupils' and families' characteristics in educational performance. The variables referring to the family background show a clear influence on school grades, in line with a well-established line of research. In particular, the parents' educational level has an influence on the attainment of high school grades in all estimations, even though the role of the mother's attainment in training done 3-4 times a week is unexpectedly negative (− 0.023 for Italian grades and − 0.53 for Maths grades). The profession of the parents seems to have a negative impact on school grades, except for the highest training frequency case, and its effect is most evident when sport is practised at a competitive level and the parents' support might prove crucial. On the whole, higher human capital performance depends more on the level of human capital accumulated by the parents than on their professional position.
The children's educational path displays a positive sign for both education regularity and nursery school attendance, which confirms that good results are more likely to be obtained when the educational path is characterised by both an early beginning and a regular development, as highlighted by Heckman et al. (2006).
The control variable related to studying facilities yields mixed results: it has the strongest impact, on average, when sports practice is more intense, but it does not have a homogeneous effect on school grades. Being of Italian nationality is always positive and significant in explaining good school results in both Italian and Maths, particularly when sport is practised 1-2 times per week. From an overall perspective, the Italian nationality yields the highest coefficients, with the exception of sport, suggesting that it might influence the human capital investment and results.
The advantage given by the Italian nationality reaches its peak when the sporting activity is moderate, but it is also positive in the case of no sport at all. Only this intermediate level could contribute to school performance, but it is not statistically significant. This is the only clear case in which the model shows total absence of explanatory power for all variables. The feeble sign of a possible positive effect of nationality may be a matter for future research.   The magnitude of the estimated effect of sport on females is generally greater than on males, as many studies have already pointed out (Lechner & Downward, 2017;Lipscomb, 2007;Lumpkin & Favor, 2012;Pfeifer & Cornelißen, 2010;Tonello, 2012;Yanık, 2018). Positive results for females are achieved under a narrow set of circumstances, with on average higher coefficients than for males. However, the coefficients are not statistically significant for levels of intensity greater than 2 times per week. It seems that girls' school outcomes benefit only from a moderate level of sporting activity.
However, the results regarding females are decidedly negative in all the other situations, i.e., both when training is very light and when it is absent. This could be ascribed to more time specifically allocated to studying, which might also be a reason for the higher grades achieved by girls. Nevertheless, sport significantly contributes to the performance of female students, since they practise it with different objectives compared to males. Indeed, recent studies have revealed that for boys sport is mainly an outlet for competition and visibility, whereas for girls it can satisfy the need for friendship and sociability (Soares et al., 2013). Thus, as far as concerns girls, the positive effect of sports could be the result of a conscious double choice about which discipline to choose and how hard to practise it. Overall, it seems that the good results attained by females might derive mainly from different time allocation choices and different levels of commitment to school activities (Eide & Ronan, 2001).
Our analysis of the impact of participating in sports follows in Table 6, where the results about non-cognitive skills are presented. Here, the outputs estimation indicates that the more sport is practised, the more non-cognitive skills are developed, both for males and females. Sport greatly contributes to the development of some personal and relational traits of children, which are important for them and will be even more vital later in life to ensure both educational and labour market success.
Indeed, sport contributes to the learning process in a different way compared to what emerges from school performance. It might beget skill formation not only later in life, as in Felfe et al. (2016), but also at the actual time of practising.
In particular, the relational dimension may be greatly enhanced in team sports, in which one can learn non-cognitive skills depending on training duration. These results might confirm that sport competition can be beneficial in supporting some personal characteristics, i.e., discipline, confidence, motivation and competitive spirit, with positive deferred spillovers in the labour market and in academic outcomes (Long & Caudill, 1991). Moreover, non-cognitive skills can benefit from peer effects and social relations when team participants are amenable to such skills (Lipscomb, 2007).
The marginal benefits of sporting activities do not appear to be nullified by the increasing marginal cost of doing sports, as happens for school performance. On the contrary, non-cognitive benefits increase substantially only after some high level of commitment and training in a sport discipline is attained.

3
The above results are in line with the literature, which states that sporting activities, especially when pursued almost every day of the week, might have a strong connection with social capital, even more than with formal human capital, since they can increase young people's social adaptability and capacity to develop their skills (Rees & Sabia, 2010). Personal and family resources and endowments are sometimes not as effective in accounting for learning and educational results as sports practice may be (Persico et al., 2004). Furthermore, time allocation cannot explain good results linked to frequent physical activity, which helps develop certain traits mentioned in the literature, such as self-discipline or teamwork, that can only be learnt by being involved in sports (Schultz, 2017). This could suggest that sport is not as secondary to the learning process as generally assumed in educational organizations over the last decades.
The role of the other variables in the model, concerning personal and family characteristics, does not change in relation to non-cognitive skills, and what has been described above for Italian and Maths grades remains valid.
Finally, a suggestion for education policy seems to emerge quite clearly from this analysis. The practice of sports should not be neglected, given its positive effects on both cognitive and non-cognitive skills. On the contrary, it should be strongly supported, particularly at school, where the learning process can be positively influenced by well-organised sports teaching activities. Moreover, sport type and intensity should be carefully planned and connected with other disciplines to achieve best results and contribute to increasing the students' human capital, both cognitive and non-cognitive.

Conclusions
The relationship between sport and human capital has been widely debated, since sports practice could be regarded either as an investment or as a consumption good, depending on how time spent doing sports impacts on school performance. In the former case, sport gives children the chance to improve their human capital, because it can increase both productivity at school and potential career opportunities on the labour market. In the latter case, sport can provide immediate gratification, but at the expense of forgoing future income.
The contribution of this study relies on data collected by the Italian National Institute for the Evaluation of Education and Training on pupils aged 10, i.e., at the end of primary school. This rich database offers the opportunity to explore both cognitive and non-cognitive knowledge. Cognitive human capital derives from standardised tests of Italian language and Mathematics, while a non-cognitive human capital indicator has been created based on a tried and tested approach considering the contribution of five personality traits to the economic performance of individuals (Nyhus & Pons, 2005).
The model uses a two-stage least square estimation and instrumental variables that are effective in tackling reversed causality, which is a rather serious problem in this type of model. In particular, the density of space/facilities devoted to sports in each municipality seems to be a very appropriate index for measuring the likelihood of children engaging in sports.
The main result, for both females and males, is that sport provides its best contribution to human capital if the time investment required is compatible with school commitments. Our estimations suggest that, in particular for girls, training 3-4 times a week seems to be the most efficient threshold and the only one for which a positive effect is revealed, whereas opting for different levels of intensity might turn out to be counterproductive. In other words, competitive sports, it appears, are not easily reconcilable with better grades at school. Additionally, sporting activities in general are a profitable investment in terms of human capital only within a threshold of n-times per week, otherwise they become quite close to a consumption good that can crowd out other activities, such as doing homework, with a negative impact on students' performance. Overall, moderate participation in sports is very positive for the performance of pupils in both Italian and Maths. The intensity of this effect is much greater for girls; for boys, more frequent (daily) training can also have a positive impact, but this would be counterproductive for girls.
Our investigation also shows that intense sports activity is positive for non-cognitive knowledge, as it helps develop and strengthen some personality traits that might lead to economic success in adulthood. These soft skills can be crucial in many circumstances to take economically relevant actions, such as, for example, making complex decisions, solving problems, acting autonomously, and interacting well with others. Moreover, all these skills can have a positive impact on school attainment and labour market performance (Brunello & Schlotter, 2011), generating fruitful interactions with cognitive skills, which should be further investigated.
Even though many control variables typical of human capital estimation models, related to family and education, have the same effect on cognitive and non-cognitive skills, this paper indicates that they react differently depending on the intensity of sports practice. This relation deserves a deeper analysis, since it might be valid only for certain categories of sports, students or educational systems. A potentially fruitful research objective could be focused on the role of sport in preventing students dropping out of education and school dispersion, at least in some difficult environments (Nosvelli, 2013).
The overall results of this research show that the famous Latin phrase mens sana in corpora sano (a healthy mind in a healthy body) is only partially true, since it all crucially depends on the quality and quantity of both sport and human capital. Education policies should take this into careful consideration.