The present model partly draws on the contribution of Akerlof and Kranton (2002) and of Autiero (2015); Autiero and O’Higgins (2016) in analysing the influence of social identity and the locus of control on scholastic effort; nevertheless, we take into consideration ethnic identity with its multidimensionality as a specific aspect of social identity. Of relevance to our different approach, in the contribution of Akerlof and Kranton (2002), students decide to identify with a social group in school and the benefits from this choice depend on the self-image characterizing such group. Changes in utility are affected by the distance of individual characteristics and behaviour respectively from the ideal promoted by the social category. Importantly, they choose to follow a specific group and therefore the effort level fitting into it, whereas, in our case in line with Autiero (2015), social identity—precisely ethnic identity—directly affects the utility from scholastic effort—e
i
—by shaping children’s motivations to exert effort. This occurs through the internalization of the values transmitted by parents, peers and ethnic community members that determine children’s perceived importance given to engaging in academic tasks, which determines the utility from effort. In detail, we characterize a child’s ethnic identity in part in terms of adaptation to the mainstream society’s school and define it as I
Oki
, which is affected by the acculturation orientations of child i’s parents belonging to the ethnic group k—I
ki
—and of her peers in school belonging to the same ethnic community—Ī
k
; the specification of children’s adaptation is \( {I}_{Oki}={I}_{k i}^{\beta (Di)}{\overline{I}}_k^{\lambda (Di)} \). Parents giving great importance to integration consider scholastic achievements as a means for their children to integrate into the host country; alternatively, they may think that adaptation to school in the host country will be fruitless in order to achieve socio-economic upward mobility. As already mentioned, parental acculturation orientations shape their offspring’s identity through the transmission of the values and cultural expectations either fostering or hampering children’s adaptation to school and thus their motivation to achieve. In school, children may frequently be exposed also to the influence of the group of peers sharing a common ethnic socio-economic and cultural background; the acculturation orientations of peers are represented by Ī
k
and behave similar to the ones of parents. As to parental acculturation orientations—I
ki
—it is important to specify that in a family where parents transmit values strongly oriented towards adaptation through education, their children derive greater utility from scholastic effort; thereby, they meet parental expectations for their behaviour in school. When parents do not give importance to education and achievements in the host society’s schools, children are not so driven by the need to comply with the behavioural requirements prescribed by them, which is a source of disutility from effort. This influence on the utility may be either strengthened or weakened by the pressure of their school peers—Ī
k
; for instance, a child identity oriented towards integration due to family influences may be undermined by the interaction with pupils of the same ethnic community who reject the values of the mainstream society. To the contrary, children’s positive acculturation orientations are reinforced by similar orientations in their peers. Thus, in the expression defining adaptation, \( {I}_{Oki}={I}_{k i}^{\beta \left({D}_i\right)}{\overline{I}}_k^{\lambda \left({D}_i\right)} \), β(D
i
) and λ(D
i
) capture the influence of parents and school peers on children’s adjustment to schools in mainstream society, respectively; the size of the parameters is affected by children’s reactivity and, in particular, by their perceived discrimination D
i
> 0 in school in the sense that when they feel more discriminated, this lowers the positive influence of parents on children’s adaptation. To the contrary, when parents and/or peers reject adaptation, perceived discrimination strengthens this negative influence.
The other part of ethnic identity E
k
—shortly defined as ethnicity—corresponds to the extent to which the culture of ethnic group k promotes education and academic success; such extent also depends on the consistence of ethnic background with mainstream school culture. Ethnicity embodies the values common to parents and community members that they transmit to children through rearing practices. Therefore, the influence of ethnicity on the utility from effort is positive implying that the more favourable to academic progress the culture of origin, the more motivated the children when following the values transmitted by their parents and ethnic community members through rearing practices. The presence of incongruities between home and mainstream school culture weakens the extent to which ethnicity furthers academic progress.
We also consider personal identity; it is individuated by the locus of control, L
i
, which is relevant to scholastic effort in as much as individuals with a sense of competence about their abilities and a stronger feeling of control of success and failure in pursuing their own personal goals are likely to be more motivated in school. Individuals who are more internal locus get greater utility for a given effort level to the extent to which they ascribe academic achievements to their own effort rather than to the external environment.
Importantly, children with some degree of integration bear a psychological cost due to the divergence of individual effort e
i
from school academic standard e(S), which capture specific knowledge and skills that students must acquire and may also reflect the socio-economic status of schools.
Ethnic identity and the locus of control enter children’s utility function as follows:
$$ {U}_i\left({e}_i,{I}_{k i},{\overline{I}}_k,{E}_k,{L}_i,{D}_i\right)=\alpha \left({e}_i{n}_i-\frac{1}{2}{e}_i^2\right)+\left(1-\alpha \right)\left[\begin{array}{c}\hfill \left({I}_{k i}^{\beta \left({D}_i\right)}{\overline{I}}_k^{\lambda \left({D}_i\right)}+\gamma {E}_{\kappa}+\varphi \left({D}_i\right){L}_i\right){e}_i-\hfill \\ {}\hfill -\frac{\vartheta \left({I}_{Oki},{E}_k\right)}{2}{\left({e}_i- e(S)\right)}^2\hfill \end{array}\right] $$
(1)
In (1), α and (1 − α)—with α ≥ 0—indicate the relative weights of the standard and identity-driven components of the utility function. When α = 0, only the identity part counts while if α = 1, standard cost/benefit considerations prevail; e
i
n
i
represents i’s marketable skill or human capital with e
i
corresponding to individual effort and n
i
to individual ability;Footnote 1 effort cost is \( \frac{1}{2}{e}_i^2 \). The components of identity in brackets before e
i
show that parents’ and peers’ acculturation orientations, ethnicity and locus of control affect the utility from a given effort level. As to parents’ and peers’ acculturation orientations, I
ki
and Ī
k
belong to the interval (1, + ∞), respectively. Parameters β(D
i
) and λ(D
i
) belong to the interval (−∞, + ∞) and precisely \( \begin{array}{cc}\beta \left({D}_i\right),\lambda \left({D}_i\right)>0& \forall {D}_i>0\end{array} \) when parents and peers are in favour of adjustment whereas β(D
i
), λ(D
i
) < 0 ∀ D
i
> 0 when they reject adaptation to host countries’ schools. In the former case, parents’ and peers’ influence complement each other in the process of youth’s identity adjustment to the dominant culture \( \left(\frac{\delta^2{I}_{Oki}}{\delta {I}_{k i}\delta {\overline{I}}_k}\right)>0 \); in the latter, when either parents or peers reject adjustment as they believe that it will not lead to their socio-economic mobility, the cross derivative is negative. This means that if, for instance, parents are in favour of adaptation and peers reject it, a higher adaptation due to parents’ influence raises the utility from effort, which in turn is curbed by the negative impact of rising peers’ aversion to adjustment. Importantly, when both parents and peers transmit values in favour of adaptation and perceived discrimination increases, β ′ (D
i
) < 0 and λ ′ (D
i
) < 0 in the sense that higher perceived discrimination weakens children’s positive attitude to adjust. While increased perceived discrimination amplifies the impact of the values against adjustment, therefore, β ′ (D
i
) < 0, λ ′ (D
i
) < 0 and the negative influence on a child’s motivation is stronger than in the previous case.
As to ethnicity, E
k
is greater than zero and γ ≥ 0. Parameter γ may capture the attachment of children to the ethnic culture transmitted by their parents and ethnic community. As to personal traits, it is assumed L
i
> 0 and φ(D
i
) > 0, and when perceived discrimination—D
i
—becomes stronger, this undermines the influence of internal locus of control on the utility from effort with φ ′ (D
i
) < 0. The second addend in square brackets corresponds to the psychological cost children bear when their effort diverges from the school standard embodying knowledge and skills that students must acquire in host countries’ schools, with e
i
≤ e(S). The component ϑ(I
Oki
, E
k
) is the unit cost of a behaviour that does not meet the standard, it is positive and increasing with respect to both children’s adaptation and ethnicity with \( {\vartheta}_{I_{Oki}}>0 \) and \( {\vartheta}_{E_k}>0 \) implying that the cost of diverging from the school academic standard e(S) rises when a child becomes more adjusted to the culture of the host country and ethnic culture gives greater importance to education. In the latter case, the presence of incongruities between home and mainstream school culture lowers the extent to which ethnicity promotes education and consequently the cost of diverging from the school standard in the host country. This cost indirectly depends also on the degree of perceived discrimination D
i
, which weakens children’s attitudes towards integration or strengthens aversion to adjustment and thereby reduces the psychological cost of diverging from the school’s standard e(S).
4.1 Some results: the influence of ethnic identity, locus of control and perceived discrimination on effort
Optimal effort is obtained from (1) above and is given by the following expression:
$$ {e}_i^{*}=\frac{1}{\alpha +\left(1-\alpha \right)\vartheta \left({I}_{oki},{E}_k\right)}\left[\alpha {n}_i+\left(1-\alpha \right)\left({I}_{k i}^{\beta \left({D}_i\right)}{\overline{I}}_k^{\lambda \left({D}_i\right)}+\gamma {E}_k+\varphi \left({D}_i\right){L}_i\right)+\left(1-\alpha \right)\vartheta \left({I}_{oki},{E}_k\right) e(S)\right] $$
(2)
In (2), it is immediately evident that for given β(D
i
) and λ(D
i
), peers’ opposition to the school culture of the host country—λ(D
i
) < 0—compared to an adaptive attitude—λ(D
i
) > 0—reduces the influence of a strong propensity of parents to adjust to the mainstream culture determined by I
ki
with β(D
i
> 0). To the contrary, if the effect of peers on children’s identity becomes increasingly oriented towards adaptation, the motivation to exert effort can be weakened by parents’ aversion to adjustment with β(D
i
< 0). Therefore, the shortcomings of family background can be overcome by peers’ influence in school and vice versa. When both parents and peers tend to discourage adaptation to the host society, this does not facilitate children’s adjustment to school and reduces the stimulus for effort.
By considering the two components of identities—adaptation and ethnicity—it is possible to hold that higher values of both adaptation I
Oki
and ethnicity E
k
imply that children are strongly integrated as they tend to adjust to mainstream school culture also through their home background, which further strengthens their effort. Moreover, the influence of low children’s adaptation I
Oki
may be counterbalanced by the one of strong ethnicity E
k
—and vice versa—as, on the one hand, parental and/or school peers’ scarce attitudes towards adaptation undermine children’s motivations to achieve in school and, on the other, ethnic culture strongly promoting education offsets this effect. Nevertheless, a low attachment of children to their ethnic culture—lower γ—may weaken the influence of the cultural values promoted by their parents and ethnic community. Thus, though these values may strongly favour education and academic progress, low attachment to them coupled with an attitude contrary to adjustment to the host country leads to a marginalized ethnic identity and undermines children’s motivation. One can obtain lower effort also when youths with a separated identity from the mainstream culture—I
Oki
close to one—follow only their ethnic culture that gives low value to education, due for instance, to a sharp contrast between home and mainstream school culture. When youths’ ethnic identity is characterized by assimilation, they are only interested in adjusting to the host society’ school and in integration and are not affected by their home country culture—γ = 0. If this type of disposition becomes stronger, it reinforces the motivation to exert effort though to a lower extent with respect to the case of children’s integrated identity.
In relation to the above aspects, as already mentioned, Schüller (2015) underlines that parents’ integrated identity based on adjustment to host countries and attachment to ethnic culture plays a relevant role in children’s educational attainment. His empirical evidence shows that in Germany, mothers’ identification with the host country positively affects children’s academic progress as they take care of their scholastic performance, which is made possible by their knowledge of the language and of the German schooling system. Fathers’ identification with home culture exerts a similar influence due also to family rules that derive from their background and shape child-rearing and practices. Similarly, Nekby et al. (2009) report that in Sweden, men with non-Nordic backgrounds and an integrated identity have a higher probability of completing tertiary education, whereas if they are characterized by either assimilation or separation, the probability is lower. In fact, the families with a bicultural orientation encourage the development of reading and writing abilities both in the host and home country language.
Nevertheless, positive parental influence may be weakened by the negative pressure of peers related to the presence of social networks in schools that are segmented by race. The empirical evidence reported by Mayer and Puller (2008) shows that racial segmentation in school may mainly be driven by preferences for same race friends. The implication is that children may become part of marginalized groups and share their values and expectations concerning the school as a means to move up the social ladder like in the case of the Mexican students who assimilated the culture of Chicanos (Portes and Zhou 1993).
From (2), one can derive the influence of children’s ethnic identity, locus of control and perceived discrimination on children’s optimal effort respectively (for further details, see the Appendix):
$$ \frac{\partial {e}_i^{*}}{\partial {I}_{k i}}{}_{<}{}^{>}0,\ \frac{\partial {e}_i^{*}}{\partial {\overline{I}}_k}{}_{<}{}^{>}0,\ \frac{\partial {e}_i^{*}}{\partial {E}_k}>0,\ \frac{\partial {e}_i^{*}}{\partial {L}_i}>0,\ \frac{\partial {e}_i^{*}}{\partial {D}_i}<0,\ \frac{\partial {e}_i^{*}}{\partial e(S)}>0 $$
(3)
From (3), the role of I
ki
and Ī
k
is straightforward as children’s greater adaptation due to the influence of either parents or school peers, on the one hand, motivates higher effort and, on the other, raises the psychological cost of diverging from academic school standard. In the opposite case when the values interiorised by children are against adjustment, they reduce effort as motivations become weaker and psychological costs lower. Ethnicity plays a similar role, for instance, when there are some incongruities between ethnic and mainstream school culture with lower E
k
, motivations may become so frail to induce lower effort; the strength of this effect depends on children’s attachment to ethnic culture γ (see (6) in the Appendix). In this respect, Hirschman and Lee (2005) through empirical evidence argue that in the Pacific Northwest East Asians (Chinese, Koreans and Japanese), Vietnamese and Cambodians have a strong commitment to education in the host country, though their socio-economic background may be poor. They hold that one of the sources of this behaviour is a higher propensity to adjust rooted in their immigrant optimism relying on the belief that hard work will help their children’s socio-economic mobility. Immigrant parents’ home background valuing culture may reinforce the positive influence of their attitude to adaptation as Kao and Thompson (2003) emphasize referring to the case of Southeast Asians. As one would expect, perceived discrimination D
i
lowers effort as it either weakens the adaptation of children’s identity to the host country or bolsters their refusal to adjust to mainstream society; it also reduces the influence of the locus of control and thereby the overall motivation to exert effort. Mickelson (1990) documents such influence: she argues that though many American black youths strongly value education, they face the reality that effort will not bring larger opportunities in labour markets, which causes underachievement. This recalls the approach of Fordham and Ogbu (1986), who show that perceived discrimination determines children’s development of an oppositional identity and undermines their scholastic effort.
In addition, discrimination lowers the psychological cost of diverging from academic school standard by undermining the adaptation of children’s identity to the dominant culture or reinforcing children’s opposition to adjustment. As one would expect, lower scholastic standard e(S) often corresponding to poor socio-economic status of schools decreases effort.
These results take into account the multiple facets of the mechanisms by which ethnic identity triggers children’s motivation to exert effort; they encompass the influence of parents and school peers belonging to the same ethnic community on their adaptation, the specificity of ethnic cultures as to the importance of school, the degree of children’s internal attitudes and their perceived discrimination and finally the academic standard. The interaction among all these factors is useful to understand the differences within and across ethnic groups. For instance, for a low level of perceived discrimination D
i
, a scant influence of parents and peers on the adaptations of youth—small size of β(D
i
) and of λ(D
i
)—may be counterbalanced by a stronger locus of control in that hard work is believed to improve academic achievements. In fact, in the case of well-adapted parents who try to transmit the same orientation, this attempt may be ineffective when children disregard their influence. Children may also overlook a similar influence by their school peers belonging to the same ethnic community. Nevertheless, if they become more aware that academic and economic success is determined by their effort, this may represent a significant incentive to effort. Notably, the influence of well-integrated parents and/or ethnic community on children’s adaptation may be weakened by higher levels of perceived discrimination D
i
, which undermines their adjustment to the host country and makes the psychological cost of diverging from the academic standard less heavy. In addition, with higher perceived discrimination, the influence of the locus of control is diminished as children become more convinced that scholastic achievement is less dependent on their own effort and more on discrimination.
Importantly, parents and pupils belonging to the same ethnic community often shape children’s adaptation in a different way. This means that, for instance, when perceived discrimination D
i
rises as the environment becomes more hostile to ethnic communities, on the one hand, children may be urged by parents with strong attitudes towards adaptation to ignore prejudices and to conform to school rules. On the other hand, they may be subject to the social pressure of their peers belonging to marginalized groups, who reject adaptation as they are particularly vulnerable to discrimination in host societies and are convinced that school does not improve one’s socio-economic status. When children are more responsive to their parents’ influence, a rise in perceived discrimination hampers children’s adaptation less (β ′ is lower in absolute value—see (8) in the Appendix). To the contrary, if they are more reactive to their peers, the same increase in discrimination undermines their adjustment to school and motivation to achieve to a greater extent (λ ′ is higher in absolute value—see (8) in the Appendix) if one takes into account that higher discrimination reinforces their opposition to mainstream culture.
Moreover, low academic standard—e(S)—may correspond to a poor socio-economic status of schools, which often are segregated and characterized by very low expectations of teachers on students’ attainments. This aspect contributes to reduce scholastic effort, which further decreases in presence of a higher level of perceived discrimination.