The impact of teachers’ expectations on students’ educational opportunities in the life course: An empirical test of a subjective expected utility explanation

Abstract

The objective of this paper is to integrate the idea of Pygmalion or self-fulfilling prophecy research into the subjective expected utility framework of inequality in educational opportunities. The theoretical section develops a formal model about the impact of teachers’ expectations on students’ educational transitions in sense of a self-fulfilling prophecy. In the empirical section, I test this model to predict both students’ educational success (in terms of high school graduations) and their university transitions. Analyses control for selection bias and unobserved heterogeneity by means of a bivariate probit model. I find that even net of both students’ performance and motivation, teachers’ expectations show significant effects on students’ educational success (Abitur), but not on their university transitions. This finding is stable against several robustness checks.

Keywords

Educational transitions inequalities in educational opportunities Pygmalion self-fulfilling prophecies social mechanisms subjective expected utility theory

Introduction

School surely is the first and the most important branching point in everybody’s life course at least in industrialized countries. Following structural functionalists such as Davis and Moore (1945) and Parsons (1959), it is the function of school ‘to internalize in its pupils both the commitments and capacities for successful performance of their future adult roles, and second (…) to allocate these human resources within the role-structure of the adult society’ (Parsons, 1959: 298). Economic literature provides numerous examples of the relationship between schooling and labor market income (Ashenfelter et al., 1999; Boissiere et al., 1985; Chetty et al., 2011). Apart from these individual returns to education, there is even evidence that in the long run human capital – measured by labor-force quality – may influence nations’ productivity and economic growth (Bishop, 1989; Hanushek and Kimko, 2000). However, although the importance of schooling and its quality is undisputed, there is still room to refine social science theories on social inequality in educational opportunities (IEO).

On the one hand, powerful conclusions can be drawn from the theoretical framework provided by social inequality theory based on rational-choice or subjective expected utility (SEU) assumptions. First, it allows us to distinguish between primary and secondary effects of social inequality (Boudon, 1974: 29ff.), i.e. between effects of socialization and effects of aspirations. Second, as differences in aspirations between the social strata are dissected into differences regarding the subjective expected utility of education, SEU theory strives to fulfill the demand of mechanism-based explanations. It replaces the mere ‘black box’ of social status effects by a more fine-grained revelation of the underlying cost-benefit structure. Third, SEU theory conventionally implies that these more fine-grained assumptions have to be formalized. This facilitates both the comparison of different hypotheses and their operationalization into empirical models.

On the other hand, social psychologists have impressively revealed how teachers’ expectations can influence students’ future performance. This phenomenon has been labeled the Pygmalion effect of self-fulfilling underestimations and the Golem effect of self-fulfilling overestimations (Rosenthal and Jacobson, 1968). Moreover, Pygmalion research showed that the variance of this effect can partially be explained by social background variables (Jussim and Harber, 2005).

The substantial aim of this paper is to integrate the main idea of Pygmalion or self-fulfilling prophecy research into the general subjective expected utility framework about IEO. In particular, I will build on Esser’s (1999: 265–275) formal SEU model of IEO that constitutes the most recent of a series of related theoretical accounts (Breen and Goldthorpe, 1997; Erikson and Jonsson, 1996; Goldthorpe, 1996). My crucial argument is that teacher treatment effects may affect a substantial parameter that has been part of all formal IEO models since Erikson and Jonsson (1996): the subjected expected probability of educational success. I will further show how self-fulfilling prophecies as understood in the paper at hand can be reconstructed as a concatenation of two belief-mediated mechanisms (Gambetta, 1998; Hedström, 2005: 47–51).

The empirical part of the paper tests the respecified SEU-IEO model by predicting:

students’ probability of achieving a high school degree, and

their propensity of beginning academic studies.

In addition to my indicators of teacher expectancy effects that I will introduce below, and also to the two terms ‘educational motivation’ and ‘investment risk’ deduced from the Esser (1999: 265–275) model, I control for parental social class and education (see Becker, 2003; Becker and Hecken, 2009a, 2009b). But in contrast to these earlier tests of the Esser model, I apply a simultaneously-estimated bivariate probit model with transition-specific instruments (Holm and Jæger, 2011) to control for both selection bias (Heckman, 1979) and unobserved heterogeneity. To the best of my knowledge, this is also the first test of Esser’s SEU model in the latter statistical framework.

The remainder of this paper is structured as follows. After a brief introduction to mechanism-based explanations in general, I will sketch the explanatory merits of rational choice and subjective expected utility-based accounts of IEO. Having summarized key findings and implications from Pygmalion and self-fulfilling prophecy research, I then propose a revision of Esser’s (1999: 265–275) SEU-IEO model. The revised model accounts for the fact that students’ subjective expected probability of educational success might be endogenously influenced by teacher treatment effects, thereby providing a formal model of the belief-mediated mechanism of a self-fulfilling prophecy. After a short description of data and indicators chosen, a series of bivariate probit models with controls for selection bias and unobserved heterogeneity will be presented and discussed. The paper ends with the conclusion that self-fulfilling prophecies (as operationalized here) may affect students’ probability to graduate from high school at the first attempt, but not their university transition propensities. Furthermore, I provide an outlook on potential extensions of educational transition analysis in general and the self-fulfilling prophecy model proposed here in particular: Concretely, I plead for relaxing the constraint of (subjective expected) utility maximization in favor of considering more habitual forms of behavior that may influence educational transition decisions as well.

Theory and hypotheses

The beginning of cost-benefit related educational transition models is rooted in Keller and Zavalloni’s (1964) seminal article. Already Hyman (1953) postulated that lower-class individuals have lower aspirations than higher-class individuals, and Keller and Zavalloni (1964) re-specified his approach by introducing the idea of class-specific relative distances towards particular values. Yet, on the one hand, Keller and Zavalloni (1964: 60) understand social class as an intervening variable between individual ambition and social achievement. On the other hand, they do not entirely discard the value-relatedness of aspirations. Boudon (1974: 29ff.) overcomes this shortcoming, first, by modeling aspirations as a social mechanism that is located between social class and educational achievement; and second, by relating class-specific differences in aspirations to differences in utility considerations (Erikson and Jonsson, 1996: 13f.).

The idea of a social mechanism can best be described with Elster’s (1985: 5) advice ‘to open the black box and show the nuts and bolts, the cog and wheels, the desires and beliefs that generate the aggregate outcome’.¹ The goal is to develop more fine-grained theoretical explanations for the social explananda to be accounted for.² By doing so, mechanism-based explanations are, in effect, understanding explanations in a very fundamental Weberian (1968: 1) sense.³

A parsimonious scheme for classifying social mechanisms is the desires, beliefs and opportunities (henceforth DBO) model proposed by Hedström (2005: 38ff.). In a nutshell, beliefs are universal propositions held to be true, a desire can be described as a wish or want, and opportunities refer to the ‘menu’ of action alternatives available to the actor (Hedström, 2005: 38f.). Important beliefs are those held about different alternatives of action at hand or about the probability of certain consequences that may emerge from different actions. Taken together, beliefs and desires are a compelling reason or have a motivational force (Hedström, 2005: 39). However, although the author lays emphasis on the fact that opportunities must always be known to the actors and thus influence actions via their beliefs (Hedström, 2005: 39), desires and beliefs are not sufficient in explaining human action since opportunities exist independently of them.

Hence, in DBO terminology, the crucial theoretical advancement of Boudon (1974) compared to Hyman (1953), but also to major parts in Keller and Zavalloni (1964), is that Boudon gives up the – less parsimonious – assumption of class-variant desires (in terms of absolute values)⁴ in favor of explaining IEO by actors’ class-variant beliefs in terms of cost-benefit considerations.

In the following subsections, I will first deal with further elaborations of this belief-mediated mechanism accounting for IEO, and I will then make the point how teachers’ expectations alter students’ educational utility function as an intervening belief-mediated mechanism.

Inequality in educational opportunities: Educational transition models

One of the most influential theoretical components of Boudon’s (1974: 29ff.) monograph for contemporary quantitatively-orientated IEO research is its distinction between primary and secondary effects of social inequality.

The primary effect of educational inequality states that the lower educational success of lower-socioeconomic status (SES) children may be due to their lower capabilities – be they defined as educational interests, intellectual skills, effort, or motivation (Jackson et al., 2007; also see Müller-Benedict, 2007). Part of the primary effect may in fact be genetic, but another, presumably greater part of the above-mentioned characteristics is acquired during socialization (Erikson and Jonsson, 1996: 10f.).

The secondary effect, contrarily, operates via stratum-specific differences in educational decision making due to differential opportunity-cost structures, and Boudon’s (1974: 29ff.) crucial assumption is that secondary effects still take place once primary effects have been controlled for.⁵

The idea that utility considerations may shape students’ (or their parents’) educational decisions was taken on in a series of consecutive theoretical models proposed by Goldthorpe (1996), Erikson and Jonsson (1996), Breen and Goldthorpe (1997) and Esser (1999). These models share the proposition that it is simpler (i.e. more parsimonious) to assume that there is no class-specific variation in either aspirations towards education per se or in potentially underlying value systems. Instead, education is regarded as an investment good the costs and benefits of which vary by social classes. Each family will strive to avoid downward mobility; but unsurprisingly, for lower-educated parents, this goal will be reached already for lower educational qualifications for their children – whereas for higher-educated parents, a far higher degree will have to be obtained. Moreover, for the offspring of parents in less advantageous positions, each failed attempt at trying a higher educational alternative will be more serious in its consequences concerning both monetary (earnings foregone; loss of financial support) and transactional costs (a loss in itself; the risk of dropping out of the educational system).

Esser (1999: 265–275) uses a subjective expected utility (henceforth referred to as SEU) model to explain the mechanisms of parental educational choices at the end of primary school education. The expected utility EU for the alternatives at hand, to continue on to lower secondary school (A_n) or to continue on to intermediate or upper secondary school tracks (A_b) will be as follows:

EU (A_{n}) = P_{sd} (- SD)

(1)

EU (A_{b}) = P_{ep} B + (1 - P_{ep}) P_{sd} (- SD) - C

(2)

In that model, SD is the value of status decline with P_sd as its impact (in terms of a subjective probability) on parental decisions; B is the benefit of higher education (e.g. in terms of labor market prospects); P_ep is the subjective expected probability of successfully completing the chosen school track; and C are the expected costs of education (see also Becker, 2003; Pietsch and Stubbe, 2007). Esser (1999) follows Breen and Goldthorpe (1997: 285) in assuming P_ep to be a function of students’ actual academic performance – which will become relevant for developing a formal model of self-fulfilling prophecies.

By simple linear transformations, Esser (1999) shows that

EU (A_{b}) > EU (A_{n}) \Leftrightarrow B + P_{sd} SD > C / P_{ep}

(3)

The term $B + P_{sd} SD$ is denoted as the educational motivation and the term $C / P_{ep}$ as the investment risk. Thus, a higher level of education will be aspired to if the educational motivation to continue exceeds the underlying investment risk. Since in case of a low P_ep, educational motivation has to be very high to exceed the critical threshold of the investment risk, the model can also account for the fact of persisting inequality in educational opportunities (Esser, 1999: 270).

In sum, though varying in formality and theoretical complexity (e.g. in terms of number of parameters), the educational transition models that have been proposed following Boudon (1974: 29ff.) share a lot of common features – such as the emphasis on students’ (or their parents’) subjective expected probabilities of educational success. Moreover, all transition models open the black box by introducing actors’ cost-benefit considerations as the underlying social mechanism in order to obtain a better understanding of social inequality in educational opportunities. In terms of mechanism-based explanations following the framework proposed by Hedström (2005), the following pattern is evident. While parents’ desires, i.e. their absolute educational and occupational aspirations, are assumed to be constant among classes (Keller and Zavalloni, 1964; Meulemann, 1979: 398, footnote 4), it is their beliefs about the expected benefit of education, the perceived amount of status decline, or the subjective expected probability of educational success that should be different among the social strata. Hence, the above-cited theoretical accounts all assume a belief-mediated social mechanism to underlie educational transition decisions.

Among these models, the Breen and Goldthorpe (1997) and the Esser (1999: 265–275) model have been tested most comprehensively (Becker, 2003; Becker and Hecken, 2009a, 2009b; Breen and Jonsson, 2000; Jonsson, 1999; Schneider, 2008; Stocké, 2007). As regards the Esser (1999: 265–275) model that will be used below to build a formal model of self-fulfilling prophecies, Becker’s (2003) operationalization controlling for selection bias via ‘Heckit’ correction (Heckman, 1979) was referred to being the best available test in terms of methodology (Stocké, 2007: 508). In this model, first the impact of parental social class on each of the parameters B, –SD, P_sp, P_ep, and C is used to correct for sample selection bias when explaining the choice of upper secondary school. Second, these effects are again used to control for selection bias in the explanation of the transition to particular school tracks. Becker (2003) justifies his three-step method with the endogeneity of the causal structure. However, the next subsection will provide theoretical arguments for the presence of another endogeneity that appears to have been neglected so far: the impact of teachers’ expectations on the students’ subjected expected probability of successfully completing the chosen school track, P_ep.

Pygmalion in the classroom

The idea of a self-fulfilling prophecy is one of the most prominent examples of a social mechanism (Hedström, 2005: 48) and was first established by Robert Merton. In his seminal paper, Merton (1948) shows how prejudices towards out-groups (e.g. African-Americans) or specific attitudes about a certain situation (e.g. the rumor about a bank’s illiquidity) might become true simply as a consequence of the former judgments. Alienated by the rumor, the first customers will withdraw their savings – which will in a second step move other costumers to follow suit. In the end, panicky withdrawals might in fact lead to the bank’s breakdown – although the original rumor did not necessarily correspond to the bank’s initial financial situation. Hence, ‘[t]he prophecy of collapse led to its own fulfillment’ (Merton, 1948: 195).

This seminal description of a self-fulfilling prophecy was convincingly reconstructed by Hedström (2005: 48) as a belief-mediated mechanism. The beliefs of the first depositors who withdraw their savings affect the beliefs of the remainders who now have good reasons to assume that there might actually be something wrong with the bank and thus also withdraw their savings. Or, phrased more analytically (Biggs, 2009: 295):

X beliefs that ‘Y is p’.

X therefore does b.

Because of (2), Y becomes p.

Self-fulfilling prophecies should be distinguished from inductively-derived prophecies which can be reconstructed as follows (Biggs, 2009: 296):

(0) Y is p.

(1) Because of (0), X beliefs that ‘Y is p’.

(2) X therefore does b.

(3) Because of (0), Y manifests p.

In the first case, it is an actor’s inaccurate belief about the social situation that makes the difference, while in the second case it is the social situation that causes an accurate belief – which can be illustrated by imposing counterfactuals on the respective first condition. If in the first case, X were to believe that ‘Y is q’, X would do c instead of b and thereby cause Y to be p – while in the second case, if Y really were p, X falsely believing Y to be q would not make a difference (Biggs, 2009: 296).⁶

In educational sciences, the notion of a self-fulfilling prophecy is conveniently used to refer to what has been labeled the Pygmalion effect. Following the well-known study of Rosenthal and Jacobson (1968), the Pygmalion effect refers to the impact of misled teachers’ expectancy effects on student’s future school achievement.⁷ The idea behind the metaphor holds that teachers’ too high or too low expectations can have an impact on the teacher-student interaction. This, in turn, might influence the students to adopt their motivations and aspirations according to their teachers’ expectations. In the words of Merton, teachers’ expectations, which had originally been misled, would in turn lead to their own fulfillment.

The classical Pygmalion

In the original study, Rosenthal and Jacobson (1968) administered a non-verbal intelligence test to elementary schoolchildren. However, they did not tell the teachers that this was an intelligence test, but that it was a new tool to identify ‘late bloomers’, i.e. children who were likely to show a sudden and dramatic intellectual spurt over the upcoming school year. Although the ‘late bloomers’ were actually selected randomly, Rosenthal and Jacobson (1968) observed that in an IQ test which was administered one year later, they achieved significantly better test scores than the control-group students. Thus, the false expectations of the teachers (led to believe in the artificially-created group of late bloomers) had become true.⁸ Whereas many social psychologists took Pygmalion as a confirmation of their thesis that social reality is mainly created by one’s own expectations, educational psychologists were much more skeptical with regard to Pygmalion’s methodological prerequisites and the possibility of alternative explanations which, according to them, Rosenthal and Jacobson (1968) had not sufficiently controlled for (Jussim and Harber, 2005: 139).⁹

However, an initial meta-analysis of the first 345 self-fulfilling prophecy studies from various research fields¹⁰ found effect sizes of Pygmalion between d = .14 and d = 1.73 and r = .07 up to r = .65 (Rosenthal and Rubin, 1978, Table 1).¹¹ Later meta-analyses based on a more narrowly-defined set of Pygmalion found effect sizes of teachers’ expectations on students’ IQ scores of .16 (Smith, 1980), .11 (Raudenbush, 1984) and .20 (Raudenbush, 1994). This led Pygmalion and self-fulfilling prophecy researchers to the conclusion that these kinds of effects do in fact exist.

Table 1.

Probit regression of teachers’ evaluations on students’ performance and motivation.

	Model 1 (Performance)	Model 2 (Motivation)	Model 3 (Full)
	beta/z-value	beta/z-value	beta/z-value
Intelligence	0.78***		0.74***
Intelligence	(8.74)		(7.91)
Grades	−1.63***		−1.41***
Grades	(−16.60)		(−13.40)
Homework effort		0.03	0.16
Homework effort		(0.34)	(1.75)
Relative school performance		1.20***	0.88***
Relative school performance		(11.61)	(7.44)
Self-confidence		0.25**	0.20
Self-confidence		(2.59)	(1.81)
Nagelkerke’s R²	0.42	0.27	0.50
N	1281	1294	1259

Significance values: *** p < .001; ** p < .01; * p < .05.

Theoretical identification challenges of self-fulfilling prophecies

While the initial Pygmalion in the Classroom was set up in a quasi-experimental design, most of what followed relied on survey data (see overviews by Jussim, 1986; Jussim et al., 1996; Jussim and Harber, 2005). Regarding the isolation of a causal effect, survey data are always inferior to a true experimental design (Biggs, 2009). Yet, econometricians have developed sophisticated methods to get rid of a great deal of heterogeneity in survey data that would not be equally problematic in an experimental setting (Gangl, 2010). What survey-driven research can and should do prior to all statistical approximations of causal effects, though, is to specify the social mechanisms that stand behind the former – leading to a better understanding of the phenomenon to be isolated by means of methods (Goldthorpe, 2001; Merton, 1987). As regards self-fulfilling prophecies in the classroom, this requires finding answers to the following two questions:

To what extent are teachers’ initial beliefs about their students accurate?

In what manner do teachers’ inaccurate perceptions affect students’ educational outcomes?¹²

With regard to the first question, on the one hand, it is hard to test the accuracy of teachers’ expectations just because they may invoke self-fulfilling prophecy effects (Jussim, 1986: 431). On the other hand, a large degree of teacher expectancy effects can be attributed to the fact that they are accurate (Jussim et al., 1996: 288; Jussim and Harber, 2005).¹³ Phrased in more analytical terms, this question relates to the above-sketched difference between the inductively-derived and the self-fulfilling prophecy (Biggs, 2009).

A promising strategy for the identification of teachers’ inaccurate expectations was proposed by Madon et al. (1997) who regressed teachers’ expectations (related to students’ performance, talent and effort) on a set of student background variables. In a second step, they used the residuals of these regressions – reflecting a student’s over- or underestimation by her teacher – as new variables to ensure that a teacher’s expectation is, to some extent, actually inaccurate (also see Hinnant et al., 2009; Madon et al., 2006; Sorhagen, 2013).

Unsurprisingly, the answer to the second question is closely related to the argument of accuracy. Only if inaccurate expectations can be identified, can it be ruled out that teacher perceptions are valid predictions of unobserved characteristics that actually cause student achievement. Madon et al. (1998) noted that the largest share of the differences that teachers identify between social groups corresponds closely to actual differences in previous grades and achievement tests. Moreover, a current study by Ready and Wright (2011) showed that holding between-group achievement differences constant, teachers are especially error-prone in lower socio-economic and lower achievement classroom contexts. A notable shortcoming of research on the efficacy of self-fulfilling prophecies in terms of teacher treatment effects is an insufficient control of student background variables as either mediators or moderators (Jussim and Harber, 2005).¹⁴ The few available studies found self-fulfilling prophecies:

to be stronger among students who had a ‘prior history of low-achievement’ (Madon et al., 1997); and

to be moderated by both social class and ethnicity-related variables (Jussim et al., 1996; Ready and Wright, 2011).¹⁵

However, what self-fulfilling prophecy studies lack entirely is an analytical specification of the underlying social mechanism that explains how self-fulfilling prophecies can have the postulated effect. Below I will argue that a formalized educational decision model explicitly including students’ social backgrounds, such as Esser’s (1999: 265–275) SEU theory, can indeed close this gap.

To be precise, just as self-fulfilling prophecy research requires a more theory-driven specification of student background variables, the SEU-IEO framework needs to consider the endogeneity concerning students’ probability of educational success which is the main point of all Pygmalion studies. The task in the next section will therefore be to integrate the main idea of a ‘net’ effect of a self-fulfilling prophecy into the SEU-IEO framework.

Development of an SEU model of self-fulfilling prophecies

Given the utility relations of the SEU-IEO model outlined above, educational decisions would be a direct function of net utility. However, this seems to be only half the truth, for it would neglect the idea of a self-fulfilling prophecy in the classroom. In line with the main idea of Pygmalion, claiming that a teacher’s expectation may have a distinct effect on students’ later school achievement implies that the ‘real’ transition rates are not only a result of ‘subjective’ parental utility comparisons, but also of ‘objective’ interactions in the classroom: ‘A shortcoming of the standard economic approach to decision making is that it ignores the endogeneity of preferences – that students’ preferences are socially constructed through interaction with peers and other significant persons’ (Lauen, 2007: 183). The consequence of admitting an endogeneity of preferences in the classroom is to also assume an endogeneity of p_ep,¹⁶ i.e. of the subjective expected probability of successfully completing the chosen school track. Breen and Goldthorpe (1997: 285) already noted that the subjective probability of educational success depends on students’ objective school performance. In accordance with Esser’s notation – who makes a similar point (Esser, 1999: 272f.) – we could write

p_{ep} = f (AP),

(4)

where AP denotes students’ academic performance. Claiming that teachers’ expectations in terms of a ‘net’ effect of self-fulfilling prophecies (Madon et al., 1997) at time t, TE_t, may influence students’ academic outcomes at a later time t + 1 can be formalized as

A P_{t + 1} = g (T E_{t}) .

(5)

For P_ept+1 thus holds that

p_{ept + 1} = f (g (T E_{t}))

(6)

– meaning that subjective probability assumptions are a function of students’ objective school performance which is, in terms of a self-fulfilling prophecy, dependent on teachers’ earlier expectations. Notably, in self-fulfilling prophecy research, many studies stress that the crucial mechanism of teacher expectancy effects also operates via students’ self-concept and their aspirations (Gill and Reynolds, 1999; Jussim, 1989; Mechtenberg, 2009; Mistry et al., 2009; Muller et al., 1999).¹⁷

Will AP_t+1 be the only variable that affects p_ept+1? Certainly not. Concretely, I assume that equation (6) can be decomposed into

p_{e p_{t + 1}} = h (p_{ep}, A P_{t + 1}, ϵ) .

(7)

Equation (7) expresses that a student’s subjective expected success probability is a function of her preceding subjective expected success probability, her actual academic performance, and an unspecified teacher treatment effect є that captures classroom praise, bilateral encouragement, and similar mechanisms (without making any assumptions about the functional form of this relationship).¹⁸

We should now apply this idea to Esser’s (1999: 265–275) formal model by tracking the logic of an SFP in its appropriate survey-data framework of teachers’ over- and underestimations. Let $δ \in {0, 1}$ indicate whether a student has been underestimated ( $δ = 0$ ) or overestimated ( $δ = 1$ ) by her teacher. Restricting the other SEU parameters to remain constant over time, let further ${\tilde{p}}_{ep .} = p_{ept} + p_{ep}$ to get rid of time indices (see Jaeger and Holm, 2011, for a similar analytic strategy) – that is, ${\tilde{p}}_{ep .}$ captures students’ initial subjective expected probability of educational success plus (or minus) the additional gain (or loss) ΔP_ep that is due to an over- (or under-)estimation as sketched in (7).¹⁹ If, finally, ${\tilde{p}}_{ep -}$ and ${\tilde{p}}_{ep +}$ denote the under- and overestimated students’ corresponding subjective expected probability of successfully completing the chosen school track, respectively, then we can rewrite equation (3) as follows:

EU (A_{b}) > EU (A_{n}) \Leftrightarrow B + p_{sd} SD > \frac{C}{δ \cdot {\tilde{p}}_{ep +} + (1 - δ) {\tilde{p}}_{ep -}}

(8)

As the argument goes, on average P_ept+1|δ=1 > P_ept+1|δ=0 since on the one hand, AP_t+1|δ=1 > AP_t+1|δ=0, and on the other hand, є_δ=1 > є_δ=0. Holding p_{ep_t} constant, it follows that> ${\tilde{p}}_{e p_{+}}$ . Since the denominator of the right-hand side of equation (8) is larger for δ = 1 than for δ = 0, it follows that

E U_{δ = 1} (A_{b}) > E U_{δ = 0} (A_{b}) .

(9)

That is, all other things being equal, students who had been overestimated by their teachers should have a higher expected utility of choosing the next higher-level school track than students who had been underestimated.²⁰

Model identification

The model assumes that self-fulfilling prophecies directly enter the student’s utility function. However, it has to be clarified which type of rationality a student’s utility function relies on. A student who has been overestimated by her teacher will dispose of a higher subjective expected probability of educational success not only because of her better grades, but also because of more subtle teacher treatment effects (above referred to as є ) that may be understood quite similarly to the ‘caress’ effect in Ovid’s Metamorphoses. As Morgan (1998: 136) writes, students ‘adopt the expectations that others have of them and add these to their own expectations formed independently through their own rational self-reflection’. Adding expectations of teachers in their role as significant others (Morgan, 1998, 2002; Sewell et al.,1969, 1970) may be an unconscious endeavor, but in altering a crucial parameter of the utility function, this might also affect rational utility considerations.

In terms of a mechanism-based explanation, the self-fulfilling prophecy of a teacher treatment effect is reconstructed as a concatenation of belief-mediated mechanisms. As outlined above, teachers first form initial beliefs about a student’s academic performance, and although these beliefs are largely accurate, a residual share of inaccuracy was shown to remain (Ready and Wright, 2011). It is exactly this residual inaccuracy that distinguishes the belief-mediated mechanism of a self-fulfilling prophecy from the inductively-derived prophecy. By an additional mechanism of dissonance reduction (Festinger, 1957; Heider, 1946), teachers might ignore positive information about negative students (and reversely) and thereby form particularly rigid expectations that are singularly conducive to self-fulfilling prophecies (Jussim, 1986).

In a second step, these – more or less rigid – expectations of the teachers affect students’ beliefs due to:

a direct teacher treatment effect including classroom praise, bilateral encouragement, etc., and

an effect of actual student achievement differences (that are likewise initiated by teachers’ inaccurate beliefs).

Assuming differences in student beliefs caused by the teacher treatment effect to induce differences in students’ subjective expected utility of educational success, I hypothesize an additional belief-mediated mechanism leading to differences in educational transition propensities in the long run.

The question is now how the crucial parameters can be estimated in an empirical model. The current framework in social psychology of residualizing teachers’ expectations (Hinnant et al., 2009; Madon et al., 1997, 2006; Sorhagen, 2013) is very helpful for identification purposes. The assumption is that when teachers’ expectations are residualized for students’ achievement, their motivation and self-concept at t₁, the relations that are addressed in (7) can be approximated also in case of lacking empirical measures. While p_ep can be measured from the data at hand (see the section on methods below), I do not have indicators for AP_t+1 and є. But I assume that by regressing teachers’ evaluations on a set of performance and motivation variables, differences in students’ academic performance between t and t+1 as well as unobserved teacher treatment factors that exceed (or undershoot) students’ motivation and their self-concept at t (and thereby take effect as a cause of p_ep) can, if admittedly not entirely isolated, at least be approximated.

Hence, I assume that residualizing teachers’ expectations as proposed by Madon et al. (1997, 2006; also see Hinnant et al., 2009; Sorhagen, 2013) provides a useful tool for approximating the unobserved mechanisms that enter students’ rational utility function.

Hypotheses

After these theoretical considerations my main hypothesis is easily outlined. I postulate that via a concatenation of two belief-mediated mechanisms, teachers’ expectations have distinct and self-fulfilling effects on students’ educational transitions. By ‘distinct effects’ I mean that there will be a significant impact of an adequate measure of self-fulfilling prophecies when controlling for the relevant (cross-sectional) SEU-IEO parameters (Esser, 1999: 265–275). Since a major claim of rational-action theories of educational transitions is that secondary effects of social inequality do not only affect the actual transition decisions but also the decision for or against continuing the chosen school track (Breen and Goldthorpe, 1997), as a first step I analyze the probability of German 10^th class Gymnasium students to achieve a high school degree (Abitur). This certificate used to be and still is the crucial prerequisite for access to tertiary education. When surveyed mid-10^th grade, German Gymnasium students are facing the decision whether:

to continue education in secondary school level II (‘Gymnasiale Oberstufe’) – that would be successfully finished by passing Abitur after three years; or

to quit secondary school at the end of the 10^th grade, or thereafter, without having passed Abitur.

As Schneider (2008, Figure 2(b)) observed by using German Socio-Economic Panel (GSOEP) data, even after nine years of secondary-school education, the survivor function modeling the probability of not dropping out of Gymnasium is considerably higher for students from the salariat than for students from the working class. Hence, one can assume that secondary school cost-benefit considerations as postulated by Breen and Goldthorpe (1997) as well as Esser (1999: 265–275) are equally important for passing Abitur.

In a second step, I will also model students’ transition propensities to tertiary education in terms of starting academic studies. Becker and Hecken (2009a, 2009b) argue that utility considerations as reflected in Esser’s (1999: 265–275) SEU model are also pivotal for university transitions.²¹ One social mechanism that could account for transition differences between the social strata at this comparably later point in students’ educational life course is their differing time horizon. The impending costs of higher education are accompanied by uncertain returns later in time – which may be more significant for students from the lower social classes than for those from the salariat (Becker and Hecken, 2009b: 235f.). Therefore, the former can be expected to make that transition less frequently than the latter.

Taking the well-tried SEU model as given, two hypotheses can be derived from its extension adding the impact of self-fulfilling prophecies:

H1 : Apart from the SEU-model indicators, students’ probability of achieving a high school degree increases with (positive) self-fulfilling prophecies, SFP.

H2 : Apart from the SEU-model indicators, students’ probability of starting academic studies increases with (positive) self-fulfilling prophecies, SFP.

Operationalization

Data

All analyses will be based on a German panel dataset which is known as the ‘Kölner Gymnasiasten-Panel’ (English ‘Cologne High School Panel’, henceforth referred to as CHiSP). The CHiSP consists of an initial (student-level) survey from 1969 (Gesis-No.: ZA0600) with N=3385 10^th-grade Gymnasium²² students in North Rhine-Westphalia with three re-surveys in 1985 (Gesis-No.: ZA1441; N=1987), 1996/97 (Gesis-No.: ZA4228; N=1596), and 2010 (N=1301; no Gesis-No. available yet). In the initial survey, students were asked about issues like their performance, interests and plans in school, about their social background, and their relationship with their parents. Simultaneously to the initial survey, the students took part in an Intelligence Structure Test (IST) consisting of four sub-scales developed by Amthauer (1957). At the same time, also, the students’ teachers (Gesis-No.: ZA0640; N=1701) and their parents (Gesis-No.: ZA0639; N=2646) were surveyed. The main items of the parent questionnaire were about their social background, their style of raising children and their aspirations for their children. Teachers were asked about several evaluative and other pedagogic issues. In an investigation of the Central Archive for Empirical Research in Cologne (today known as Gesis - Leibniz Institute for the Social Sciences), students’ 10^th class and Abitur grades (if passed) could be examined and were merged with the data. In the two re-surveys, former students provided detailed information on their educational and occupational careers until the age of 43. I chose this admittedly older data, because to the best of my knowledge, it is the only available longitudinal dataset that comprises appropriate measures of both indicators of the SEU model outlined by Esser (1999: 265–275) and of teachers’ expectations that are required to construct over- and underestimations in order to operationalize self-fulfilling prophecies adequately. The latter indicator will be described in the next but one paragraph.

Variables

Dependent variables

In the hypotheses section, I identified two dependent variables. The first dependent variable measures whether students have achieved a high school degree (Abitur) or not. While the CHiSP also includes information about whether the former students have ever passed Abitur in their later life, I will focus only on those students who passed Abitur during the regular schooling time. This appears to be logically consistent since secondary effects of social inequality can also be understood as a decision for versus against continuing higher education (Breen and Goldthorpe, 1997; Schneider, 2008). Hence, I focus on those students only who passed Abitur at the first attempt (event=1) using all observations that did not pass Abitur within three years after the 10^th class survey in 1969 as a reference (event=0).²³

The second dependent variable is given by whether the former students have ever started academic studies. Since my analysis is based on panel data, I have to take into account that from a theoretical point of view, it would be possible for the former students to start academic studies at any later point in time – including data points set after the last survey of the CHiSP (currently 2010). This problem will be solved empirically in the results section.

Independent variables

The expected benefit of education, B, is operationalized by students’ answer to the question whether they consider Abitur to be a prerequisite for attaining their aim in life. Students had the following reply options: 1 ‘yes, necessary’; 2 ‘useful, but not necessary’; and 3 ‘not important’. The value of status decline, –SD, is measured by parents’ disappointment if their child did not pass Abitur. The categories of this variable are 1 ‘not much’; 2 ‘little’; 3 ‘very disappointed’; 4 ‘would be the worst’. I operationalize the expected status decline, p_sd by parents’ assessments about the importance of good Abitur grades for students’ later occupational success (1 ‘little’; 2 ‘not that much’; 3 ‘big’; 4 ‘very big’). Students’ subjective educational performance p_ep is measured by parents’ probability assumptions whether their offspring is able to complete the chosen school track (1 ‘definitely’; 2 ‘probably’; 3 ‘don’t know’; 4 ‘probably not’). The expected costs of education, C, are operationalized by parents’ assessment if they had to make financial sacrifices in order to offer higher education to their children (1 ‘no’, 2 ‘little’ and 3 ‘yes’).²⁴ I follow previous tests of the SEU model (Becker, 2000, 2003; Becker and Hecken, 2009a, 2009b) in computing the product terms for students’ educational motivation (EDMOT) and their investment risk (INVRISK) as required by the Esser (1999: 265–275) model.²⁵

Self-fulfilling prophecies

SFP, should adequately be operationalized based on teachers’ expectations. The CHiSP entails a suitable measure in terms of teachers’ evaluations. Teachers were asked to evaluate whether they considered a student eligible for academic studies or not. Since the question was phrased openly, teachers could mention students as being eligible, not eligible, or not at all eligible.

This data structure causes two problems. First, each student could be evaluated by more than one teacher, and each teacher could evaluate more than one student. An analysis of the intra-class correlations (ICC) with teachers’ evaluations nested in both students and teachers (cross-classified model) revealed a considerable variance of multiple evaluations for each student (not shown, available upon request). Second, the question’s openness constitutes another challenge, because it has to be clarified whether the category of students who were not explicitly referred to as being eligible or not eligible can be treated technically as a missing value, or if we were to lose substantive information when proceeding on this assumption.

To overcome the first problem, my analyses here will focus on class teachers’ evaluations only. I expect that the intra-individual variance of teachers’ evaluations partially depends on the quality of teacher-student relationships. I assume that class teachers have a more intense relationship with and a better knowledge of their students than other teachers. Thus, looking only at class teachers’ evaluations will both simplify the data structure and overcome the problem of variance.²⁶ In order to overcome the second problem, two logistic regressions of the chances of getting a positive evaluation versus getting a negative one, or none at all, on students’ intelligence, GPA, social background, motivation and gender were estimated (not shown, available upon request). Results indicate that for the chances of getting a positive evaluation versus not getting one at all, the effect sizes of all independent variables point to the same direction, but they are notably lower than for the chances of getting a positive evaluation versus getting a negative one. Thus, we can conclude that students who are not mentioned at all rank lower in teachers’ perceptions than students who obtained a positive evaluation from their teacher, but they score higher than students who obtained a negative one. However, in these analyses I will only look at the unambiguous values of this variable in terms of the opposition of positive versus negative evaluations.

Based on this dichotomy, SFP is measured as follows. Teachers’ evaluations are regressed on two sets of students’ backgrounds: an ability component, and a motivational component. The ability component consists of students’ scores in the Intelligence Structure Test (IST; Amthauer, 1957) and the mean of the subject grades their class teacher gives in a particular class (CTGRADE; up to three, z-transformed). The motivational component comprises three 11-point Likert-scaled items of students’ subjective assessments of:

their homework effort (HOMEFF),

their relative school performance (RPERF), and

their self-confidence (SCONF).

While preceding analyses (Hinnant et al., 2009; Madon et al., 1997, 2006; Sorhagen, 2013) used the residuals from logistic regression analysis, I aim to refine the method of estimating teachers’ over- and underestimations by residualizing teachers’ expectations using generalized probit residuals (Gourieroux et al., 1987). While the logit residuals may still share some amount of statistical association with their predictors, the generalized probit residuals are uncorrelated with all predictor variables by construction (Vella, 1998: 136).

Teachers’ evaluations are subsequently regressed on these two sets of student backgrounds, resulting in three different probit regression models: one for each set, and a ‘full’ model with all predictors. The models read as follows:

p {(TE = 1)}_{perf} = Φ (β_{o} + β_{1} I S T + β_{2} CTGRADE)

(10)

\begin{array}{l} p {(TE = 1)}_{mot} = Φ (β_{0} + β_{3} HOMEFF + \\ β_{4} RPERF + β_{5} SCONF) \end{array}

(11)

\begin{array}{l} p {(TE = 1)}_{mot} = Φ (β_{0} + β_{1} IST + β_{2} CTGRADE + \\ β_{3} HOMEFF + β_{4} RPERF + β_{5} SCONF) \end{array}

(12)

where (10) denotes the performance model, (11) the motivation model, and (12) the full model. Φ is the cumulative distribution function (cdf) of the probability density function (pdf) of the normal distribution φ with $Φ (x) \equiv {\int^{}}_{- \infty}^{x} ϕ (t) d (t)$ (which means to integrate over φ ) and $ϕ (x) = {(2 π)}^{- 1 / 2} \exp {(- x^{2} / 2)}^{- \infty}$ for all real numbers x (Greene, 2003: 666; Wooldridge, 2002: 458).

The residuals of (10) to (12) are stored in order to be used as predictors of students’ probability to pass Abitur and to start academic studies, respectively (Hinnant et al., 2009; Madon et al., 1997, 2006; Sorhagen, 2013). The generalized probit residuals u_i are defined as follows (Gourieroux et al., 1987: 14f.):

u_{i} = \frac{ϕ (x_{i} β)}{Φ (x_{i} β) [1 - Φ (x_{i} β)]} [y_{i} - Φ (x_{i} β)]

(13)

When $y_{i} = TE = 1$ (a student obtained a positive evaluation by her teacher), (13) reduces to $u_{i} = \frac{ϕ (x_{i} β)}{Φ (x_{i} β)}$ , and in case of $y_{i} = TE = 0$ (a student obtained a negative evaluation by her teacher), $u_{i} = \frac{ϕ (x_{i} β)}{1 - Φ (x_{i} β)}$ . Just as in the case of logistic regression, positive generalized probit residuals indicate relative overestimations and negative ones relative underestimations compared to the respective set of predictors in the probit models. But as an advantage, the latter residuals are uncorrelated with their predictors. By this procedure, it is possible to separate a ‘net’ effect of self-fulfilling prophecies from a varying set of background variables (Madon et al., 1997, 2006).

Hence, admittedly, I am not able to test for a direct impact of teachers’ expectations on students’ future school performance (as Pygmalion in its initial form would require) due to data restrictions. However, I assume that given the (in my view) adequate operationalization of SFP in terms of over- and underestimations – approximating the factors that affect student differences in their subjective expected probability of educational success p_ep –, we can identify an estimate that gets quite close to the unobserved mechanisms of the ‘real’ self-fulfilling prophecy.²⁷ In particular, in both the performance model and the full model, differences in the distribution of teachers’ evaluations which are due to primary effects of social inequality are explicitly ruled out.²⁸

Covariates

To ensure that social inequality in educational opportunities is exhaustively modeled by the two terms ‘educational motivation’ and ‘investment risk’, analyses control for parental social class and educational attainment.²⁹ Social class is measured by the occupational prestige (Treiman scores) of the head of household – while the latter is based on a variable that takes the highest value of occupational prestige from either mother or father.

Parental educational attainment was measured by 13 categories reaching from lower secondary school without an apprenticeship up to a university degree. I categorized this variable into: 1 ‘lower education’; 2 ‘middle education’; 3 ‘higher education’ and 4 ‘degree’. I will refer to both covariates as SES.

The bivariate probit model that I will describe below requires use of transition-specific instruments. I will make use of students’ z-transformed 10^th class grade point average (GPA) and of the mean grade (z-transformed) of students’ final high school exam (FGRADE).³⁰

Models

For a long time, the state-of-the-art model in educational transition analysis has been the Mare (1980, 1981) model. In that model, each student’s individual transition probability is estimated against the proportion of students remaining after a preceding transition, i.e. those at risk, by means of logistic regression analysis. However, econometricians have demonstrated that a sequence of logistic regression models may suffer from selection bias when the percentage of those at risk can be expected to become more and more homogeneous over transition points. While Becker (2000, 2003) applied a so-called Heckman model (1979) to account for unobserved heterogeneity, more recently, Holm and Jæger (2011) as well as Bernardi (2012) estimated a bivariate probit model that yields more robust estimates when the outcome in the equation of primary interest is dichotomous (Freedman and Sekhon, 2010).

Since these models are only identified via functional form assumptions unless good instruments are introduced for each transition point, the following models are estimated. For the first transition of whether or not students passed German highest-track final school exams (Abitur), students’ 10^th class grade point average (GPA) is used as an instrument, and for the second transition of whether or not students started academic studies, their final exam average grade (FGRADE) is included. This follows the strategy proposed by Holm and Jæger (2011: 317) to opt for instruments that ‘should affect the probability of making a specific educational transition but should not have any direct effect on other educational transitions’.

The bivariate probit model estimated below reads as follows:

p (t_{2} = 1 | t_{1} = 1) = {\int^{​}}_{- \infty}^{u_{i}} {\int^{​}}_{- \infty}^{v_{i}} ϕ_{2} (x_{1 k} β_{1 k}, x_{2} β_{2 k}, ρ) d u_{i}; d v_{i}

(14)

Here, $p (t_{2} = 1 | t_{1} = 1)$ refers to the probability of university transitions (t₂) conditional on having passed Abitur (t₁), and $x_{1 k} β_{1 k}$ as well as $x_{2} β_{2 k}$ are the respective predictors of both equations. u and v are the error terms of both transition equations, and the parameter of ρ refers to the correlation that these error terms may share if there is unobserved heterogeneity over educational transitions due to omitted predictors. To account for this correlation, a bivariate normal distribution is imposed over u and v, which can be estimated by integrating over their joint probability density function φ₂ .³¹

In my case, the transition-specific predictors $x_{1 k} β_{1 k}$ and $x_{2} β_{2 k}$ are EDMOT, INVRISK, GPA, SFP, and SES for t₁ and EDMOT, INVRISK, FGRADE, SFP, and SES for t₂.

SES shall account for class-specific variation in both EDMOT and INVRISK, GPA serves as an instrument for the first transition of passing Abitur, and FGRADE serves as an instrument for the second transition of starting academic studies. First, from a statistical perspective, there is solid reason to assume no direct effect of GPA on t₂ once FGRADE has been controlled for (see Holm and Jæger, 2011, for an analogous strategy). Second, from a theoretical perspective, using distinct measures of students’ performance as transition-specific instruments also controls for a substantial part of primary effects of social inequality that might affect my measures of secondary effects, EDMOT and INVRISK.³² Finally, including SES in the equation tests for residual variance of educational transitions by social backgrounds that is captured neither by indicators of primary nor of secondary effects of educational inequality.

Results

Distribution of variables

Dependent variables

In Figure 1(a), the distribution of the time-span until students passed Abitur is displayed. Recall that the zero point of counting has been backdated to January 1967. We can see that the distribution of passing Abitur over time corresponds to the chosen cut-off value of 80 months. Most of the students passed Abitur at the first attempt, a quite small number at the second attempt, and even fewer at the third attempt. Figure 1(b) captures the distribution of the time-span until the former students began academic studies. Most of the students took up academic studies immediately after having passed Abitur, and a smaller number did so after a delay of one to two years. After 106 months counting from the starting point – which is equal to October two years after high school graduation – the number of students who begin academic studies drops substantially. Thus, I choose this value as the cut-off for dichotomization of the second dependent variable.

Figure 1.

Distribution of educational success and university transitions over time. (a) Distribution of educational success over time. (b) Distribution of university transitions over time.

This procedure is also in line with theoretical arguments. As Morgan (2002: 287) writes, ‘[t]he decision of whether or not to enter college immediately following high school is perhaps the most crucial determinant of alternative lifecourse transitions from adolescence to adulthood (…)’ since delayed college entry ‘(…) yields different payoffs that result in alternative lifecourse outcomes’. Hence, from panel data, it is of course possible to investigate university transitions at later points in time (see Hillmert and Jacob, 2010, for such an analysis based on the German Life History Study), but both related utility considerations and subsequent path dependencies may differ.

Main independent variable: teachers’ evaluations

Now I present the distribution of teachers’ evaluations both numerically (Figure 2(a)) and graphically (Figure 2(b)). It can be noted that the number of students who received a positive evaluation by their teacher (30.9%) is higher than the number of students who received a negative one (25.4%) – but evidently most students did not obtain any evaluation at all (43.7%). As mentioned above, for the following operationalization of self-fulfilling prophecies I will only focus on positive versus negative teachers’ evaluations.

Figure 2.

Distribution of teachers’ evaluations: ability for academic studies. (a) Numerical distribution of teachers’ evaluations. (b) Graphical distribution of teachers’ evaluations.

Residuals of over- and underestimations

Next I present the results of probit equations (10) to (12) that I use to extract the ‘net’ effects of self-fulfilling prophecies. Model 1 lists the performance model, Model 2 the motivation model, and Model 3 the full model with all predictors from both Models 1 and 2 (see Table 1).³³ In the performance model (Model 1), we can observe that both students’ intelligence and their school grades significantly predict teachers’ evaluations. The fit of this model is satisfactory. However, except for the measure of students’ relative school performance, in the motivation model, the z-values are much lower (self-confidence) or do not even reach statistical significance (homework effort). This also results in a model fit little more than half as high as for the performance model. Considering the predictors of both models together in the full model, except for students’ relative school performance, only the performance-model indicators remain significant – while the explained variance of the full model is only slightly higher than for the performance model. Thus, we can conclude that for their teachers, students’ performance is far more important than their motivation.

As mentioned, I now store the residuals in order to use them as an operationalization of a ‘net’ effect of self-fulfilling prophecies. Figure 3 displays the distribution of the residuals from the three different probit models. Positive residuals indicate an overestimation relative to the predictors of the probit models, negative residuals a relative underestimation. Also the figures show that the performance model (Figure 3(a)) is a better approximation of teachers’ evaluations than the motivation model (Figure 3(b)). The best model – also in terms of distribution of the generalized probit residuals – is the full model (Figure 3(c)) which is very close to a normal distribution. Hence, for subsequent analyses, the parameter of SFP will refer to the residuals from this most conservative sub-model.

Figure 3.

Distribution of residuals of teachers’ evaluations on students’ performance and motivation, and the combination of both. (a) Performance model. (b) Motivation model. (c) Full model.

Social selectivity of the predictors

Figure 4 summarizes results from separate bivariate regressions of educational motivation and investment risk on the one hand and the full-model residuals on the other hand on parental social class and education, respectively. The dichotomous variables EDMOT and INVRISK are regressed via probit regression, the metric variable SFP is regressed via a conventional linear OLS model. Dark grey bars indicate significant coefficients, light grey bars refer to insignificant coefficients.

Figure 4.

Standardized bivariate regression coefficients of educational motivation, investment risk, and the full-model residual on parental social class and education. (a) Educational motivation. (b) Investment Risk. (c) Full-model residual.

Figure 4(a) shows that EDMOT is only significantly predicted by parental social class, but not by education. Apparently, the mechanism of relative risk aversion is more important regarding parental occupational prestige (which is the indicator for their social class) than for their education. In Figure 4(b), we find very strong negative standardized effects for both predictors on INVRISK. The surprisingly high effect sizes might be explained by the historicity of the data. Before educational expansion began, the lower social strata could have been much more concerned with regard to their educational chances than today, and the same might hold for their perceived financial burden. Finally, Figure 4(c) shows moderate positive significant effects of parental social class and education on the full-model residuals. Hence, students from the higher social strata are more likely to be overestimated by their teachers compared to their actual performance and motivation (and vice versa).

Multivariate analyses

Below, the following bivariate probit models are presented. Model 1 is a baseline model only consisting of the parameters EDMOT and INVRISK as derived from Esser’s (1999: 265–275) SEU model of educational transitions. Model 2 introduces transition-specific instruments in terms of students’ 10^th class GPA (the instrument for passing Abitur) and their final exam average grade, FGRADE (the instrument for university transitions), in order to prevent that the bivariate probit model is only identified via functional form assumptions. In Model 3, I remove these instruments again but add the full-model self-fulfilling prophecy residuals SFP to the model. Model 4 consists of both transition-specific instruments and self-fulfilling prophecy residuals, and Model 5 additionally controls for SES. I first present the results for the model parameters, before discussing evidence for potential selection effects and unobserved heterogeneity.

Model parameters

Model 1 shows a significant positive effect of EDMOT on both students’ probability of passing Abitur (t₁) and their propensities to start academic studies (t₂). The fact that the effect size is higher for t₁ than for t₂ would be in line with the life course or selection hypothesis (Mare, 1980, 1993; Müller and Karle, 1993; Shavit and Blossfeld, 1993) which postulates that the effects of social inequality decrease in the course of students’ education. The estimate of INVRISK, in contrast, is not significant.

When instruments for each transition point are added in Model 2, the estimate of EDMOT loses statistical significance. This holds for both t₁ and t₂ even though only the instrument for t₁, GPA, is statistically significant itself.³⁴

In Model 3, these instruments are removed again, and the residuals SFP are included. Results show that SFP positively affects students’ probability to pass t₁ but not t₂. Yet, the coefficient of EDMOT remains significant for t₁, but not for t₂. Apparently, modeling teacher treatment effects captures a considerable part of the variance of students’ educational motivation that is relevant for students’ university transitions.³⁵

Model 4 again controls for transition-point-specific instruments. Importantly, for students’ probability to pass Abitur, only the parameter of educational motivation loses statistical significance, but the full-model self-fulfilling prophecy residuals remain highly significant. Hence, even when controlling for students’ 10^th class GPA as an instrument that is supposed to predict students’ probability to pass Abitur (but not directly their university transitions), there is evidence for a distinct and robust teacher treatment effect – operationalized in terms of residuals indicating over- and underestimations, respectively – on students’ probability to pass Abitur. According to the formal model presented in the theoretical section, I assume this effect to be induced by the belief-mediated mechanism of differences in later (thus unobserved) subjective expected probabilities of educational success. Controlling for selection effects in terms of the preceding transition point, there is, however, no evidence of a distinct teacher treatment effect on students’ university transitions.

In Model 5, I test first whether there are remaining social background effects that are not captured by EDMOT and INVRISK, and second, whether the teacher treatment effect on students’ probability to pass Abitur is mediated by these social backgrounds. As Table 2 shows, both questions have to be answered negatively.

Table 2.

Bivariate probit model of students’ educational transitions with controls for sample selection.

	Model 1		Model 2		Model 3		Model 4		Model 5
	Abitur beta (z-value)	University beta (z-value)	Abitur beta v	University beta (z-value)	Abitur beta (z-value)	University beta (z-value)	Abitur beta (z-value)	University beta (z-value)	Abitur beta (z-value)	University beta (z-value)
Constant	0.102	−0.021	0.161	1.525***	0.0121	1.91***	−0.0201	1.82***	−0.452	2.06**
	(1.26)	(−0.26)	(1.80)	(5.67)	(0.09)	(7.40)	(−0.14)	(4.86)	(−1.37)	(3.14)
Educational motivation	0.27**	0.20*	0.13	−0.109	0.39**	−0.493	0.246	−0.285	0.227	−0.28
Educational motivation	(3.20)	(2.39)	(1.40)	(−0.52)	(2.85)	(−1.83)	(1.60)	(−0.83)	(1.47)	(-0.81)
Investment risk	−0.02	0.0181	−0.0628	0.258	0.0765	0.0694	0.0331	0.277	0.117	0.23
Investment risk	(−0.31)	(0.27)	(−0.84)	(1.65)	(0.68)	(0.41)	(0.26)	(1.17)	(0.82)	(0.88)
10th class GPA			−0.62***				−0.72***		−0.72***
10th class GPA			(−14.60)				(−10.27)		(−10.23)
Final exam GPA				−0.1152				−0.132		−0.138
Final exam GPA				(−1.37)				(−1.08)		(−1.12)
Full model residuals					0.68***	−0.137	0.45***	0.00709	0.44***	0.0196
Full model residuals					(7.51)	(−0.77)	(4.72)	(0.03)	(4.52)	(0.09)
Parental social class									0.00825	−0.00404
Parental social class									(1.28)	(−0.36)
Parental education									0.00139	−0.0132
Parental education									(0.02)	(−0.12)
Rho	0.99		0.13		−0.78		−0.29		−.27
Wald Chi²	5.761		4.827		4.878		2.991		3.222
p	0.0561		0.185		0.181		0.559		0.78
Log likelihood	−1221.98		−915.72		−456.58		−326.46		−325.02
N	1419		1317		570		539		538

Significance values: *** p < .001; ** p < .01; * p < .05.

Model fit, selection effects and unobserved heterogeneity

Comparing log likelihoods as indicators of model fit, shows that even though the parameter of educational motivation in Model 1 and students’ 10^th class GPA in Model 2 are statistically significant, the most notable improvement in model fit can be obtained when the teacher treatment effect modeled by SFP is included in Model 3 (the log likelihood drops to almost half its former value). Note again that this difference cannot be due to the impact of student performance or motivation since the generalized probit residuals are uncorrelated with the predictors from these models by definition (Vella, 1998: 136). While the transition-specific instruments evidently have distinct explanatory power (at least for students’ probability of passing Abitur) and thus a visible improvement is gained moving from Model 1 to Model 2 as well as from Model 3 to Model 4, no such improvement can be noted when parental social class and education are controlled for in Model 5. This also indicates that there is neither a hint for residual social background effects apart from EDMOT and INVRISK, nor for parental social backgrounds mediating the teacher treatment effect.

The corresponding likelihood ratio test informs us whether there is evidence on potential selection effects induced by unobserved heterogeneity between the two educational transition points. As Table 2 shows, in Model 1, the associated p-value is significant at the 10% level and even quite close to the 5% level – which could be a hint that the model indeed suffers from unobserved heterogeneity. However, Model 1 does not control for transition-specific instruments, and when these instruments are included in Model 2, there is a strong increase in p. This underlines the importance of using selective and accurate instruments as Holm and Jæger (2011) have pled for, and that researchers should refrain from solely identifying the model via untestable functional form assumptions. Notably, a similar decrease in p can be observed when teacher treatment effects but no other instruments are introduced in Model 3. This allows the conclusion that SFP already captures a good deal of heterogeneity that is unobserved in the ‘baseline’ SEU-IEO Model 1. The strongest increase in p can be noted when both SFP and transition-specific instruments are controlled for.

The parameter of ρ measures the correlation between the error terms of both equations (passing Abitur, and university transitions, respectively) that is due to unobserved factors. In neither of the models is ρ statistically significant. However, its sign changes from Model 2 to Model 3 – which may be another hint that there might be some extent of unobserved heterogeneity that is captured by the teacher treatment effect.

In sum, there is only very weak evidence for selection effects induced by unobserved heterogeneity, but results underline the importance of using good instruments instead of relying on model identification by functional form assumptions only.³⁶

Conclusion

The objective of this paper was to provide both theoretical and empirical evidence for the distinct effect of self-fulfilling prophecies, which goes beyond the subjective expected utility (SEU) model of inequality in educational opportunities (IEO) as applied hitherto. My aim was first to develop a formal model, and second to test this model in order to predict students’ probability to graduate from high school (Abitur) as well as their subsequent university transitions.

Having outlined the foundations of mechanism-based explanations, in the theoretical section, I started with a rough sketch of cost-benefit-related models of IEO in general (Breen and Goldthorpe, 1997; Boudon, 1974: 29ff.; Erikson and Jonsson, 1996; Goldthorpe, 1996) and a more elaborate discussion of summarizing the basic assumptions of Esser’s (1999: 265–275) SEU-IEO model in particular. After a literature review of Pygmalion and self-fulfilling prophecy studies (Jussim and Harber, 2005; Madon et al., 1997; Rosenthal and Jacobson, 1968) I brought in the argument that the main finding from this research, i.e. that teachers’ expectations may influence students’ academic performance, requires an extension of the present SEU-IEO model. I thus proposed an integration of self-fulfilling prophecies into Esser’s (1999: 265–275) formal SEU-IEO model in terms of a teacher treatment effect on students’ subjective expected probability of educational success.

Methodologically, self-fulfilling prophecies were operationalized as the residuals of a regression of a specific form of teachers’ evaluations on a performative and a motivational set of variables (also see Madon et al., 1997). Although it turned out that the performance model was able to predict teachers’ evaluations more satisfactorily than the motivation model, for the educational transition models in the empirical section I only used the residuals from the full model comprising both sets of predictors due to distributional considerations (henceforth referred to as SFP).

In the bivariate probit models controlling for selection bias and unobserved heterogeneity (Holm and Jæger, 2011) that were based on the Cologne High School Panel (CHiSP), I found that from the two parameters ‘educational motivation’ (EDMOT) and ‘investment risk’ (INVRISK) that were deduced from the original SEU-IEO model (Esser, 1999: 265–275), only the former significantly predicts students’ educational transitions. However, this effect is partialed out once students’ 10^th class GPA and their final high school exam grade as transition-specific instruments are controlled for, respectively. The fact that the predictive power of the SEU-IEO model is on average weaker than in previous studies (Becker, 2003; Becker and Hecken, 2009a) could be a corroboration of the life-course hypothesis (Mare, 1980, 1993; Müller and Karle, 1993) which postulates that the effects of social inequality decrease during students’ educational career. Yet, findings also indicate that results from educational transition analyses are highly sensitive towards controlling for transition-specific instruments.

Notwithstanding this finding, the estimate of SFP is significant for students’ probability of graduating from high school at the first attempt, but not for university transitions, even when transition-specific instruments are controlled for. Moreover, results do not change when parental social class (in terms of occupational prestige) and parental education are introduced as additional covariates in order to control for both IEO that may be passed on neither EDMOT nor INVRISK as well as for social background effects that might mediate the efficacy of self-fulfilling prophecies. Thus, the tentative conclusion from these models would be that self-fulfilling prophecies indeed have distinct effects on students’ educational success in high school, but there is no reason to assume that self-fulfilling prophecies affect students’ propensity of university transitions conditional on having passed Abitur. Hence, the effect of teachers’ expectations is limited on students’ success in school, and it does not influence their decision for or against starting academic studies. This finding is robust against specifying a multivariate probit model (Cappellari and Jenkins, 2003) with students’ social backgrounds as first-stage regressors as well as against a sensitivity analysis modeling unobserved heterogeneity as the weighted sum of a random variable (Buis, 2011) within a reasonable bound of intercorrelations (cf. footnote 36 below).

However, I see several needs for improvement regarding cost-benefit-related IEO research in general and the self-fulfilling prophecy model proposed here in particular. First, Esser’s model (1999: 265–275) comprises parameters that also form part of the model proposed by Erikson and Jonsson (1996). The latter authors emphasized that two educational alternatives i and j can yield the same expected educational utility ( $P_{i} B_{i} = P_{j} B_{j}$ ) if $P_{i} < P_{j}$ and $B_{i} > B_{j}$ . However, a more risk averse (Jæger and Holm, 2012) person would always opt for alternative j, notwithstanding the higher expected benefit of alternative i. Hence, one improvement of conventional cost-benefit-related models of IEO would be to incorporate theoretical parameters of risk aversion which are then accurately operationalized in empirical studies.

Second, evidence by Stocké (2011) challenges the assumption of constant aspirations among social classes. The author finds that among the working class, the difference between idealistic (i.e. most wanted) and realistic (i.e. most probable) aspirations (Gottfredson, 1981) is higher than among the service class (also see Stocké, 2009). However, Stocké’s analyses did not follow either of the above-reviewed utility frameworks. Therefore, it will have to be clarified how realistic aspirations actually differ from students’ subjective expected probability of successfully completing a given school track – which would still suit the (more succinct) assumption of constant desires and varying beliefs among social strata.

Third, while all cost-benefit models of educational transitions assume that desires (i.e. the absolute value of education) are constant between the social strata, it might well be possible that additional opportunity-mediated mechanisms (e.g. of classroom socio-economic composition or achievement context; see Ready and Wright, 2011) affect the respective utility attached to educational transitions in general and the effect of a self-fulfilling prophecy as described above in particular (also see Blalock and Wilken, 1979, ch. 3).

Fourth, apart from improvement within the framework of rational choice or SEU models of educational transitions, it has to be noted that a recent theoretical advancement of action theory, the model of frame selection (MFS), suggests that actors’ conscious cost-benefit consideration (rc-mode) is only a very special case of individual behavior which may be expected to occur particularly in high-cost situations. In many – if not most – cases, however, individuals may rely on a rather unconscious, automatic-spontaneous (as-mode) type of information processing (Kroneberg, 2006; Kroneberg and Kalter, 2012; also see Esser, 2010; Kroneberg, 2011). Hence, also formal models of educational transitions should try to model respective situational frames and related action scripts that might prime educational transition decisions in a comparable automatic-spontaneous manner (also see Becker, 2012a, 2012b). This endeavor would be of utmost relevance for self-fulfilling prophecy research as well. As outlined above, I appreciate one referee’s remark that teachers and students might be partly unaware of the effect of є on students’ educational transitions. It might therefore be debatable whether one can assume that є enters anyone’s utility function. Consequently, my extension of the SEU model should only be regarded as a starting point that has to be amended by the more automatic frames and scripts that shape both teachers’ evaluations and students’ decisions but that might be unconscious to both types of actors.

Regarding a more thorough analysis of self-fulfilling prophecy effects in particular, future studies should, fifth, tackle the shortcoming of an insufficient consideration of mediator and moderator variables such as students’ grade level or teachers’ duration of teaching in a particular class. Thus, future studies should also include potential covariates apart from action-theoretical variables to ensure a better understanding of the social mechanisms behind the efficacy of self-fulfilling prophecies. This holds in particular if the empirical model per se is, as in the case of this article, only an approximation of the theoretical or substantive model. Considering both teacher- and student-level variables would require estimating a cross-classified hierarchical model (cf. Hox, 2010, ch. 9) wherein teachers’ evaluations as the lowest unit are nested in both teacher and student contexts.This might also necessitate a refined operationalization of self-fulfilling prophecies (e.g. in terms of random effect models).

Footnotes

Appendix 1

Table A.

Descriptive statistics.

	count	mean	sd	min	max
Time of high school graduation	1415	81.9	14.66	46	228
Graduation at first attempt	1987	0.53	0.5	0	1
Time of university transition	1987	154.57	108.17	44	367
University transition within 3 years after graduation	1987	0.48	0.5	0	1
Teachers’ evaluation (dichotomized)	1367	0.55	0.5	0	1
Intelligence [IST]	3230	110.45	11.35	76	151
Mean of class teacher subject grades [CTGRADE]	2297	0	1	−2.97	3.34
Subj. homework effort [HOMEFF]	3224	5.71	2.08	1	11
Subj. rel. school performance [RELPERF]	3208	6.65	1.91	1	11
Subj. self-confidence [SCONF]	3213	8.13	1.51	1	11
Residuals, performance model	1281	0	0.69	−2.21	2.3
Residuals, motivation model	1294	0	0.74	−1.79	2.1
Residuals, full model [SFP]	1259	0	0.66	−2.18	3.02
Expected benefit [B]	3225	0.69	0.46	0	1
Value of status decline [-SD]	2355	0.41	0.49	0	1
Expected probability of status decline [psd]	2674	0.37	0.48	0	1
Subj. Expectation of success [pep]	2695	0.95	0.23	0	1
Expected costs [C]	2695	0.46	0.5	0	1
Educational motivation [EDMOT]	2290	0.8	0.4	0	1
Investment risk [INVRISK]	2691	0.44	0.5	0	1
10th class Grade Point Average [GPA]	3228	0	1	−3.9	3.46
Final high school exam grade [FGRADE]	1420	0	1	−3.26	2.35
Parental occupational prestige [OCCPRES]	2687	49.37	12.63	18	78
Parental educational attainment [EDUC]	3374	2.14	1.23	1	4

Acknowledgements

An earlier version of this paper was presented at the international conference Higher education and beyond – Inequalities regarding entrance to higher education and educational credentials (4–9 July 2010, Monte Verita). I thank all participants for their helpful comments and suggestions. Furthermore, I also thank Rolf Becker, Klaus Birkelbach, Heiner Meulemann, Christina Zuber and two anonymous referees for their valuable comments on later versions of this contribution. Finally, I am grateful to Manuel Junck and Christina Zuber for proofreading different versions of the manuscript.

Funding

Most of this research was supported by a research grant of the Deutsche Forschungsgemeinschaft (DO 325/4)) and a PhD fellowship awarded by the Cologne Graduate School in Management, Economics and Social Sciences (University of Cologne, Germany).

Notes

References

Amthauer

(1957) Intelligenz-Struktur-Test. Göttingen: Hogrefe.

Ashenfelter

Harmon

Oosterbeek

(1999) A review of estimates of the schooling/earnings relationship, with tests for publication bias. Labour Economics 6(4): 453–470.

Becker

(2000) Klassenlage und Bildungsentscheidungen – Eine empirische Anwendung der Wert-Erwartungstheorie. Zeitschrift für Soziologie 52(3): 450–474.

Becker

(2003) Educational expansion and persistent inequalities of education. European Sociological Review 19(1): 1–24.

Becker

(2012a) Bildungsungleichheit im Lichte aktueller Theorieanwendung in der soziologischen Bildungsforschung. Bildung – Arbeit – Erwachsenwerden. Ein interdisziplinärer Blick auf die Transition im Jugend und jungen Erwachsenenalter. Wiesbaden: VS Verlag für Sozialwissenschaften, pp. 43–75.

Becker

(2012b) Der Übergang ins Hochschulstudium Prozesse und Mechanismen am Beispiel der deutschen Schweiz. In: Bergmann

Hupka-Brunner

Meyer

. (eds) Bildung – Arbeit – Erwachsenwerden. Ein interdisziplinärer Blick auf die Transition im Jugend und jungen Erwachsenenalter. Wiesbaden: VS Verlag für Sozialwissenschaften, pp. 305–331.

Becker

Hecken

(2009a) Higher education or vocational training? An empirical test of the rational action model of educational choices suggested by Breen and Goldthorpe and Esser. Acta Sociologica 52(1): 25–45.

Becker

Hecken

(2009b) Why are working-class children diverted from universities? An empirical assessment of the diversion thesis. European Sociological Review 25(2): 233–250.

Bernardi

(2012) Unequal transitions: selection bias and the compensatory effect of social background in educational careers. Research in Social Stratification and Mobility 30(2): 159–174.

10.

Biggs

(2009) Self-fulfilling prophecies. In: Baerman

Hedström

(eds) The Oxford Handbook of Analytical Sociology. Oxford: Oxford University Press, pp. 294–314.

11.

Birkelbach

(2011) Teacher evaluations over the life course: valid prognosis or self-fulfilling prophecy?. In: Mica

Peisert

Winczorek

(eds) Sociology and the Unintended – Robert Merton Revisited. Frankfurt aMain: Peter Lang, pp. 133–153.

12.

Bishop

(1989) Is the test score decline responsible for the productivity growth decline? American Economic Review 79(1): 178–197.

13.

Blalock

Wilken

(1979) Intergroup Processes: A Micro-Macro Perspective. New York: The Free Press.

14.

Boissiere

Knight

Sabot

(1985) Earnings, schooling, ability, and cognitive skills. American Economic Review 75(5): 1016–1030.

15.

Boudon

(1974) Education, Opportunity and Social Inequality: Changing Prospects in Western Society. New York: John Wiley & Sons

16.

Brattesani

Weinstein

Marshall

(1984) Student perceptions of differential teacher treatment as moderators of teacher expectation effects. Journal of Educational Psychology 76(2): 236–247.

17.

Breen

(1999) Beliefs, rational choice and Bayesian learning. Rationality and Society 11(4): 463–479.

18.

Breen

García-Peñalosa

(2002) Bayesian learning and gender segregation. Journal of Labor Economics 20(4): 899–922.

19.

Breen

Goldthorpe

(1997) Explaining educational differentials: towards a formal rational action theory. Rationality and Society 9(3): 275–305.

20.

Breen

Jonsson

(2000) Analyzing educational careers: a multinomial transition model. American Sociological Review 65(5): 754–772.

21.

Buis

(2011) The consequences of unobserved heterogeneity in a sequential logit model. Research in Social Stratification and Mobility 29(3): 247–262.

22.

Cappellari

Jenkins

(2003) Multivariate probit regression using simulated maximum likelihood. Stata Journal 3(3): 278–294.

23.

Chetty

Friedman

Rockoff

(2011) The long-term impact of teachers: teacher value added and student outcomes in adulthood. NBER Working Paper Series 17699: 1–94.

24.

Cox

(1990) Role of models in statistical analysis. Statistical Science 5(3): 169–174.

25.

Cunha

Heckman

(2007) Identifying and estimating the distributions of ex post and ex ante returns to schooling. Labour Economics 14(6): 870–893.

26.

Cunha

Heckman

Navarro

(2005) Separating uncertainty from heterogeneity in life cycle earnings. Oxford Economic Papers 57(2): 191–261.

27.

Daido

Itoh

(2005) The Pygmalion and Galatea effects: an agency model with reference-dependent preferences and applications to self-fulfilling prophecy. CESifo working papers, 1444. Available at: http://ideas.repec.org/p/ces/ceswps/_1444.html

28.

Davis

Moore

(1945) Some principles of stratification. American Sociological Review 10(2): 242–249.

29.

DiPrete

Eirich

(2006) Cumulative advantage as a mechanism for inequality: a review of theoretical and empirical developments. Annual Review of Sociology 32: 271–297.

30.

Elashoff

Snow

(1971) Pygmalion Reconsidered: A Case Study in Statistical Inference: Reconsideration of the Rosenthal-Jacobson Data on Teacher Expectancy. Worthington, OH: C. A. Jones Pub. Co.

31.

Elster

(1985) Making Sense of Marx. Cambridge: Cambridge University Press.

32.

Enders

(2010) Applied Missing Data Analysis. New York: The Guilford Press.

33.

Erikson

Jonsson

(1996) Introduction: explaining class inequality in education: the Swedish test case. In: Erikson

Jonsson

(eds) Can Education be Equalized? The Swedish Case in Comparative Perspective. Boulder, CO: Westview Press, pp. 1–63.

34.

Esser

(1996) What is wrong with “variable sociology”? European Sociological Review 12(2): 159–166.

35.

Esser

(1999) Soziologie. Spezielle Grundlagen. Bd. 1: Situationslogik und Handeln. Frankfurtam Main/New York: Campus Verlag.

36.

Esser

(2010) Das Modell der Frame-Selektion. Eine allgemeine Theorie der Sozialwissenschaften. In: Albert

Sigmund

(eds) Soziologische Theorie kontrovers [Sonderheft 50 der Kölner Zeitschrift für Soziologie und Sozialpsychologie]. Wiesbaden: VS Verlag für Sozialwissenschaften, pp. 50–62.

37.

Festinger

(1957) A Theory of Cognitive Dissonance. Evanston, IL: Row, Peterson.

38.

Freedman

Sekhon

(2010) Endogeneity in probit response models. Political Analysis 18(2): 138–150.

39.

Gambetta

(1998) Concatenations of mechanisms. In: Hedström

Swedberg

(eds) Social Mechanisms: An Analytical Approach to Social Theory. Cambridge: Cambridge University Press, pp. 102–124.

40.

Gangl

(2010) Causal inference in sociological research. Annual Review of Sociology 36: 21–47.

41.

Gill

Reynolds

(1999) Educational expectations and school achievement of urban African American children. Journal of School Psychology 37(4): 403–424.

42.

Goldthorpe

(1996) Class analysis and the reorientation of class theory: the case of persisting differentials in educational attainment. British Journal of Sociology 47(3): 481–505.

43.

Goldthorpe

(2001) Causation, statistics, and sociology. European Sociological Review 17(1): 1–20.

44.

Gottfredson

(1981) Circumscription and compromise: a developmental theory of occupational aspirations. Journal of Counseling Psychology 28(6): 545–579.

45.

Gourieroux

Monfort

Renault

. (1987) Generalised residuals. Journal of Econometrics 34(1–2): 5–32.

46.

Greene

(2003) Econometric Analysis. Upper Saddle River, NJ: Prentice Hall.

47.

Gross

(2009) A pragmatist theory of social mechanisms. American Sociological Review 74(3): 358–379.

48.

Hanushek

Kimko

(2000) Schooling, labor-force quality, and the growth of nations. American Economic Review 90(5): 1184–1208.

49.

Heckman

(1979) Sample selection bias as a specification error. Econometrica: Journal of the Econometric Society 47(1): 153–161.

50.

Hedström

(2005) Dissecting the Social. On the Principles of Analytical Sociology. Cambridge: Cambridge University Press.

51.

Hedström

Swedberg

(1996) Social mechanisms. Acta Sociologica 39(3): 281–308.

52.

Hedström

Ylikoski

(2010) Causal mechanisms in the social sciences. Annual Review of Sociology 36: 49–67.

53.

Heider

(1946) Attitudes and cognitive organization. Journal of Psychology 21(1): 107–112.

54.

Hillmert

Jacob

(2010) Selections and social selectivity on the academic track: a life-course analysis of educational attainment in Germany. Research in Social Stratification and Mobility 28(1): 59–76.

55.

Hinnant

O’Brien

Ghazarian

(2009) The longitudinal relations of teacher expectations to achievement in the early school years. Journal of Educational Psychology 101(3): 662–670.

56.

Holm

Jæger

(2011) Dealing with selection bias in educational transition models: the bivariate probit selection model. Research in Social Stratification and Mobility 29(3): 311–322.

57.

Hox

(2010) Multilevel Analysis – Techniques and Applications. 2nd ed. New York and Hove: Routledge.

58.

Hyman

(1953) The Value systems of different classes: a social psychological contribution to the analysis of stratification. In: Bendix

Lipset

(eds) Class, Status and Power. Glencoe: The Free Press, pp. 426–442.

59.

Jackson

Erikson

Goldthorpe

. (2007) Primary and secondary effects in class differentials in educational attainment. Acta Sociologica 50(3): 211–229.

60.

Jaeger

Holm

(2011) Relative risk aversion and educational decision making: a dynamic model with ability updating and heterogeneous RRA behavior. Paper presented at the 2011 Spring Meeting of the ISA RC28, University of Essex, UK, 13–16 April. Available at: https://www.iser.essex.ac.uk/uploads/paper/document/38/rc28_jaeger_holm.pdf

61.

Jæger

Holm

(2012) Conformists or rebels? Relative risk aversion, educational decisions and social class reproduction. Rationality and Society 24(2): 221–253.

62.

Jonsson

(1999) Explaining sex differences in educational choice: an empirical assessment of a rational choice model. European Sociological Review 15(4): 391–404.

63.

Jürges

Schneider

(2006) Age at school entry and teachers’ recommendations for secondary school track choice in Germany. Paper presented at the 20th annual ESPE conference, Verona, Italy, 22–24 June.

64.

Jussim

(1986) Self-fulfilling prophecies: a theoretical and integrative review. Psychological Review 93(4): 429–445.

65.

Jussim

(1989) Teacher expectations: self-fulfilling prophecies, perceptual biases, and accuracy. Journal of Personality and Social Psychology 57(3): 469–480.

66.

Jussim

Harber

(2005) Teacher expectations and self-fulfilling prophecies: knowns and unknowns, resolved and unresolved controversies. Personality and Social Psychology Review 9(2): 131–155.

67.

Jussim

Eccles

Madon

(1996) Social perception, social stereotypes, and teacher expectations: accuracy and the quest for the powerful self-fulfilling prophecy. In: Zanna

(ed.) Advances in Experimental Social Psychology. San Diego, CA: Academic Press, pp. 281–388.

68.

Keller

Zavalloni

(1964) Ambition and social class: a respecification. Social Forces 43(1): 58–70.

69.

Kroneberg

(2006) The Definition of the Situation and Variable Rationality: The Model of Frame Selection as a General Theory of Section (Sonderforschungsbereich 504 Publications), University of Mannheim, Mannheim. Available at: http://ideas.repec.org/p/xrs/sfbmaa/06-05.html

70.

Kroneberg

(2011) Die Erklärung sozialen Handelns. Grundlagen und Anwendung einer integrativen Theorie. Wiesbaden: VS Verlag für Sozialwissenschaften.

71.

Kroneberg

Kalter

(2012) Rational choice theory and empirical research: methodological and theoretical contributions in Europe. Annual Review of Sociology 38: 73–92.

72.

Ladd

Walsh

(2002) Implementing value-added measures of school effectiveness: getting the incentives right. Economics of Education Review 21(1): 1–17.

73.

Lauen

(2007) Contextual explanations of school choice. Sociology of Education 80(3): 179–209.

74.

Madon

Jussim

Eccles

(1997) In search of the powerful self-fulfilling prophecy. Journal of Personality and Social Psychology 72(4): 791–809.

75.

Madon

Jussim

Keiper

. (1998) The accuracy and power of sex, social class, and ethnic stereotypes: a naturalistic study in person perception. Personality and Social Psychology Bulletin 24(12): 1304–1318.

76.

Madon

Willard

Guyll

. (2006) Self-fulfilling prophecy effects of mothers’ beliefs on children’s alcohol use: accumulation, dissipation, and stability over time. Journal of Personality and Social Psychology 90(6): 911–926.

77.

Mare

(1980) Social background and school continuation decisions. Journal of the American Statistical Association 75(370): 295–305.

78.

Mare

(1981) Change and stability in educational stratification. American Sociological Review 46(1): 72–87.

79.

Mare

(1993) Educational stratification on observed and unobserved components of family background. In: Blossfeld

H-P

Shavit

(eds) Persistent Inequality – Changing Educational Attainment in Thirteen Countries. Boulder, CO: Westview Press, pp. 351–376.

80.

Mechtenberg

(2009) Cheap talk in the classroom: how biased grading at school explains gender differences in achievements, career choices and wages. Review of Economic Studies 76(4): 1431–1459.

81.

Merton

(1948) The self-fulfilling prophecy. Antioch Review 8(2): 193–210.

82.

Merton

(1987) Three fragments from a sociologist’s notebooks: establishing the phenomenon, specified ignorance, and strategic research materials. Annual Review of Sociology 13: 1–29.

83.

Meulemann

(1979) Klassenlage, Entscheidungsfeld und Bildungsaspirationen - Ein Versuch zur theoretischen Präzisierung und kausalen Erklärung von Zusammenhängen zwischen sozialer Struktur und individueller Lebensplanung. Zeitschrift für Soziologie 8(4): 391–414.

84.

Mistry

White

Benner

. (2009) A longitudinal study of the simultaneous influence of mothers’ and teachers’ educational expectations on low-income youth’s academic achievement. Journal of Youth and Adolescence 38(6): 826–838.

85.

Morgan

(1998) Adolescent educational expectations. Rationality and Society 10(2): 131–162.

86.

Morgan

(2002) Modeling preparatory commitment and non-repeatable decisions. Rationality and Society 14(4): 387–429.

87.

Muller

Katz

Dance

(1999) Investing in teaching and learning: dynamics of the teacher-student relationship from each actor’s perspective. Urban Education 34(3): 292–337.

88.

Müller

Karle

(1993) Social selection in educational systems in Europe. European Sociological Review 9(1): 1–23.

89.

Müller-Benedict

(2007) Wodurch kann die soziale Ungleichheit des Schulerfolgs am stärksten verringert werden? Kölner Zeitschrift für Soziologie und Sozialpsychologie 59(4): 615–639.

90.

Need

De Jong

(2001) Educational differentials in the Netherlands. Rationality and Society 13(1): 71–98.

91.

Neugebauer

Schindler

(2012) Early transitions and tertiary enrolment: the cumulative impact of primary and secondary effects on entering university in Germany. Acta Sociologica 55(1): 19–36.

92.

Parsons

(1959) The school class as a social system: some of its functions in American society. Harvard Educational Review 29(4): 297–318.

93.

Pietsch

Stubbe

(2007) Inequality in the transition from primary to secondary school: school choices and educational disparities in Germany. European Educational Research Journal 6(4): 424–445.

94.

Raudenbush

(1984) Magnitude of teacher expectancy effects on pupil IQ as a function of the credibility of expectancy induction: a synthesis of findings from 18 experiments. Journal of Educational Psychology 76(1): 85–97.

95.

Raudenbush

(1994) Random effects models. In: Cooper

Hedges

(eds) The Handbook of Research Synthesis. New York: SAGE, pp. 301–321.

96.

Ready

Wright

(2011) Accuracy and inaccuracy in teachers’ perceptions of young children’s cognitive abilities. American Educational Research Journal 48(2): 335–360.

97.

Rivkin

Hanushek

Kain

(2005) Teachers, schools, and academic achievement. Econometrica: Journal of the Econometric Society 73(2): 417–458.

98.

Rogosa

(1987) Casual models do not support scientific conclusions: a comment in support of Freedman. Journal of Educational Statistics 12(2): 185–195.

99.

Rosenthal

(1987) “Pygmalion” effects: existence, magnitude, and social importance. A reply to Wineburg. Educational Researcher 16(9): 37–41.

100.

Rosenthal

DiMatteo

(2001) Meta-analysis: recent developments in quantitative methods for literature reviews. Annual Review of Psychology 52: 59–82.

101.

Rosenthal

Jacobson

(1968) Pygmalion in the Classroom: Teacher Expectation and Pupils’ Intellectual Development. New York: Holt, Rinehart & Winston.

102.

Rosenthal

Rubin

(1978) Interpersonal expectancy effects: the first 345 studies. Behavioral and Brain Sciences 1(3): 377–415.

103.

Roth

(1995) We can throw teacher expectations on the IQ scrap heap. New York Times, 02 January 1995, A25.

104.

Schindler

Lörz

(2012) Mechanisms of social inequality development: primary and secondary effects in the transition to tertiary education between 1976 and 2005. European Sociological Review 28(5): 647–660.

105.

Schneider

(2008) Social inequality in educational participation in the German school system in a longitudinal perspective: pathways into and out of the most prestigious school track. European Sociological Review 24(4): 511–526.

106.

Sewell

Haller

Ohlendorf

(1970) The educational and early occupational status attainment process: replication and revision. American Sociological Review 35(6): 1014–1027.

107.

Sewell

Haller

Portes

(1969) The educational and early occupational attainment process. American Sociological Review 34(1): 82–92.

108.

Shavit

Blossfeld

H-P

(1993) Persistent inequality. Changing educational attainment in thirteen countries. San Francisco, CA/Oxford: Westview Press.

109.

Smith

(1980) Meta-analysis of research in teacher expectation. Evaluation in Education 4: 53–56.

110.

Snow

(1969) Unfinished Pygmalion. Contemporary Psychology 14(4): 197–199.

111.

Sørensen

(1998) Theoretical mechanisms and the empirical study of social processes. In: Hedström

Swedberg

(eds) Social Mechanisms: An Analytical Approach to Social Theory. Cambridge: Cambridge University Press, pp. 238–266.

112.

Sorhagen

(2013) Early teacher expectations disproportionately affect poor children’s high school performance. Journal of Educational Psychology 105(2): 465–477.

113.

Stocké

(2007) Explaining educational decision and effects of families’ social class position: an empirical test of the Breen Goldthorpe model of educational attainment. European Sociological Review 23(4): 505–519.

114.

Stocké

(2009) Adaptivität oder Konformität? Die Bedeutung der Bezugsgruppe und die Leistungsrealität der Kinder auf die Entwicklung elterlicher Bildungsaspirationen am Ende Grundschulzeit. Bildungsentscheidungen. Sonderheft der Zeitschrift für Erziehungswissenschaften 12: 257–280.

115.

Stocké

(2011) Educational aspirations and inequality in educational opportunity: the difference between realistic and idealistic aspirations. Paper presented at the 2011 Spring Meeting of the ISA RC28, University of Essex, UK, 13–16 April.

116.

Thorndike

(1968) Review of Pygmalion in the classroom. American Educational Research Journal 5(4): 708–711.

117.

Vella

(1998) Estimating models with sample selection bias: a survey. Journal of Human Resources 33(1): 127–169.

118.

Von Wright

(1971) Explanation and Understanding. London: Routledge & Kegan Paul.

119.

Weber

(1968) Economy and Society: An Outline of Interpretive Sociology (eds Roth

Wittich

) New York: Bedminster Press.

120.

Wooldridge

(2002) Econometric Analysis of Cross-Section and Panel Data. Cambridge, MA: MIT Press.