## Abstract

Up to now, there exist several studies documenting the educational expansion in Austria in the 20th century but only few studies measureing the degree of persistence of educational attainment over generations. Furthermore, for Austria there are no internationally comparable persistence-measures of educational attainment available. This study aims to fill this gap and delivers key-measures for intergenerational persistence of educational attainment. The Austrian Household Survey on Housing Wealth includes information on socioeconomic characteristics of respondents and their parents. The results demonstrate strong persistence in educational attainment in Austria. Using uni- as well as multivariate econometric techniques and a Markovian approach we show that educational persistence decreased over time. Overall, Austria ranks third in terms of intergenerational educational attainment persistence among a number of european countries and the US. Our results therefore allow to question the significance of meritocratic values and equal opportunity for educational advancement in the Austrian society compared to other European countries and the USA.

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## Notes

- 1.
For a detailed analysis of the gender aspects of this phenomenon using the same dataset see Fessler and Schneebaum (2011).

- 2.
For a discussion of the differences between controlling for parental endowments versus controlling for children’s endowments in order to estimate total causal effects, see Dardanoni et al. (2008).

- 3.
Note that even if a panel data series existed, it would hardly be long enough to include a sample of the representative descendant population and their parents. Nevertheless there are cross section datasets (as the HSHW 2008) in which the education of parents is recalled by the interviewed descendants which represent the population as a whole.

- 4.
In Bourdieu’s work,

*habitus*is a system of dispositions (perception, thought and action). The individual agent develops these dispositions in response to the determining structures (such as class, family, and education) and external conditions (fields) they encounter. They are therefore neither wholly voluntary nor wholly involuntary. - 5.
This is comparable to high-school (grammar school, upper secondary education), but with the addition of being a university entrance exam.

- 6.
EU-SILC 2005 contains the information on parental education for Austria. By examining the dataset, we found that there must have been some problems in the fieldwork concerning these variables, because their quality is insufficient for scientific analyses. Furthermore, the microcensus of 1996 contains educational background of parents (see Spielauer 2004).

- 7.
Fieldwork was carried out by the Institut für Empirische Sozialforschung (Institute for Empirical Social Studies).

- 8.
102 cases have been droped because descendants are too old or too young and annother 61 have been droped because education of father and/or mother is missing.

- 9.
In doing so we use all categorical information available and replace them with appropriate statuory schooling years: maximum compulsory school = 9, apprenticeship and vocational school = 10, medium technical school = 11, Matura and higher vocational school = 12.5, University and Fachhochschule = 16. Due to the complex educational system it is not clear which would be the

*right*statutory values. Especially persons with maximum compulsory school finishing school before the compulsory schooling refom in 1962 only had 8 years of statutory education. As we set the number to 9 years even for people not even finishing cumpolsory education it seems to make sense for those finishing compulsory school before 1962, too. Nevertheless, we tried different specifications and for a set of reasonable values results are robust. - 10.
1. no degree; 2. compulsory school level; 3. apprenticeship or vocational school degree; 4. medium-level or technical school; 5. Matura and higher level vocational school; 6. University, Fachhochschule.

- 11.
The classification is basically maximum primary, secondary and high education, but splitting up the secondary education into two parts: one is the original class 3 (taking 10 or less statuory school years to finish and is more manual labor oriented). The other is the aggregated original classes 4 and 5 (taking 11 and more statuory school years to finish and they are in general not manual labor oriented). For a detailed discussion of the Austrian Educational System in an economical context see Fersterer (2001).

- 12.
Note that peaks are presumably due to the rather small sample sizes in a certain educational attainment group and cohort.

- 13.
- 14.
For the Markovian approach one needs categorical data. The mean of parental schooling years is therefore not an appropriate solution.

- 15.
In the 1970s, the Austrian government introduced several policies to increase educational attainment in general, but particularly for children from a low-income background (1971, Schulorganisationsnovelle; 1972, free university access; 1974, Schulorganisationsgesetz).

- 16.
For detailed information on the necessary conditions for the use of these measures and their construction see Appendix.

- 17.
This measure was calculated using the joint distribution of the variables, the transition matrices are based on.

- 18.
Note that also the educational expansion is clearly captured by the model.

- 19.
The relevant axioms are

(i)

*Monotonicity*: \( P \succ P^{\prime} \) when \( p_{ij} \ge \mathop {p^{\prime}}\nolimits_{ij} \forall i \ne j \) and \( p_{ij} > \mathop {p^{\prime}}\nolimits_{ij} \) for some \( i \ne j \). Therefore \( M(P) > M(P^{\prime}) \).(ii)

*Immobility*: \( M(I) = 0 \). Minimum should be reached for identity matrix.(iii)

*Perfect Mobility*: Let \( P^{\prime\prime} = (1/n)uu^{\prime} \) where \( u \) is an n-dimensional vector of ones. Then \( \forall P \ne P^{\prime\prime} \in P \) it follows that \( M(P^{\prime\prime}) > M(P) \)Clearly (i) and (iii) are inconsistent on the domain of P.

- 20.
Sometimes referred to as Shorrocks Mean Exit Time or Prais Index.

## References

Bacher J (2003) Soziale Ungleichheit und Bildungspartizipation im weiterführenden Schulsystem Österreichs. Österreichische Zeitschrift für Soziologie, 3 2003

Bauer P, Riphan, Regina T (2004) Heterogeneity in the intergenerational transmission of educational attainment: evidence from Switzerland on natives and second generation immigrants. IZA discussion paper, no 1354

Becker GS, Tomes N (1189) 1979. An equilibrium theory of the distribution of income and intergenerational mobility J Polit Econ(87):6–1153

Becker GS, Tomes N (1986) Human capital and the rise and fall of families. J Labor Econ vol 4, no 3, part 2 The family and the distribution of economic rewards (July 1986), pp S1–S39

Behrman JR, Rosenzweig MR (2002) Does increasing women’s schooling raise the schooling of the next generation? Am Econ Rev 92:323–334

Belzil C, Hansen J (2003) Structural estimates of the intergenerational educational correlation. In: J Applied Econ vol 18 no 5

Biffl G (2002) Der Bildungswandel in Österreich in den Neunziger Jahren. Wifo-Monatsberichte 6/2002, pp 377–384, Vienna

Black SE, Devereux P (2010) Recent developments in intergenerational mobility, IZA discussion paper series, discussion paper no 4866

Black SE, Devereux PJ, Salvanes KG (2005) Why the apple doesn’t fall far: understanding intergenerational transmission of human capital. Am Econ Rev 95:437–449

Blanden J, Machin S (2007) Recent changes in intergenerational mobility in Britain. Report for Sutton Trust

Blau PM, Duncan OD (1967) The American occupational structure. Free Press New York

Bourdieu P (1984) Die feinen Unterschiede. STW Frankfurt

Checchi D, Fiorio CV, Leonardi M (2008) Intergenerational persistence in educational attainment in Italy, presented at the 30th general conference of the international association for research in income and wealth, August

Chevalier A, Denny K, McMahon D (2003) A multi-country study of inter-generational educational mobility, School of economics, University College Dublin, working paper 200314

D’Addio (2007) Intergenerational transmission of disadvantage, mobility or immobility across generations? OECD Social Employment and Migration WP no. 52

Daouli J, Demoussis M, Giannakopoulos N (2008) Mothers, fathers and daughters: intergenerational transmission of education in Greece. Available at SSRN: http://ssrn.com/abstract=1161014 (22.11.2010)

Dardanoni V, Fiorini M, Forcina A (2008) Stochastic monotonicity in intergenerational mobility tables, working paper available at http://dse.univr.it/it/documents/it4/dff-final.pdf (20.11.2009)

Dardanoni V, Forcina A, Modica S (2008) Direct causal effects in education transmission, working paper available at http://dse.univr.it/it/documents/it4/dfm-final.pdf (20.11.2009)

Fersterer J (2001) Erträge der Schulbildung in Österreich—Eine empirische Untersuchung, Dissertation, University of Linz, Austria

Fessler P, Schneebaum A (2011) Gender aspects of the intergenerational persistence of educational attainment in Austria, Feminist economics, (forthcoming)

Fields GS, Ok EA (1996) The measurement of income mobility: an introduction to the literature, working papers 96–05, C.V. Starr Center for Applied Economics, New York University

Geweke J, Marshall RC, Zarkin GA (1423) 1986. Mobility indices in continous time markov chains Econometrica(54):6–1407

Haveman R, Wolfe B (1995) The determinants of children’s attainments: a review of methods and findings. J Econ Lit vol 33, no 4 (Dec, 1995), pp 1829–1878

Heckman J, Carneiro P (2003) Human capital policy NBER Working Paper 9495

Hertz T, Jayasundera T, Piraino P, Selcuk S, Smith N, Verashchagina A (2008) The inheritance of educational inequality: international comparisons and fifty-year trends. Adv Econ Anal Policy, Berkeley Electronic Press, vol 7(2)

Holmlund H, Lindahl M, Plug E (2008) The causal effect of parent’s schooling on children’s schooling: a comparison of estimation methods, IZA Discussion Paper Series, no 3630

Landler F (1997) Das österreichische Bildungswesen in Zahlen–Analyse und Computersimulation des Schulsystems und der Qualifikationsstruktur der Bevölkerung. Vienna, WUV-Universitätsverlag

Loehlin JC (2005) Resemblance in personality and attitudes between parents and their children: genetic and environmental contributions. In: Bowles S et al. Princeton University Press

Mazumder B (2005) Fortunate sons: new estimates of intergenerational mobility in the United States using social security earnings data. Rev Econ Stat 87(2):235–255

Mulligan CB (1999) Galton versus the human capital approach to inheritance. J Polit Econ, vol 107, no 6, Part 2: Symposium on the Economic Analysis of Social Behavior in Honor of Gary S. Becker (Dec., 1999), pp S184–S224

Norris JR (1997) Markov Chains. Cambridge University Press, Cambridge

OECD (2008) Growing unequal. Chapter 8 Intergenerational Monility, pp 203–221

Osborne Groves MA (2005) Personality and the intergenerational transmission of earnings from fathers to sons. In: Bowles S, Gintis H, Osborne Groves M (eds) Unequal chances: family background and economic success. Princeton University Press, New Jersey

Plug E (2004) Estimating the effect of mother’s schooling using a sample of adoptees. Am Econ Rev 94:358–368

Prais SJ (1955) Measuring social mobility. J R Stat Soc Series A 118:56–66

Shorrocks AF (1978) The measurement of mobility. Econometrica vol 46, no 5, September

Solon G (2002) Cross-country differences in intergenerational income mobility In: J Econ Perspect, vol 16

Solon G (2004) A model of intergenerational mobility variation over time and place. In: Corak M (ed) Generational income mobility in North America and Europe. Cambridge University Press, Cambridge

Spielauer M (2004) Intergenerational educational transmission within families: an analysis and microsimulation projection for Austria. Vienna Yearbook of Population Research

Steiner M (1998) Empirische Befunde zur Chancengleichheit im österreichischen Bildungssystem, Erziehung Heute, 4/98, Innsbruck, 1998

Van de Gaer D, Schokkaert E, Martinez M (2001) Three meanings of intergenerational mobility. Economica 68:519–837

Wagner K Zottel S (2009) OeNB-Immobilienvermögenserhebung 2008 der privaten Haushalte—Beschreibung, verwendete Methoden und Bewertungsansätze, Statistiken Q4/09, OeNB, 45–65

Wiborg N Hansen M (2009) Change over time in the intergenerational transmission of social disadvantage. In: European Sociological Review, Vol. 25, Nr. 3, 379–394

## Acknowledgment

Valuable comments from Alyssa Schneebaum, Oliver Gorbach, Verena Halsmayer, Markus Knell, Peter Lindner, Ina Matt and Rita Schwarz are gratefully acknowledged.

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## Additional information

STATA was used for all calculations. Furthermore the user written STATA programme matrxmob by Phillipe van Kerm was used for some calculations.

## Appendix: Markovian approach

### Appendix: Markovian approach

### Transition matrix

In Sect. 3.2 we calculate right stochastic matrices for the transitions of the Markovian process, which describes the intergenerational educational transmission. For the reader’s convenience we recall the basic framework as well as the basic measurement issues concerning the Markovian approach for analyzing intergenerational transmission of education.

Let \( E \) be a finite state space, where \( e_{i} \in E \) are the states and \( e \) is the number of states. Let \( P = \left[ {p_{ij} } \right] \in R_{ + }^{e \times e} \) be a stochastic matrix where the probability of moving from state \( e_{i} \) to state \( e_{j} \) is defined as \( Pr(j|i) = p_{ij} \ge 0 \), given by the element in row \( i \) and column \( j \) of the matrix \( P \) (see Table 5). The transition probability is given by \( Pr(j|i) = p_{ij} = w_{ij} /\sum\nolimits_{j = 1}^{e} \,w_{ij} \), where \( w_{ij} \) is the sum of the weights for father-descendant pairs associated with educational transition from educational class \( i \) to class \( j \) for \( i,j = 1,2, \ldots ,e \). Of course, \( \sum\nolimits_{j = 1}^{e} \,p_{ij} = 1 \), meaning that every origin state leads to some final state with probability \( 1 \).

In the case of educational attainment, the states \( e_{i} \) are given by the set of different educational levels. \( E^{p} \)denotes the row vector which gives the marginal distribution of the education levels of the parent (either father or mother or as in our case the maximum of both). \( E^{d} \) is that of the descendants. Therefore, a row vector \( p_{i1} ,p_{i2} , \ldots ,p_{ie} \) is the educational “lottery” faced by a descendant whose parent belongs to educational class \( i \).

One way of ordering the lotteries that any two descendants face given their parents’ education is the stochastic dominance ordering. Let \( p_{i} \) denote the row vector of the \( i \)th row of a right stochastic transition matrix \( P \). Let us assume an “at least as good as” preference relation ≽ on educational lotteries. In the sense of stochastic dominance, the lottery \( p_{i} \) is “at least as good as” lottery \( p_{j} \) if p_{i,1} + p_{i,2} + ⋯ + p_{i,k} ≥ p_{j,1} + p_{j,2} + ⋯ + p_{j,k} (for all) k = 1, 2, ⋯, e-1 and “better” \( ( \succ ) \) if at least one inequality holds. In the case of Table 5 this translates to \( p_{1} \succ p_{2} \succ p_{3} \succ p_{4} \). Therefore, the transition matrix is said to be monotone because (for all) *i* = 1, 2, …, e-1, ∑
^{k}_{j=1}
p_{i,j} ≥ ∑
^{k}_{j=1}
p_{i+1,j}, (for all) k = 1, 2, …, e-1. Put simply, let us choose two people from the descendant population whose parents have different education levels. The following statement is always true: The one with the more highly educated parent faces a “better” lottery in the stochastic dominance sense.

Let P be the set of transition matrices. To follow an independence approach, which requires that the highest mobility is achieved if a matrix induces perfect origin independence, it is convenient to assert for a certain mobility measure M that \( M(I) \le M(P) \le M(\bar{P}) \), where \( I \in {\rm P} \) is the identity matrix, \( P \in {\rm P} \) is any transition matrix, and \( \bar{P} \in {\rm P} \) is a transition matrix whose rows are identical. The identity matrix generates no transition between states and should be assigned with the least level of mobility. The matrix \( \bar{P} \in {\rm P} \), on the other hand, should be assigned the highest level of mobility, because it induces perfect origin independence (Fields and Ok 1996; Prais 1955). Of course, this property is not always desirable especially when mobility is defined as movement. However, for an intergenerational framework, such a conception is relevant because we consider mobility to be independence in relation to parental characteristics. For convenience, the measures are normalised to the interval \( [0,1] \). Van de Gaer et al. (2001) show that because the axioms introduced by Shorrocks (1978) are inconsistent on the full domain of \( {\rm P} \),^{Footnote 19} the standard measures are not appropriate to measure mobility defined as independence on the full domain of \( {\rm P} \). Van de Gaer et al. (2001) introduce suitable measures for the full domain of \( {\rm P} \) but since we only have to deal with monotone transition matrices, we can restrict our set to \( \Upxi \subset {\rm P} \), which contains only monotone transition matrices in order to be able to use conventional measures (Fields and Ok 1996; Van de Gaer et al. 2001).

### Mobility measures

One widely used measure of the independence family of indices is the Second Eigenvalue Index. The eigenvalues of a given transition matrix ordered by the absolute value of their real part are given by \( \lambda_{i} = |\lambda_{1} | \ge |\lambda_{2} | \ge \cdots , \ge |\lambda_{n} | \). Every transition matrix has \( \lambda_{1} = 1 \). The Second Eigenvalue Index measures the distance of any given transition matrix to the origin independent matrix \( \bar{P} \); it is given by \( M^{SE} (P) \equiv 1 - \left| {\lambda_{2} } \right| \). If \( \lambda_{2} \) is equal to zero, then the transition matrix is equivalent to the limiting origin independent matrix. Therefore \( M^{SE} \) equals \( 1 \) when the outcome distribution is independent of the original distribution. If, on the other hand, \( M^{SE} \) equals \( 0 \), then the educational attainment of the descendant population is perfectly determined by the educational attainment of the parent population.

A second measure in this family of indices is the measure proposed by Shorrocks (1978).^{Footnote 20} Based on the trace of the transition matrix, this index evaluates the concentration arround the diagonal of the matrix: \( M^{S} (P) \equiv {\tfrac{e - trace\;P}{e - 1}} \). We use the Determinant Index, given as \( M^{D} (P) \equiv 1 - det(P)^{1/n - 1} \) as our third index fullfilling Shorroks axioms on \( \Upxi \). It is related to the average magnitude of the moduli of the eigenvalues of \( P \).

The three indices above provide no indication of the number of classes an average descendant stands away from the educational class of his or her parent. Therefore, we also take a look at an ad-hoc measure which does so. The so-called absolute average jump *AAJ(P)* gives the mean number of classes moved in absolute value. One more possibilty to summarize the information of a transition matrix, which is based on rank order correlation, is Kendall’s tau-b which lies in the intervall \( \left[ { - 1; + 1} \right] \), where a value of zero would be independence and values of −1 and +1 perfect negative respectively positive dependence.

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Fessler, P., Mooslechner, P. & Schürz, M. Intergenerational transmission of educational attainment in Austria.
*Empirica* **39, **65–86 (2012). https://doi.org/10.1007/s10663-010-9156-x

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### Keywords

- Intergenerational transfers
- Educational attainment
- Educational transmission
- Austria

### JEL Classifications

- J62
- I38