Skip to main content
Log in

Semi-parametric estimation of income mobility with D‑vines using bivariate penalised splines

Semi-parametrische Schätzung von Einkommensmobilität mit D‑vines unter der Verwendung von bivariaten penalisierten Splines

  • Originalveröffentlichung
  • Published:
AStA Wirtschafts- und Sozialstatistisches Archiv Aims and scope Submit manuscript

Abstract

The article evaluates the distribution of income mobility in Germany. We employ official data from the German Federal Employment Agency and compare relative changes in income and their serial dependency over time during the 1980s, 1990s and 2000s to obtain both a cross-sectional and a longitudinal perspective with an intra-generational focus. The data set is separated with respect to the education of the individuals and job changes. Nonparametric smoothing techniques are applied for the modelling of the multivariate distribution of individual income. We detect very low income mobility for the low-educated workforce but significantly higher income mobility for highly educated individuals.

Zusammenfassung

Der Artikel analysiert die Verteilung von Einkommensmobilität in Deutschland. Wir verwenden die offiziellen Daten der Deutschen Bundesagentur für Arbeit und vergleichen relative Einkommensveränderungen und ihre seriellen Abhängigkeiten über die Zeit in den Jahrzehnten 1980, 1990 und 2000 um eine Querschnitts- und eine Längsperspektive mit einem Fokus auf Veränderungen innerhalb der Generationen zu erhalten. Die Daten werden in Bezug auf die Erziehung der Einzelpersonen und für Änderungen der Beschäftigung getrennt. Für die Modellierung der multivariaten Verteilung des individuellen Einkommens werden nichtparametrische Glättungstechniken angewandt. Als Ergebnis erkennen wir sehr niedrige Einkommensmobilität für die gering ausgebildeten Arbeitskräfte, aber deutlich höhere Einkommensmobilität für die hochgebildeten Personen.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  1. Therefore, we do not present the graphical results of the parametric approach.

References

  • Agency GFE (2015) Sample of integrated labour market biographies (siab). http://fdz.iab.de/en/FDZ_Individual_Data/integrated_labour_market_biographies.aspx. Accessed 01.03.2016

    Google Scholar 

  • Bedford T, Cooke RM (2002) Vines: a new graphical model for dependent random variables. Ann Stat 30(4):1031–1068

    Article  MATH  MathSciNet  Google Scholar 

  • Bowlus A, Robin J-M (2012) An international comparison of lifetime inequalilty: How continental europe resembles North America. J Eur Econ Assoc 10(6):1236–1262

    Article  Google Scholar 

  • Chau TW (2009) Estimating mobility and lifetime inequality of labor income in the united states and germany using extensions of the copula approach. In: T. W. Chau (Eds.), Essays on earnings mobility within and across generations using copula. University of Rochester, ProQuest Dissertations Publishing: 1–49

  • Czado C (2010) Pair-copula constructions of multivariate copulas. In: Bickel P, Diggle P, Fienberg S, Gather U, Olkin I, Zeger S, Jaworski P, Durante F, Härdle WK, Rychlik T (eds) Copula theory and its applications. Lecture notes in statistics, vol 198. Springer, Berlin Heidelberg, pp 93–109

    Chapter  Google Scholar 

  • de Boor C (1978) A practical guide to splines. Springer, Berlin

    Book  MATH  Google Scholar 

  • Derumigny A, Fermanian J-D (2017) About tests of the ‘‘simplifying’’ assumption for conditional copulas. ArXiv e‑prints.

    Google Scholar 

  • Eilers PHC, Marx BD (1996) Flexible smoothing with B‑splines and penalties. Stat Sci 11(2):89–121

    Article  MATH  MathSciNet  Google Scholar 

  • Flinn C (2002) Labour market structure and inequality: a comparison of italy and the U.S. Rev Econ Stud 69:611–645

    Article  MATH  Google Scholar 

  • Gijbels I, Omelka M, Veraverbeke N (2017) Nonparametric testing for no covariate effects in conditional copulas. Statistics (Ber) 51(3):475–509

    Article  MATH  MathSciNet  Google Scholar 

  • Härdle W, Okhrin O (2009) De copulis non est disputandum – copulae: an overview. AStA Adv Stat Anal 94(1):1–31

    Article  MathSciNet  Google Scholar 

  • Jäntti M, Jenkins SP (2015) Chapter 10 – income mobility. In: Atkinson AB, Bourguignon F (eds) Handbook of income distribution, vol 2. Elsevier, Amsterdam, pp 807–935

    Google Scholar 

  • Jaworski P, Durante F, Härdle W, Rychlik T (2010) Copula theory and its applications. Lecture notes in statistics, vol. 198. Springer, Berlin Heidelberg (Proceedings)

    MATH  Google Scholar 

  • Joe H (1996) Families of m‑variate distributions with given margins and m(m-1)/2 bivariate dependence parameters. In: Rüschendorf L, Schweizer B, Taylor M (eds) Distributions with fixed marginals and related topics, vol 28. Institute of Mathematical Statistics, Hayward, pp 120–141

    Chapter  Google Scholar 

  • Kauermann G, Schellhase C (2014) Flexible pair-copula estimation in D‑vines with penalized splines. Stat Comput 24(6):1081–1100

    Article  MATH  MathSciNet  Google Scholar 

  • Kolev N, Anjos U, Mendes B (2006) Copulas: a review and recent developments. Stoch Models 22(4):617–660

    Article  MATH  MathSciNet  Google Scholar 

  • Kurz MS (2017) pacotest: testing for partial copulas and the simplifying assumption in vine copulas. R package version 0.2

    Google Scholar 

  • Kurz MS, Spanhel F (2016) Testing the simplifying assumption in high-dimensional vine copulas. Dependence Modeling in Finance, Insurance and Environmental Science, Munich, 17.–19. May, pp 17–19

    Google Scholar 

  • Lemieux T, MacLeod WB, Parent D (2009) Performance pay and wage inequality. Q J Econ 124(1):1–49

    Article  Google Scholar 

  • Lorentz G (1953) Bernstein polynomials. Mathematical Expositions, no. 8. Univ. of Toronto Press, Toronto

    MATH  Google Scholar 

  • McNeil A, Frey R, Embrechts P (2005) Quantitative risk management. Princeton Series in Finance. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Nagler T, Czado C (2016) Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas. J Multivar Anal 151:69–89

    Article  MATH  MathSciNet  Google Scholar 

  • Nagler T, Schellhase C, Czado C (2017) Nonparametric estimation of simplified vines: comparison of methods. Depend Model. doi:10.1515/demo-2017-0007

    MathSciNet  Google Scholar 

  • Nelsen R (2006) An introduction to copulas, 2nd edn. Springer, Berlin

    MATH  Google Scholar 

  • R Core Team (2017) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna

    Google Scholar 

  • Rank J (ed) (2007) Copulas. Risk Books, London

    Google Scholar 

  • Rivlin T (1969) An introduction to the approximation of functions. Blaisdell Publishing, Ginn & Co, Waltham

    MATH  Google Scholar 

  • Sawhill IV, Morton JE (2007) Economic mobility: is the American dream alive and well? The brookings institution. Report of the Economic Mobility Project.

    Google Scholar 

  • Schellhase C (2015) penDvine: flexible pair-copula estimation in D‑vines using bivariate penalized splines. R package version 0.2.4..

    MATH  Google Scholar 

  • Schellhase C (2016) pendensity: density estimation and comparison with a penalized mixture approach. R package version 0.2.11.

    Google Scholar 

  • Schellhase C, Kauermann G (2012) Density estimation and comparison with a penalized mixture approach. Comput Stat 27(4):757–777

    Article  MATH  MathSciNet  Google Scholar 

  • Schellhase C, Spanhel F (2017) Estimating non-simplified vine copulas using penalized splines. Stat Comput :1–23. doi:10.1007/s11222-017-9737-7

    Google Scholar 

  • Schepsmeier U, Brechmann EC (2015) CDVine: statistical inference of C‑ and D‑vine copulas. R package version 1.4.

    Google Scholar 

  • Sklar A (1959) Fonctions de répartition à n dimensions et leurs marges vol. 8. Institut Statistique de l’Université de Paris, Paris, pp 229–231

    MATH  Google Scholar 

  • Smith M, Min A, Almeida C, Czado C (2010) Modeling longitudinal data using a pair-copula construction decomposition of serial dependence. J Am Stat Assoc 105:1467–1479

    Article  MATH  Google Scholar 

  • Spanhel F, Kurz MS (2015) Simplified vine copula models: approximations based on the simplifying assumption. ArXiv e‑prints.

    Google Scholar 

  • vom Berge P, König M, Seth S (2013) Sample of integrated labour market biographies (SIAB) 1975–2010. FDZ-Datenreport, 01/2013 (en). Documentation of labour market data

    Google Scholar 

  • Wahba G (1990) Spline models for observational data. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  • Nagler T, Schellhase C, Czado C (2017) Nonparametric estimation of simplified vines: comparison of methods. Depend Model 5(1):99–120

  • Kurz MS, Spanhel F (2017) Testing the simplifying assumption in high-dimensional vine copulas. ArXiv e‑prints https://arxiv.org/abs/1706.02338

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Christian Schellhase.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Schellhase, C., Kuhlenkasper, T. Semi-parametric estimation of income mobility with D‑vines using bivariate penalised splines. AStA Wirtsch Sozialstat Arch 11, 107–134 (2017). https://doi.org/10.1007/s11943-017-0205-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11943-017-0205-9

Keywords

Schlüsselwörter

Navigation