Skip to main content
Log in

GEE estimation of the covariance structure of a bivariate panel data model with an application to wage dynamics and the incidence of profit-sharing in West Germany

  • Original Paper
  • Published:
AStA Advances in Statistical Analysis Aims and scope Submit manuscript

Abstract

We propose a generalized estimating equations (GEE) approach to the estimation of the mean and covariance structure of bivariate time series processes of panel data. The one-step approach allows for mixed continuous and discrete dependent variables. A Monte Carlo Study is presented to compare our particular GEE estimator with more standard GEE-estimators. In the empirical illustration, we apply our estimator to the analysis of individual wage dynamics and the incidence of profit-sharing in West Germany. Our findings show that time-invariant unobserved individual ability jointly influences individual wages and participation in profit sharing schemes.

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.

Similar content being viewed by others

References

  • Abowd, J., Card, D.: On the covariance structure of earnings and hours changes. Econometrica 57, 411–445 (1989)

    Article  Google Scholar 

  • Amemiya, T.: Advanced Econometrics. Harvard University Press, Cambridge (1985)

    Google Scholar 

  • Biewen, M.: The covariance structure of East and West German incomes and its implications for the persistence of poverty and inequality. Ger. Econ. Rev. 6, 445–469 (2005)

    Article  Google Scholar 

  • Booth, A., Frank, J.: Earnings, productivity, and performance-related pay. J. Labor Econ. 17, 447–463 (1999)

    Article  Google Scholar 

  • Cappellari, L.: The dynamics and inequality of Italian men’s earnings: long-term changes or transitory fluctuations? J. Hum. Resour. 39, 475–499 (2004)

    Article  Google Scholar 

  • Carter, R.A.L., Nagar, A.L.: Coefficients of correlation for simultaneous equation systems. J. Econom. 6, 39–50 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  • Fahrmeir, L., Tutz, G.: Multivariate Statistical Modelling Based on Generalized Linear Models, 2nd edn. Springer, New York (2001)

    MATH  Google Scholar 

  • Glahn, H.R.: Some relationships derived from canonical correlation theory. Econometrica 37, 252–256 (1969)

    Article  Google Scholar 

  • Godambe, V.P.: An optimum property of regular maximum likelihood estimation. Ann. Math. Stat. 31, 1208–1212 (1960)

    Article  MathSciNet  Google Scholar 

  • Godambe, V.P.: Comment on “Inference based on estimating functions in the presence of nuisance parameters” by K.-Y. Liang and S.L. Zeger. Stat. Sci. 10, 173–174 (1995)

    Article  Google Scholar 

  • Hall, R.E., Mishkin, F.S.: The sensitivity of consumption to transitory income: estimates from panel data on households. Econometrica 50, 461–481 (1982)

    Article  Google Scholar 

  • Hansen, L.P.: Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  • Hart, R.A., Hübler, O.: Wage, labour mobility and working time effects of profit sharing. Empirica 17, 115–130 (1990)

    Article  Google Scholar 

  • Harville, D.A.: Matrix Algebra from a Statistician’s Perspective. Springer, New York (1997)

    MATH  Google Scholar 

  • Heywood, J.S., Jirjahn, U.: Payment schemes and gender in Germany. Ind. Labor Relat. Rev. 56, 44–64 (2002)

    Article  Google Scholar 

  • Hübler, O.: Productivity, earnings, and profit sharing—an econometric analysis of alternative models. Empir. Econ. 18, 357–380 (1993)

    Article  Google Scholar 

  • Kraft, K., Ugarkovic, M.: Profit Sharing: Supplement or Substitute? DP Dortmund/Mannheim (2005)

  • Liang, K.-Y., Zeger, S.L.: Longitudinal data analysis using generalized linear models. Biometrika 73, 13–22 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  • Liang, K.-Y., Zeger, S.L.: Inference based on estimating functions in the presence of nuisance parameters. Stat. Sci. 10, 158–173 (1995)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  • MaCurdy, T.E.: The use of time series processes to model the error structure of earnings in a longitudinal data analysis. J. Econ. 18, 83–114 (1982)

    Google Scholar 

  • McCullagh, P.: Quasi-likelihood functions. Ann. Stat. 11, 59–67 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  • McCullagh, P., Nelder, J.A.: Generalized Linear Models, 2nd edn. Chapman and Hall, London (1989)

    MATH  Google Scholar 

  • Newey, W.K.: Efficient estimation of models with conditional moment restrictions. In: Maddala, G.S., Rao, C.R., Vinod, H.D. (eds.) Handbook of Statistics, vol. 11, pp. 419–454. Elsevier, Amsterdam (1993)

    Google Scholar 

  • Newey, W.K., McFadden, D.: Large sample estimation and hypothesis testing. In: Engle, R.F., McFadden, D.L. (eds.) Handbook of Econometrics, vol. IV, pp. 2111–2245. Elsevier, Amsterdam (1994)

    Google Scholar 

  • Pannenberg, M., et al.: Sampling and weighting. In: Haisken-DeNew, J., Frick, J. (eds.) Desktop Companion to the GSOEP, Berlin, pp. 153–191 (2005)

  • Prentice, R.L.: Correlated binary regression with covariates specific to each binary observation. Biometrics 44, 1033–1048 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  • Qu, Y., Williams, G.W., Beck, G.J., Medendorp, S.V.: Latent variable models for clustered dichotomous data with multiple subclusters. Biometrics 48, 1095–1102 (1992)

    Article  Google Scholar 

  • Qu, Y., Piedmonte, M.R., Williams, G.W.: Small sample validity of latent variable models for correlated binary data. Commun. Stat., Simul. Comput. 23, 243–269 (1994)

    Article  MATH  Google Scholar 

  • Reboussin, B.A., Liang, K.-Y.: An estimating equations approach for the LISCOMP model. Psychometrika 63, 165–182 (1998)

    Article  MATH  Google Scholar 

  • SOEP Group: The German socio-economic panel after more than 15 years—overview. Vierteljahrsh. Wirtschaftsforsch. 70, 7–14 (2001)

    Google Scholar 

  • Spiess, M.: Analyse von Längsschnittdaten mit fehlenden Werten. Grundlagen, Verfahren und Anwendungen. Habilitationsschrift: Bremen (2005). http://nbn-resolving.de/urn:nbn:de:gbv:46-diss000012631

  • Spiess, M., Keller, F.: A mixed approach and a distribution free multiple imputation technique for the estimation of a multivariate probit model with missing values. Br. J. Math. Stat. Psychol. 52, 1–17 (1999)

    Article  MathSciNet  Google Scholar 

  • Spiess, M., Tutz, G.: Alternative measures of the explanatory power of general multivariate regression models. J. Math. Soc. 28, 125–146 (2004)

    Article  MATH  Google Scholar 

  • Wagner, G., Burkhauser, R., Behringer, F.: The English language public use file of the German socio-economic panel. J. Hum. Resour. 28, 429–433 (1993)

    Google Scholar 

  • Wolf, E.: Lower wage rates for lesser hours? A simultaneous wage-hours model for Germany. Labour Econ. 9, 643–663 (2002)

    Article  Google Scholar 

  • Wooldridge, J.M.: Econometric Analysis of Cross Section and Panel Data. MIT Press, Cambridge (2002)

    Google Scholar 

  • Zhao, L.P., Prentice, R.L.: Correlated binary regression using a quadratic exponential model. Biometrika 77, 642–648 (1990)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Markus Pannenberg or Martin Spiess.

Additional information

We are grateful to an associate editor and two anonymous referees for their helpful comments and suggestions.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pannenberg, M., Spiess, M. GEE estimation of the covariance structure of a bivariate panel data model with an application to wage dynamics and the incidence of profit-sharing in West Germany. AStA Adv Stat Anal 93, 427–447 (2009). https://doi.org/10.1007/s10182-009-0117-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10182-009-0117-2

Navigation