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Two-Part Models for Fractional Responses Defined as Ratios of Integers

Author

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  • Harald Oberhofer

    () (Department of Economics and Social Sciences, University of Salzburg, Residenzplatz 9, 5010 Salzburg, Austria
    The Austrian Center for Labor Economics and the Analysis of the Welfare State,c/o Rudolf Winter-Ebmer, Altenbergerstr. 69, 4040 Linz, Austria)

  • Michael Pfaffermayr

    () (Department of Economics, University of Innsbruck, Universitaetsstrasse 15, 6020 Innsbruck, Austria
    Austrian Institute of Economic Research (WIFO), Objekt 20, Arsenal, 1030 Vienna, Austria)

Abstract

This paper discusses two alternative two-part models for fractional response variables that are defined as ratios of integers. The first two-part model assumes a Binomial distribution and known group size. It nests the one-part fractional response model proposed by Papke and Wooldridge (1996) and, thus, allows one to apply Wald, LM and/or LR tests in order to discriminate between the two models. The second model extends the first one by allowing for overdispersion in the data. We demonstrate the usefulness of the proposed two-part models for data on the 401(k) pension plan participation rates used in Papke and Wooldridge (1996).

Suggested Citation

  • Harald Oberhofer & Michael Pfaffermayr, 2014. "Two-Part Models for Fractional Responses Defined as Ratios of Integers," Econometrics, MDPI, Open Access Journal, vol. 2(3), pages 1-22, September.
  • Handle: RePEc:gam:jecnmx:v:2:y:2014:i:3:p:123-144:d:40457
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    References listed on IDEAS

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    1. Santos Silva, J.M.C. & Murteira, J.M.R., 2009. "Estimation of default probabilities using incomplete contracts data," Journal of Empirical Finance, Elsevier, vol. 16(3), pages 457-465, June.
    2. José M. R. Murteira & Joaquim J. S. Ramalho, 2016. "Regression Analysis of Multivariate Fractional Data," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 515-552, April.
    3. Esmeralda A. Ramalho & Joaquim J. S. Ramalho & José M. R. Murteira, 2014. "A Generalized Goodness-of-functional Form Test for Binary and Fractional Regression Models," Manchester School, University of Manchester, vol. 82(4), pages 488-507, July.
    4. Joaquim J.S. Ramalho & Jacinto Vidigal da Silva, 2009. "A two-part fractional regression model for the financial leverage decisions of micro, small, medium and large firms," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 621-636.
    5. Papke, Leslie E. & Wooldridge, Jeffrey M., 2008. "Panel data methods for fractional response variables with an application to test pass rates," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 121-133, July.
    6. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    7. Cragg, John G, 1971. "Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods," Econometrica, Econometric Society, vol. 39(5), pages 829-844, September.
    8. John Mullahy, 2010. "Multivariate Fractional Regression Estimation of Econometric Share Models," NBER Working Papers 16354, National Bureau of Economic Research, Inc.
    9. Harald Oberhofer & Michael Pfaffermayr, 2014. "Two-Part Models for Fractional Responses Defined as Ratios of Integers," Econometrics, MDPI, Open Access Journal, vol. 2(3), pages 1-22, September.
    10. Esmeralda A. Ramalho & Joaquim J.S. Ramalho & José M.R. Murteira, 2011. "Alternative Estimating And Testing Empirical Strategies For Fractional Regression Models," Journal of Economic Surveys, Wiley Blackwell, vol. 25(1), pages 19-68, February.
    11. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    12. Cameron,A. Colin & Trivedi,Pravin K., 2008. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9787111235767, April.
    13. Harald Oberhofer & Michael Pfaffermayr, 2012. "Fractional Response Models - A Replication Exercise of Papke and Wooldridge (1996)," Contemporary Economics, University of Finance and Management in Warsaw, vol. 6(3), September.
    14. Ospina, Raydonal & Ferrari, Silvia L.P., 2012. "A general class of zero-or-one inflated beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1609-1623.
    15. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    16. Cook, Douglas O. & Kieschnick, Robert & McCullough, B.D., 2008. "Regression analysis of proportions in finance with self selection," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 860-867, December.
    17. Heckman, James J & Willis, Robert J, 1977. "A Beta-logistic Model for the Analysis of Sequential Labor Force Participation by Married Women," Journal of Political Economy, University of Chicago Press, vol. 85(1), pages 27-58, February.
    18. Davidson, Russell & MacKinnon, James G, 1981. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Econometrica, Econometric Society, vol. 49(3), pages 781-793, May.
    19. Paolino, Philip, 2001. "Maximum Likelihood Estimation of Models with Beta-Distributed Dependent Variables," Political Analysis, Cambridge University Press, vol. 9(04), pages 325-346, January.
    20. Papke, Leslie E & Wooldridge, Jeffrey M, 1996. "Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 619-632, Nov.-Dec..
    21. Lin, Tsai-Fen & Schmidt, Peter, 1984. "A Test of the Tobit Specification against an Alternative Suggested by Cragg," The Review of Economics and Statistics, MIT Press, vol. 66(1), pages 174-177, February.
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    1. Harald Oberhofer & Michael Pfaffermayr, 2014. "Two-Part Models for Fractional Responses Defined as Ratios of Integers," Econometrics, MDPI, Open Access Journal, vol. 2(3), pages 1-22, September.

    More about this item

    Keywords

    fractional response models for ratios of integers; one-part versus two-part models; Wald test; LM test; LR test;

    JEL classification:

    • B23 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Econometrics; Quantitative and Mathematical Studies
    • C - Mathematical and Quantitative Methods
    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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