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An introduction to hypergeometric functions for economists

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  • Karim Abadir

Abstract

Hypergeometric functions are a generalization of exponential functions. They are explicit, computable functions that can also be manipulated analytically. The functions and series we use in quantitative economics are all special cases of them. In this paper, a unified approach to hypergeometric functions is given. As a result, some potentially useful general applications emerge in a number of areas such as in econometrics and economic theory. The greatest benefit from using these functions stems from the fact that they provide parsimonious explicit (and interpretable) solutions to a wide range of general problems.

Suggested Citation

  • Karim Abadir, 1999. "An introduction to hypergeometric functions for economists," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 287-330.
  • Handle: RePEc:taf:emetrv:v:18:y:1999:i:3:p:287-330
    DOI: 10.1080/07474939908800447
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    References listed on IDEAS

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    1. Marco Antonio Bonomo & Rene Garcia, 1993. "Disappointment aversion as a solution to the equity premium and the risk-free rate puzzles," Textos para discussão 308, Department of Economics PUC-Rio (Brazil).
    2. Sutherland, Alan, 1997. "Fiscal crises and aggregate demand: can high public debt reverse the effects of fiscal policy?," Journal of Public Economics, Elsevier, vol. 65(2), pages 147-162, August.
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    Cited by:

    1. Abadir, Karim M. & Talmain, Gabriel, 2005. "Autocovariance functions of series and of their transforms," Journal of Econometrics, Elsevier, vol. 124(2), pages 227-252, February.
    2. Abadir, Karim M. & Lucas, Andre, 2004. "A comparison of minimum MSE and maximum power for the nearly integrated non-Gaussian model," Journal of Econometrics, Elsevier, vol. 119(1), pages 45-71, March.
    3. Proietti, Tommaso & Lütkepohl, Helmut, 2013. "Does the Box–Cox transformation help in forecasting macroeconomic time series?," International Journal of Forecasting, Elsevier, vol. 29(1), pages 88-99.
    4. A. Sancetta & Satchell, S.E., 2001. "Bernstein Approximations to the Copula Function and Portfolio Optimization," Cambridge Working Papers in Economics 0105, Faculty of Economics, University of Cambridge.
    5. Abadir, Karim M. & Lawford, Steve, 2004. "Optimal asymmetric kernels," Economics Letters, Elsevier, vol. 83(1), pages 61-68, April.
    6. Boucekkine, R. & Ruiz-Tamarit, J.R., 2008. "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 33-54, January.
    7. Giacomini, Raffaella & Gottschling, Andreas & Haefke, Christian & White, Halbert, 2008. "Mixtures of t-distributions for finance and forecasting," Journal of Econometrics, Elsevier, vol. 144(1), pages 175-192, May.
    8. José Ramón Ruiz Tamarit & Manuel Sánchez Moreno, 2006. "Optimal Regulation And Growth In A Natural-Resource-Based Economy," Working Papers. Serie AD 2006-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    9. Bu, Ruijun & Cheng, Jie & Hadri, Kaddour, 2016. "Reducible diffusions with time-varying transformations with application to short-term interest rates," Economic Modelling, Elsevier, vol. 52(PA), pages 266-277.
    10. Castle, Jennifer L. & Hendry, David F., 2010. "A low-dimension portmanteau test for non-linearity," Journal of Econometrics, Elsevier, vol. 158(2), pages 231-245, October.
    11. Lubrano, Michel & Ndoye, Abdoul Aziz Junior, 2016. "Income inequality decomposition using a finite mixture of log-normal distributions: A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 830-846.
    12. Ruijun Bu & Kaddour Hadri, 2005. "Estimating the Risk Neutral Probability Density Functions Natural Spline versus Hypergeometric Approach Using European Style Options," Research Papers 200510, University of Liverpool Management School.
    13. Mark Vancauteren & Daniel Weiserbs, 2011. "Intra-European Trade of Manufacturing Goods: An Extension of the Gravity Model," International Econometric Review (IER), Econometric Research Association, vol. 3(1), pages 1-24, April.
    14. M. Karanasos & J. Kim, 2003. "Moments of the ARMA--EGARCH model," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 146-166, June.
    15. Abadir, Karim M. & Distaso, Walter, 2007. "Testing joint hypotheses when one of the alternatives is one-sided," Journal of Econometrics, Elsevier, vol. 140(2), pages 695-718, October.
    16. Ruijun Bu & Ludovic Giet & Kaddour Hadri & Michel Lubrano, 2009. "Modeling Multivariate Interest Rates using Time-Varying Copulas and Reducible Stochastic Differential Equations," Working Papers halshs-00408014, HAL.
    17. Abadir, Karim M. & Caggiano, Giovanni & Talmain, Gabriel, 2013. "Nelson–Plosser revisited: The ACF approach," Journal of Econometrics, Elsevier, vol. 175(1), pages 22-34.
    18. Karim M. Abadir & Adriana Cornea, 2012. "Approximating Moments by Nonlinear Transformations," Working Paper series 22_12, Rimini Centre for Economic Analysis.
    19. Raffaella Giacomini & Andreas Gottschling & Christian Haefke & Halbert White, 2002. "Hypernormal Densities," Boston College Working Papers in Economics 584, Boston College Department of Economics.
    20. Jennifer Castle & David Hendry, 2010. "Automatic Selection for Non-linear Models," Economics Series Working Papers 473, University of Oxford, Department of Economics.
    21. Menelaos Karanasos & J. Kim, "undated". "Alternative GARCH in Mean Models: An Application to the Korean Stock Market," Discussion Papers 00/25, Department of Economics, University of York.
    22. Ruijun Bu & Ludovic Giet & Kaddour Hadri & Michel Lubrano, 2009. "Modelling Multivariate Interest Rates using Time-Varying Copulas and Reducible Non-Linear Stochastic Differential," Economics Working Papers 09-02, Queen's Management School, Queen's University Belfast.

    More about this item

    Keywords

    and phrases; Hypergeometric functions; distribution theory; non-linear models and discontinues; differential equations; economic theory; utility; production and cost functions;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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