IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v18y1999i3p287-330.html
   My bibliography  Save this article

An introduction to hypergeometric functions for economists

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/07474939908800447
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Prescott, Edward C., 1986. "Theory ahead of business-cycle measurement," Carnegie-Rochester Conference Series on Public Policy, Elsevier, pages 11-44.
    3. Geweke, John, 1988. "Antithetic acceleration of Monte Carlo integration in Bayesian inference," Journal of Econometrics, Elsevier, vol. 38(1-2), pages 73-89.
    4. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
    5. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(03), pages 409-431, August.
    6. Engle, Robert F & Hendry, David F & Richard, Jean-Francois, 1983. "Exogeneity," Econometrica, Econometric Society, pages 277-304.
    7. Zellner, Arnold, 1985. "Bayesian Econometrics," Econometrica, Econometric Society, vol. 53(2), pages 253-269, March.
    8. Kiefer, Nicholas M. & Salmon, Mark, 1983. "Testing normality in econometric models," Economics Letters, Elsevier, pages 123-127.
    9. Steel, Mark F. J. & Richard, Jean-Francois, 1991. "Bayesian multivariate exogeneity analysis : An application to a UK money demand equation," Journal of Econometrics, Elsevier, pages 239-274.
    10. Poirier, Dale J, 1988. "Frequentist and Subjectivist Perspectives on the Problems of Model Building in Economics," Journal of Economic Perspectives, American Economic Association, pages 121-144.
    11. Diaz-Gimenez, Javier & Prescott, Edward C. & Fitzgerald, Terry & Alvarez, Fernando, 1992. "Banking in computable general equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, pages 533-559.
    12. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
    13. Anglin, Paul M & Gencay, Ramazan, 1996. "Semiparametric Estimation of a Hedonic Price Function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 633-648, Nov.-Dec..
    14. Edward C. Prescott & Stephen L. Parente, 1999. "Monopoly Rights: A Barrier to Riches," American Economic Review, American Economic Association, pages 1216-1233.
    15. Geweke, John, 1989. "Exact predictive densities for linear models with arch disturbances," Journal of Econometrics, Elsevier, vol. 40(1), pages 63-86, January.
    16. Poirier, Dale J., 1997. "Comparing and choosing between two models with a third model in the background," Journal of Econometrics, Elsevier, vol. 78(2), pages 139-151, June.
    17. Geweke, John, 1996. "Monte carlo simulation and numerical integration," Handbook of Computational Economics,in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 15, pages 731-800 Elsevier.
    18. Roberts, G. O. & Smith, A. F. M., 1994. "Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms," Stochastic Processes and their Applications, Elsevier, vol. 49(2), pages 207-216, February.
    19. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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, 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, pages 33-54.
    7. Giorgio Coricelli & Dietmar Fehr & Gerlinde Fellner, 2004. "Partner Selection in Public Goods Experiments," Journal of Conflict Resolution, Peace Science Society (International), pages 356-378.
    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, 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. 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.
    15. M. Karanasos & J. Kim, 2003. "Moments of the ARMA--EGARCH model," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 146-166, June.
    16. Abadir, Karim M. & Distaso, Walter, 2007. "Testing joint hypotheses when one of the alternatives is one-sided," Journal of Econometrics, Elsevier, pages 695-718.
    17. 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.
    18. Abadir, Karim M. & Caggiano, Giovanni & Talmain, Gabriel, 2013. "Nelson–Plosser revisited: The ACF approach," Journal of Econometrics, Elsevier, pages 22-34.
    19. Karim M. Abadir & Adriana Cornea, 2012. "Approximating Moments by Nonlinear Transformations," Working Paper series 22_12, Rimini Centre for Economic Analysis.
    20. Raffaella Giacomini & Andreas Gottschling & Christian Haefke & Halbert White, 2002. "Hypernormal Densities," Boston College Working Papers in Economics 584, Boston College Department of Economics.
    21. Castle, Jennifer L. & Hendry, David F., 2010. "A low-dimension portmanteau test for non-linearity," Journal of Econometrics, Elsevier, pages 231-245.
    22. 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.
    23. Hadri, Kaddour & Kurozumi, Eiji, 2008. "A Simple Panel Stationarity Test in the Presence of Cross-Sectional Dependence," CCES Discussion Paper Series 7, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:emetrv:v:18:y:1999:i:3:p:287-330. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://www.tandfonline.com/LECR20 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.