IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2011-05.html
   My bibliography  Save this paper

Fourth Order Pseudo Maximum Likelihood Methods

Author

Listed:
  • Alberto HOLLY

    (Crest)

  • Alain MONFORT

    (Crest)

  • Michael ROCKINGER

    (Crest)

Abstract

The objective of this paper is to extend the results on Pseudo Maximum Likelihood (PML) theory derived in Gourieroux, Monfort, and Trognon (GMT) (1984) to a situation where the first four conditional moments are specified. Such an extension is relevant in light of pervasive evidence that conditional distributions are non-Gaussian in many economic situations. The key statistical tool here is the quartic exponential family, which allows us to generalize the PML2 and QGPML1 methods proposed in GMT(1984) to PML4 and QGPML2 methods, respectively. An asymptotic theory is developed which shows, in particular, that the QGPML2 method reaches the semi-parametric bound. The key numerical tool that we use is the Gauss-Freud integration scheme which solves a computational problem that has previously been raised in several econometric fields. Simulation exercises show the feasibility and robustness of the methods.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Alberto HOLLY & Alain MONFORT & Michael ROCKINGER, 2011. "Fourth Order Pseudo Maximum Likelihood Methods," Working Papers 2011-05, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2011-05
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2011-05.pdf
    File Function: Crest working paper version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    2. D. Ormoneit & H. White, 1999. "An efficient algorithm to compute maximum entropy densities," Econometric Reviews, Taylor & Francis Journals, vol. 18(2), pages 127-140.
    3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    4. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    5. Ziliak, James P, 1997. "Efficient Estimation with Panel Data When Instruments Are Predetermined: An Empirical Comparison of Moment-Condition Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(4), pages 419-431, October.
    6. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
    7. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521471626, October.
    8. Altonji, Joseph G & Segal, Lewis M, 1996. "Small-Sample Bias in GMM Estimation of Covariance Structures," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 353-366, July.
    9. Andersen, Torben G & Sorensen, Bent E, 1996. "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 328-352, July.
    10. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    11. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, September.
    12. Zellner, Arnold & Highfield, Richard A., 1988. "Calculation of maximum entropy distributions and approximation of marginalposterior distributions," Journal of Econometrics, Elsevier, vol. 37(2), pages 195-209, February.
    13. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    14. Tauchen, George, 1986. "Statistical Properties of Generalized Method-of-Moments Estimators of Structural Parameters Obtained from Financial Market Data: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(4), pages 423-425, October.
    15. Manning, Willard G. & Basu, Anirban & Mullahy, John, 2005. "Generalized modeling approaches to risk adjustment of skewed outcomes data," Journal of Health Economics, Elsevier, vol. 24(3), pages 465-488, May.
    16. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    17. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    18. Doran, Howard E. & Schmidt, Peter, 2006. "GMM estimators with improved finite sample properties using principal components of the weighting matrix, with an application to the dynamic panel data model," Journal of Econometrics, Elsevier, vol. 133(1), pages 387-409, July.
    19. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 465-487, December.
    20. Christian Gouriéroux & Alain Monfort, 2006. "Pricing with Splines," Annals of Economics and Statistics, GENES, issue 82, pages 3-33.
    21. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    22. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
    23. repec:adr:anecst:y:2006:i:82:p:01 is not listed on IDEAS
    24. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    25. Tauchen, George, 1986. "Statistical Properties of Generalized Method-of-Moments Estimators of Structural Parameters Obtained from Financial Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(4), pages 397-416, October.
    26. Sawa, Takamitsu, 1978. "Information Criteria for Discriminating among Alternative Regression Models," Econometrica, Econometric Society, vol. 46(6), pages 1273-1291, November.
    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. Bernardi, Mauro & Catania, Leopoldo, 2018. "Portfolio optimisation under flexible dynamic dependence modelling," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 1-18.
    2. Fries, Sébastien, 2018. "Conditional moments of noncausal alpha-stable processes and the prediction of bubble crash odds," MPRA Paper 97353, University Library of Munich, Germany, revised Nov 2019.
    3. Jules Tinang & Nour Meddahi, 2016. "GMM estimation of the Long Run Risks model," 2016 Meeting Papers 1107, Society for Economic Dynamics.
    4. Damir Filipović & Sander Willems, 2020. "A term structure model for dividends and interest rates," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1461-1496, October.
    5. Andrew M. Jones & James Lomas & Peter T. Moore & Nigel Rice, 2016. "A quasi-Monte-Carlo comparison of parametric and semiparametric regression methods for heavy-tailed and non-normal data: an application to healthcare costs," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(4), pages 951-974, October.
    6. Giuseppe arbia, 2014. "Least quartic Regression Criterion with Application to Finance," Papers 1403.4171, arXiv.org.
    7. Mauro Bernardi & Leopoldo Catania, 2016. "Portfolio Optimisation Under Flexible Dynamic Dependence Modelling," Papers 1601.05199, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:hal:journl:peer-00815562 is not listed on IDEAS
    2. Joachim Inkmann, 2000. "Finite Sample Properties of One-Step, Two-Step and Bootstrap Empirical Likelihood Approaches to Efficient GMM Estimation," Econometric Society World Congress 2000 Contributed Papers 0332, Econometric Society.
    3. Lee, Seojeong, 2014. "Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 178(P3), pages 398-413.
    4. Rockinger, Michael & Jondeau, Eric, 2002. "Entropy densities with an application to autoregressive conditional skewness and kurtosis," Journal of Econometrics, Elsevier, vol. 106(1), pages 119-142, January.
    5. David Roodman, 2009. "A Note on the Theme of Too Many Instruments," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(1), pages 135-158, February.
    6. Prosper Dovonon, 2016. "Large Sample Properties of the Three-Step Euclidean Likelihood Estimators under Model Misspecification," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 465-514, April.
    7. Nour Meddahi & Eric Renault, 1998. "Quadratic M-Estimators for ARCH-Type Processes," CIRANO Working Papers 98s-29, CIRANO.
    8. Ramalho Joaquim J.S., 2005. "Small Sample Bias of Alternative Estimation Methods for Moment Condition Models: Monte Carlo Evidence for Covariance Structures," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(1), pages 1-20, March.
    9. Gouriéroux, Christian & Monfort, Alain & Zakoian, Jean-Michel, 2017. "Pseudo-Maximum Likelihood and Lie Groups of Linear Transformations," MPRA Paper 79623, University Library of Munich, Germany.
    10. Krishnakumar, Jaya & Kabili, Andi & Roko, Ilir, 2012. "Estimation of SEM with GARCH errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3153-3181.
    11. Joaquim Ramalho, 2003. "Small Sample Bias of Alternative Estimation Methods for Moment Condition Models: Monte Carlo Evidence for Covariance Structures and Instrumental Variables," Economics Working Papers 9_2003, University of Évora, Department of Economics (Portugal).
    12. Doran, Howard E. & Schmidt, Peter, 2006. "GMM estimators with improved finite sample properties using principal components of the weighting matrix, with an application to the dynamic panel data model," Journal of Econometrics, Elsevier, vol. 133(1), pages 387-409, July.
    13. C. Gouriéroux & A. Monfort & J.‐M. Zakoïan, 2019. "Consistent Pseudo‐Maximum Likelihood Estimators and Groups of Transformations," Econometrica, Econometric Society, vol. 87(1), pages 327-345, January.
    14. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    15. Windmeijer, Frank, 2005. "A finite sample correction for the variance of linear efficient two-step GMM estimators," Journal of Econometrics, Elsevier, vol. 126(1), pages 25-51, May.
    16. Kim, Jae-Young, 2014. "An alternative quasi likelihood approach, Bayesian analysis and data-based inference for model specification," Journal of Econometrics, Elsevier, vol. 178(P1), pages 132-145.
    17. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    18. repec:bla:ecorec:v:91:y:2015:i::p:1-24 is not listed on IDEAS
    19. So Im, Kyung & Ahn, Seung C. & Schmidt, Peter & Wooldridge, Jeffrey M., 1999. "Efficient estimation of panel data models with strictly exogenous explanatory variables," Journal of Econometrics, Elsevier, vol. 93(1), pages 177-201, November.
    20. Gregory, Allan W. & Lamarche, Jean-Francois & Smith, Gregor W., 2002. "Information-theoretic estimation of preference parameters: macroeconomic applications and simulation evidence," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 213-233, March.
    21. Fedderke, Johannes & Klitgaard, Robert, 2013. "How Much Do Rights Matter?," World Development, Elsevier, vol. 51(C), pages 187-206.
    22. Clémentine Florens & Eric Jondeau & Hervé Le Bihan, 2001. "Assessing GMM Estimates of the Federal Reserve Reaction Function," Econometrics 0111003, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:crs:wpaper:2011-05. See general information about how to correct material in RePEc.

    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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.