IDEAS home Printed from https://ideas.repec.org/p/fir/econom/wp2010_01.html
   My bibliography  Save this paper

The Method of Simulated Scores for Estimating Multinormal Regression Models with Missing Values

Author

Listed:

Abstract

Given a set of continuous variables with missing data, we prove in this paper that the iterative application of a simple “least-squares estimation/multivariate normal simulation” procedure produces an efficient parameters estimator. There are two main assumptions behind our proof: (1) the missing data mechanism is ignorable; (2) the data generating process is a multivariate normal linear regression. Disentangling the iterative procedure and its convergence conditions, we show that the estimator is a “method of simulated scores” (a particular case of McFadden’s “method of simulated moments”), thus equivalent to maximum likelihood if the number of replications is conveniently large. We thus provide a non-Bayesian re-interpretation of the estimation/simulation problem. The computational procedure is obtained introducing a simple modification into existing algorithms. Its software implementation is straightforward (few simple statements in any programming language) and easily applicable to datasets with large number of variables.

Suggested Citation

  • Giorgio Calzolari & Laura Neri, 2010. "The Method of Simulated Scores for Estimating Multinormal Regression Models with Missing Values," Econometrics Working Papers Archive wp2010_01, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    • Handle: RePEc:fir:econom:wp2010_01
    as

    Download full text from publisher

    File URL: https://labdisia.disia.unifi.it/ricerca/pubblicazioni/working_papers/2010/wp2010_01.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    2. Horton N. J. & Lipsitz S. R., 2001. "Multiple Imputation in Practice: Comparison of Software Packages for Regression Models With Missing Variables," The American Statistician, American Statistical Association, vol. 55, pages 244-254, August.
    3. Pollock, D. S. G., 2003. "Recursive estimation in econometrics," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 37-75, October.
    4. Vassilis A. Hajivassiliou, 1991. "Simulation Estimation Methods for Limited Dependent Variable Models," Cowles Foundation Discussion Papers 1007, Cowles Foundation for Research in Economics, Yale University.
    5. Bianchi, Carlo & Calzolari, Giorgio & Corsi, Paolo, 1978. "A Program for Stochastic Simulation of Econometric Models," Econometrica, Econometric Society, vol. 46(1), pages 235-236, January.
    6. Vassilis A. Hajivassiliou & Daniel McFadden, 1990. "The Method of Simulated Scores for the Estimation of LDV Models with an Application to External Debt Crisis," Cowles Foundation Discussion Papers 967, Cowles Foundation for Research in Economics, Yale University.
    7. Paul Kofman & Ian G. Sharpe, 2003. "Using Multiple Imputation in the Analysis of Incomplete Observations in Finance," Journal of Financial Econometrics, Oxford University Press, vol. 1(2), pages 216-249.
    8. Foschi, Paolo & Belsley, David A. & Kontoghiorghes, Erricos J., 2003. "A comparative study of algorithms for solving seemingly unrelated regressions models," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 3-35, October.
    9. Belsley, David A. & John Kontoghiorghes, Erricos, 2005. "Second Special issue on Computational Econometrics," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 283-285, April.
    10. Mariano,Roberto & Schuermann,Til & Weeks,Melvyn J. (ed.), 2000. "Simulation-based Inference in Econometrics," Cambridge Books, Cambridge University Press, number 9780521591126.
    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. Doretti, Marco, 2012. "Modelli di scoring per il rischio paese [Scoring models for country risk]," MPRA Paper 38898, University Library of Munich, Germany.

    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. Inkmann, Joachim, 2000. "Misspecified heteroskedasticity in the panel probit model: A small sample comparison of GMM and SML estimators," Journal of Econometrics, Elsevier, vol. 97(2), pages 227-259, August.
    2. Vassilis Argyrou Hajivassiliou, 1993. "Simulating Normal Rectangle Probabilities and Their Derivatives: The Effects of Vectorization," Working Papers _025, Yale University.
    3. Keane, Michael, 1993. "Simulation estimation for panel data models with limited dependent variables," MPRA Paper 53029, University Library of Munich, Germany.
    4. Asea, Patrick K. & Turnovsky, Stephen J., 1998. "Capital income taxation and risk-taking in a small open economy," Journal of Public Economics, Elsevier, vol. 68(1), pages 55-90, April.
    5. Bolduc, Denis & Kaci, Mustapha, 1993. "Estimation des modèles probit polytomiques : un survol des techniques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 69(3), pages 161-191, septembre.
    6. Lee, Lung-Fei, 1997. "Simulated maximum likelihood estimation of dynamic discrete choice statistical models some Monte Carlo results," Journal of Econometrics, Elsevier, vol. 82(1), pages 1-35.
    7. Ricardo A. Daziano & Martin Achtnicht, 2014. "Forecasting Adoption of Ultra-Low-Emission Vehicles Using Bayes Estimates of a Multinomial Probit Model and the GHK Simulator," Transportation Science, INFORMS, vol. 48(4), pages 671-683, November.
    8. Lixin Cai & Guyonne Kalb, 2007. "Health status and labour force status of older working-age Australian men," Australian Journal of Labour Economics (AJLE), Bankwest Curtin Economics Centre (BCEC), Curtin Business School, vol. 10(4), pages 227-252.
    9. GRAMMIG, Joachim & HUJER, Reinhard & SCHEIDLER, Michael, 2001. "The econometrics of airline network management," LIDAM Discussion Papers CORE 2001055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Jacques Huguenin & Florian Pelgrin & Alberto Holly, 2009. "Estimation of multivariate probit models by exact maximum likelihood," Working Papers 0902, University of Lausanne, Institute of Health Economics and Management (IEMS).
    11. Kristensen, Dennis & Salanié, Bernard, 2017. "Higher-order properties of approximate estimators," Journal of Econometrics, Elsevier, vol. 198(2), pages 189-208.
    12. Matteo Richiardi, 2003. "The Promises and Perils of Agent-Based Computational Economics," LABORatorio R. Revelli Working Papers Series 29, LABORatorio R. Revelli, Centre for Employment Studies.
    13. Vassilis A. Hajivassiliou & Daniel McFadden & Paul A. Ruud, 1994. "Simulation of Multivariate Normal Rectangle Probabilities: Theoretical and Computational Results," Cowles Foundation Discussion Papers 1021R, Cowles Foundation for Research in Economics, Yale University.
    14. Giorgio Calzolari & F. Mealli & C. Rampichini, 2001. "Alternative Simulation-Based Estimators of Logit Models with Random Effects," Econometrics Working Papers Archive quaderno48, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    15. Chihwa Kao & Lung-fei Lee & Mark M. Pitt, 2001. "Simulated Maximum Likelihood Estimation of the Linear Expenditure System with Binding Non-Negativity Constraints," Annals of Economics and Finance, Society for AEF, vol. 2(1), pages 215-235, May.
    16. Michael Creel & Dennis Kristensen, "undated". "Indirect Likelihood Inference," Working Papers 558, Barcelona School of Economics.
    17. Koppelman, Frank S. & Wen, Chieh-Hua, 2000. "The paired combinatorial logit model: properties, estimation and application," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 75-89, February.
    18. Heinz König & Michael Lechner, 1994. "Some Recent Developments in Microeconometrics - A Survey," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 130(III), pages 299-331, September.
    19. Denis Bolduc, "undated". "A Fast Maximum Simulated Likelihood Estimation Technique for NMP Models," Computing in Economics and Finance 1997 155, Society for Computational Economics.
    20. Lee, Donghoon & Song, Kyungchul, 2015. "Simulated maximum likelihood estimation for discrete choices using transformed simulated frequencies," Journal of Econometrics, Elsevier, vol. 187(1), pages 131-153.

    More about this item

    Keywords

    Simulated scores; missing data; multivariate normal regression model; estimation/simulation; general pattern of missingness; simultaneous equations; structural form; reduced form;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:fir:econom:wp2010_01. 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: Fabrizio Cipollini (email available below). General contact details of provider: https://edirc.repec.org/data/dsfirit.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.