IDEAS home Printed from https://ideas.repec.org/p/qed/wpaper/1299.html
   My bibliography  Save this paper

Least Squares Model Averaging By Prediction Criterion

Author

Listed:
  • Tian Xie

    (Queen's University)

Abstract

This paper proposes a new estimator for least squares model averaging. A model average estimator is a weighted average of common estimates obtained from a set of models. We propose computing weights by minimizing a model average prediction criterion (MAPC). We prove that the MAPC estimator is asymptotically optimal in the sense of achieving the lowest possible mean squared error. For statistical inference, we derive asymptotic tests for single hypotheses and joint hypotheses on the average coefficients for the ``core'' regressors. These regressors are of primary interest to us and are included in every approximation model. To improve the finite sample performance, we also consider bootstrap tests. In simulation experiments the MAPC estimator is shown to have significant efficiency gains over existing model selection and model averaging methods. We also show that the bootstrap tests have more reasonable rejection frequency than the asymptotic tests in small samples. As an empirical illustration, we apply the MAPC estimator to cross-country economic growth models.

Suggested Citation

  • Tian Xie, 2012. "Least Squares Model Averaging By Prediction Criterion," Working Paper 1299, Economics Department, Queen's University.
  • Handle: RePEc:qed:wpaper:1299
    as

    Download full text from publisher

    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1299.pdf
    File Function: First version 2012
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robert J. Barro, 1991. "Economic Growth in a Cross Section of Countries," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(2), pages 407-443.
    2. Chun Liu & John M. Maheu, 2009. "Forecasting realized volatility: a Bayesian model-averaging approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(5), pages 709-733.
    3. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    4. Pagan, Adrian, 1987. "Three Econometric Methodologies: A Critical Appraisal," Journal of Economic Surveys, Wiley Blackwell, vol. 1(1), pages 3-24.
    5. David F. Hendry & Bent Nielsen, 2007. "Preface to Econometric Modeling: A Likelihood Approach," Introductory Chapters, in: Econometric Modeling: A Likelihood Approach, Princeton University Press.
    6. Wan, Alan T.K. & Zhang, Xinyu & Zou, Guohua, 2010. "Least squares model averaging by Mallows criterion," Journal of Econometrics, Elsevier, vol. 156(2), pages 277-283, June.
    7. Xavier Sala-I-Martin & Gernot Doppelhofer & Ronald I. Miller, 2004. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach," American Economic Review, American Economic Association, vol. 94(4), pages 813-835, September.
    8. Barro, Robert J. & Lee, Jong-Wha, 1994. "Sources of economic growth," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 40(1), pages 1-46, June.
    9. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
    10. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    11. Hjort N.L. & Claeskens G., 2003. "Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 879-899, January.
    12. Claeskens G. & Hjort N.L., 2003. "The Focused Information Criterion," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 900-916, January.
    13. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    14. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    15. Hendry, David F., 1976. "The structure of simultaneous equations estimators," Journal of Econometrics, Elsevier, vol. 4(1), pages 51-88, February.
    Full references (including those not matched with items on IDEAS)

    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. Liu, Chu-An, 2015. "Distribution theory of the least squares averaging estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 142-159.
    2. Mark F. J. Steel, 2020. "Model Averaging and Its Use in Economics," Journal of Economic Literature, American Economic Association, vol. 58(3), pages 644-719, September.
    3. Giuseppe Luca & Jan R. Magnus & Franco Peracchi, 2023. "Weighted-Average Least Squares (WALS): Confidence and Prediction Intervals," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1637-1664, April.
    4. Shou-Yung Yin & Chu-An Liu & Chang-Ching Lin, 2021. "Focused Information Criterion and Model Averaging for Large Panels With a Multifactor Error Structure," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 54-68, January.
    5. Liu, Chu-An, 2012. "A plug-in averaging estimator for regressions with heteroskedastic errors," MPRA Paper 41414, University Library of Munich, Germany.
    6. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
    7. Antonio Ciccone & Marek Jarociński, 2010. "Determinants of Economic Growth: Will Data Tell?," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(4), pages 222-246, October.
    8. Neil R. Ericsson, 2021. "Dynamic Econometrics in Action: A Biography of David F. Hendry," International Finance Discussion Papers 1311, Board of Governors of the Federal Reserve System (U.S.).
    9. David F. Hendry & Grayham E. Mizon, 2016. "Improving the teaching of econometrics," Cogent Economics & Finance, Taylor & Francis Journals, vol. 4(1), pages 1170096-117, December.
    10. Haili Zhang & Guohua Zou, 2020. "Cross-Validation Model Averaging for Generalized Functional Linear Model," Econometrics, MDPI, vol. 8(1), pages 1-35, February.
    11. Bloom, David E. & Canning, David & Kotschy, Rainer & Prettner, Klaus & Schünemann, Johannes, 2024. "Health and economic growth: Reconciling the micro and macro evidence," World Development, Elsevier, vol. 178(C).
    12. Dalgaard, C. & Olsson, O., 2007. "Why Are Market Economies Politically Stable? A Theory of Capitalist Cohesion," Cambridge Working Papers in Economics 0765, Faculty of Economics, University of Cambridge.
    13. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2021. "Economic Predictions With Big Data: The Illusion of Sparsity," Econometrica, Econometric Society, vol. 89(5), pages 2409-2437, September.
    14. Feng, Guohua & Gao, Jiti & Peng, Bin, 2022. "An integrated panel data approach to modelling economic growth," Journal of Econometrics, Elsevier, vol. 228(2), pages 379-397.
    15. Keisuke Okada & Sovannroeun Samreth, 2014. "How Does Corruption Influence the Effect of Foreign Direct Investment on Economic Growth?," Global Economic Review, Taylor & Francis Journals, vol. 43(3), pages 207-220, September.
    16. Laura Recuero Virto & Denis Couvet & Frédéric Ducarme, 2018. "The determinants of economic growth in countries with high marine biodiversity," Working Papers 2018.03, FAERE - French Association of Environmental and Resource Economists.
    17. Philip Arestis & Hüseyin Şen & Ayşe Kaya, 2021. "On the linkage between government expenditure and output: empirics of the Keynesian view versus Wagner’s law," Economic Change and Restructuring, Springer, vol. 54(2), pages 265-303, May.
    18. Lee, Jim, 2011. "Export specialization and economic growth around the world," Economic Systems, Elsevier, vol. 35(1), pages 45-63, March.
    19. Yuting Wei & Qihua Wang & Wei Liu, 2021. "Model averaging for linear models with responses missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 535-553, June.
    20. Michael Schomaker & Christian Heumann, 2020. "When and when not to use optimal model averaging," Statistical Papers, Springer, vol. 61(5), pages 2221-2240, October.

    More about this item

    Keywords

    Model Averaging; MAPC; Convex Optimization; Optimality; Statitstical Inference;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - 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:qed:wpaper:1299. 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: Mark Babcock (email available below). General contact details of provider: https://edirc.repec.org/data/qedquca.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.