IDEAS home Printed from https://ideas.repec.org/p/aah/aarhec/2006-08.html

On determining the importance of a regressor with small and undersized samples

Author

Listed:
  • Peter Sandholt Jensen
  • Allan H. Würtz

    (Department of Economics, University of Aarhus, Denmark)

Abstract

A problem encountered in, for instance, growth empirics is that the number of explanatory variables is large compared to the number of observations. This makes it infeasible to condition on all variables in order to determine the importance of a variable of interest. We prove identifying assumptions under which the problem is not ill-posed. Under these assumptions, we derive properties of the most commonly used methods: Extreme bounds analysis, Sala-i-Martin’s method, BACE, generalto- specific, minimum t-statistics, BIC and AIC. We propose a new method and show that it has good finite sample properties.

Suggested Citation

  • Peter Sandholt Jensen & Allan H. Würtz, 2006. "On determining the importance of a regressor with small and undersized samples," Economics Working Papers 2006-08, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:aarhec:2006-08
    as

    Download full text from publisher

    File URL: https://repec.econ.au.dk/repec/afn/wp/06/wp06_08.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Durlauf, Steven N. & Johnson, Paul A. & Temple, Jonathan R.W., 2005. "Growth Econometrics," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.),Handbook of Economic Growth, edition 1, volume 1, chapter 8, pages 555-677, Elsevier.
    2. Fernandez, Carmen & Ley, Eduardo & Steel, Mark F. J., 2001. "Benchmark priors for Bayesian model averaging," Journal of Econometrics, Elsevier, vol. 100(2), pages 381-427, February.
    3. Granger, Clive W. J. & Uhlig, Harald F., 1990. "Reasonable extreme-bounds analysis," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 159-170.
    4. McAleer, Michael, 1994. "Sherlock Holmes and the Search for Truth: A Diagnostic Tale," Journal of Economic Surveys, Wiley Blackwell, vol. 8(4), pages 317-370, December.
    5. Bleaney, Michael & Nishiyama, Akira, 2002. "Explaining Growth: A Contest between Models," Journal of Economic Growth, Springer, vol. 7(1), pages 43-56, March.
    6. Kevin D. Hoover & Stephen J. Perez, 2004. "Truth and Robustness in Cross‐country Growth Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(5), pages 765-798, December.
    7. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77, Elsevier.
    8. Philip J. Cross & Charles F. Manski, 2002. "Regressions, Short and Long," Econometrica, Econometric Society, vol. 70(1), pages 357-368, January.
    9. McAleer, Michael & Pagan, Adrian R & Volker, Paul A, 1985. "What Will Take the Con out of Econometrics?," American Economic Review, American Economic Association, vol. 75(3), pages 293-307, June.
    10. Levine, Ross & Renelt, David, 1992. "A Sensitivity Analysis of Cross-Country Growth Regressions," American Economic Review, American Economic Association, vol. 82(4), pages 942-963, September.
    11. Durlauf, Steven N., 2001. "Manifesto for a growth econometrics," Journal of Econometrics, Elsevier, vol. 100(1), pages 65-69, January.
    12. Philippe Aghion & Steven Durlauf (ed.), 2005. "Handbook of Economic Growth," Handbook of Economic Growth, Elsevier, edition 1, volume 1, number 1.
    13. Bruce E. Hansen, 1999. "Discussion of 'Data mining reconsidered'," Econometrics Journal, Royal Economic Society, vol. 2(2), pages 192-201.
    14. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    15. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    16. Leamer, Edward E, 1983. "Let's Take the Con Out of Econometrics," American Economic Review, American Economic Association, vol. 73(1), pages 31-43, March.
    17. Trevor S. Breusch, 1986. "Hypothesis Testing in Unidentified Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 635-651.
    18. David F. Hendry & Hans‐Martin Krolzig, 2004. "We Ran One Regression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(5), pages 799-810, December.
    19. Sala-i-Martin, Xavier, 1997. "I Just Ran Two Million Regressions," American Economic Review, American Economic Association, vol. 87(2), pages 178-183, May.
    20. David F. Hendry & Hans-Martin Krolzig, 2004. "We Ran One Regression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(5), pages 799-810, December.
    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. Capolupo, Rosa, 2009. "The New Growth Theories and Their Empirics after Twenty Years," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-72.
    2. Peter Jensen, 2010. "Testing the null of a low dimensional growth model," Empirical Economics, Springer, vol. 38(1), pages 193-215, February.
    3. Anatolyev, Stanislav, 2012. "Inference in regression models with many regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 368-382.

    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. Ulaşan, Bülent, 2011. "Cross-country growth empirics and model uncertainty: An overview," Economics Discussion Papers 2011-37, Kiel Institute for the World Economy (IfW Kiel).
    2. Melisa Chanegriha & Chris Stewart & Christopher Tsoukis, 2017. "Identifying the robust economic, geographical and political determinants of FDI: an Extreme Bounds Analysis," Empirical Economics, Springer, vol. 52(2), pages 759-776, March.
    3. Ulaşan, Bülent, 2012. "Cross-country growth empirics and model uncertainty: An overview," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 6, pages 1-69.
    4. Peter Jensen, 2010. "Testing the null of a low dimensional growth model," Empirical Economics, Springer, vol. 38(1), pages 193-215, February.
    5. Ahmed, Walid M.A., 2022. "Robust drivers of Bitcoin price movements: An extreme bounds analysis," The North American Journal of Economics and Finance, Elsevier, vol. 62(C).
    6. W. Robert Reed, 2009. "The Determinants Of U.S. State Economic Growth: A Less Extreme Bounds Analysis," Economic Inquiry, Western Economic Association International, vol. 47(4), pages 685-700, October.
    7. Capolupo, Rosa, 2009. "The New Growth Theories and Their Empirics after Twenty Years," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-72.
    8. Ulrike Schneider & Martin Wagner, 2012. "Catching Growth Determinants with the Adaptive Lasso," German Economic Review, Verein für Socialpolitik, vol. 13(1), pages 71-85, February.
    9. Steven N. Durlauf & Andros Kourtellos & Chih Ming Tan, 2008. "Empirics of Growth and Development," Chapters, in: Amitava Krishna Dutt & Jaime Ros (ed.), International Handbook of Development Economics, Volumes 1 & 2, volume 0, chapter 3, Edward Elgar Publishing.
    10. repec:rim:rimwps:18-30 is not listed on IDEAS
    11. Wagner, Martin & Hlouskova, Jaroslava, 2009. "Growth Regressions, Principal Components and Frequentist Model Averaging," Economics Series 236, Institute for Advanced Studies.
    12. R Burger & S du Plessis, 2011. "Examining the Robustness of Competing Explanations of Slow Growth in African Countries," Studies in Economics and Econometrics, Taylor & Francis Journals, vol. 35(3), pages 21-47, December.
    13. Derek Headey, 2008. "The Principal Components of Growth in the Less Developed Countries," Kyklos, Wiley Blackwell, vol. 61(4), pages 568-598, November.
    14. Jesus regstdpo-Cuaresma & Neil Foster & Robert Stehrer, 2011. "Determinants of Regional Economic Growth by Quantile," Regional Studies, Taylor & Francis Journals, vol. 45(6), pages 809-826.
    15. Sachs, Andreas & Schleer, Frauke, 2013. "Labour market performance in OECD countries: A comprehensive empirical modelling approach of institutional interdependencies," ZEW Discussion Papers 13-040, ZEW - Leibniz Centre for European Economic Research.
    16. Neil R. Ericsson, 2008. "The Fragility of Sensitivity Analysis: An Encompassing Perspective," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 895-914, December.
    17. Walid M. A. Ahmed, 2024. "On the robust drivers of cryptocurrency liquidity: the case of Bitcoin," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-32, December.
    18. Alan Martina, 2007. "A Class of Poverty Traps: A Theory and Empirical Tests," ANU Working Papers in Economics and Econometrics 2007-482, Australian National University, College of Business and Economics, School of Economics.
    19. Henderson, Daniel J. & Papageorgiou, Chris & Parmeter, Christopher F., 2008. "Are any growth theories linear? Why we should care about what the evidence tells us," MPRA Paper 8767, University Library of Munich, Germany.
    20. Yang, Haisheng & He, Jie & Chen, Shaoling, 2015. "The fragility of the Environmental Kuznets Curve: Revisiting the hypothesis with Chinese data via an “Extreme Bound Analysis”," Ecological Economics, Elsevier, vol. 109(C), pages 41-58.
    21. Martin Gassebner & Jerg Gutmann & Stefan Voigt, 2016. "When to expect a coup d’état? An extreme bounds analysis of coup determinants," Public Choice, Springer, vol. 169(3), pages 293-313, December.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    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:aah:aarhec:2006-08. 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: the person in charge (email available below). General contact details of provider: http://www.econ.au.dk/afn/ .

    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.