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Selecting a Regression Saturated by Indicators

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  • Søren Johansen
  • David F. Hendry
  • Carlos Santos

    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

We consider selecting a regression model, using a variant of Gets, when there are more variables than observations, in the special case that the variables are impulse dummies (indicators) for every observation. We show that the setting is unproblematic if tackled appropriately, and obtain the finite-sample distribution of estimators of the mean and variance in a simple location-scale model under the null that no impulses matter. A Monte Carlo simulation confirms the null distribution, and shows power against an alternative of interest.We consider selecting a regression model, using a variant of Gets, when there are more variables than observations, in the special case that the variables are impulse dummies (indicators) for every observation. We show that the setting is unproblematic if tackled appropriately, and obtain the finite-sample distribution of estimators of the mean and variance in a simple location-scale model under the null that no impulses matter. A Monte Carlo simulation confirms the null distribution, and shows power against an alternative of interest.

Suggested Citation

  • Søren Johansen & David F. Hendry & Carlos Santos, 2007. "Selecting a Regression Saturated by Indicators," CREATES Research Papers 2007-36, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2007-36
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    References listed on IDEAS

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    1. Kevin D. Hoover & Stephen J. Perez, 1999. "Data mining reconsidered: encompassing and the general-to-specific approach to specification search," Econometrics Journal, Royal Economic Society, vol. 2(2), pages 167-191.
    2. 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.
    3. David F. Hendry & Carlos Santos, 2005. "Regression Models with Data‐based Indicator Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(5), pages 571-595, October.
    4. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    5. David F. Hendry & Hans-Martin Krolzig, 2005. "The Properties of Automatic "GETS" Modelling," Economic Journal, Royal Economic Society, vol. 115(502), pages 32-61, March.
    6. Krolzig, Hans-Martin & Hendry, David F., 2001. "Computer automation of general-to-specific model selection procedures," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 831-866, June.
    7. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    8. David Hendry & Carlos Santos, 2007. "AUTOMATIC TESTS for SUPER EXOGENEITY," Working Papers de Economia (Economics Working Papers) 11, Católica Porto Business School, Universidade Católica Portuguesa.
    9. Salkever, David S., 1976. "The use of dummy variables to compute predictions, prediction errors, and confidence intervals," Journal of Econometrics, Elsevier, vol. 4(4), pages 393-397, November.
    10. Granger, Clive W.J. & Hendry, David F., 2005. "A Dialogue Concerning A New Instrument For Econometric Modeling," Econometric Theory, Cambridge University Press, vol. 21(1), pages 278-297, February.
    11. Hendry, David F., 1995. "Dynamic Econometrics," OUP Catalogue, Oxford University Press, number 9780198283164.
    12. Julia Campos & David F. Hendry & Hans‐Martin Krolzig, 2003. "Consistent Model Selection by an Automatic Gets Approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 803-819, December.
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    2. Collier, Paul & Hoeffler, Anke, 2009. "Testing the neocon agenda: Democracy in resource-rich societies," European Economic Review, Elsevier, vol. 53(3), pages 293-308, April.

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    More about this item

    Keywords

    Indicators; regression saturation; subset selection; model selection.;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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