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Some Consequences of Including Impulse-Indicator Dummy Variables in Econometric Models

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  • David E. Giles

    (University of Victoria)

Abstract

Suppose that a regression model includes a regressor that is a dummy variable that takes a non-zero value for only one observation. Then the least squares estimates of the coefficients of the other regressors are the same as would be obtained by dropping that observation from the sample and omitting the dummy variable. This is well-known, but is frequently overlooked by practitioners. In this note we extend this result to the case of instrumental variables estimation, and to maximum likelihood estimation of models for count data, binary dependent variables, and duration data. These extensions also allow for the inclusion of many such “impulse-indicator” variables in the model, not just one.

Suggested Citation

  • David E. Giles, 2022. "Some Consequences of Including Impulse-Indicator Dummy Variables in Econometric Models," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(2), pages 329-336, June.
    • Handle: RePEc:spr:jqecon:v:20:y:2022:i:2:d:10.1007_s40953-022-00294-y
    DOI: 10.1007/s40953-022-00294-y
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    References listed on IDEAS

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    1. David E. Giles, 2017. "On the Inconsistency of Instrumental Variables Estimators for the Coefficients of Certain Dummy Variables," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 15(1), pages 15-26, March.
    2. 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.
    3. Cameron, A Colin & Trivedi, Pravin K, 1986. "Econometric Models Based on Count Data: Comparisons and Applications of Some Estimators and Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(1), pages 29-53, January.
    4. 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.
    5. Greene, William, 2008. "Functional forms for the negative binomial model for count data," Economics Letters, Elsevier, vol. 99(3), pages 585-590, June.
    6. Carlos Santos & David Hendry & Soren Johansen, 2008. "Automatic selection of indicators in a fully saturated regression," Computational Statistics, Springer, vol. 23(2), pages 317-335, April.
    7. Lancaster,Tony, 1992. "The Econometric Analysis of Transition Data," Cambridge Books, Cambridge University Press, number 9780521437899, September.
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    More about this item

    Keywords

    Dummy variables; Impulse-indicator variables; Instrumental variables; Count data; Duration data; Binary data;
    All these keywords.

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies

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