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.
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Acknowledgements
I am very grateful to Ryan Godwin and Jacob Schwartz for helpful discussions relating to an earlier version of this paper, and to an anonymous referee for their helpful comments.
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Giles, D.E. Some Consequences of Including Impulse-Indicator Dummy Variables in Econometric Models. J. Quant. Econ. 20, 329–336 (2022). https://doi.org/10.1007/s40953-022-00294-y
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DOI: https://doi.org/10.1007/s40953-022-00294-y