Regression Models with Data-based Indicator Variables

OLS estimation of an impulse-indicator coefficient is inconsistent, but its variance can be consistently estimated. Although the ratio of the inconsistent estimator to its standard error has a t-distribution, that test is inconsistent: one solution is to form an index of indicators. We provide Monte Carlo evidence that including a plethora of indicators need not distort model selection, permitting the use of many dummies in a general-to-specific framework. Although White’s (1980) heteroskedasticity test is incorrectly sized in that context, we suggest an improvement. Finally, a possible modification to impulse ‘intercept corrections’ is considered.