Small Sample Evidence on the Impact of Generated Variables in Event Studies

This paper provides some small sample evidence on the appropriateness of ordinary least squares (OLS) and instrumental variable (IV) estimators of the structural equation, and on the appropriate method of performing hypothesis testing in event studies when generated variables are present. In event studies, the number of observations used to estimate the auxiliary equations (and compute the generated variables) and the structural equation can differ quite substantially. In certain circumstances, this means the appropriate estimator of the structural equation is the IV estimator rather than OLS estimator. Some Monte Carlo suggests that an IV estimator of the parameters of interest can lead to considerably smaller biases than the biases of the OLS estimator. Sizes and powers of tests associated with the coefficient of the generated variable do not seem to be affected by the presence of the generated variable. In contrast, the sizes of tests associated with the constant are considerably distorted when the generated variable should be included in the structural equation.