Private information and limitations of Heckman's estimator in banking and corporate finance research

Private information is a common problem in banking and corporate finance research. Heckman's (1979) two-step estimator is commonly used to test for sample selection using a simple t-test on the inverse Mills ratio (IMR) coefficient. Following Puri (1996), this test is often interpreted as a test for private information. We conduct a series of Monte Carlo simulations to show that researchers can reliably use the Heckman estimator to test for private information when this private information is random. However, private information often takes the form of an omitted variable with a deterministic relationship to selection and outcomes. In this case, we show that the IMR coefficient is biased and inconsistent and that t-tests lead to incorrect conclusions regarding the significance of private information as well as its impact on selection and outcomes. We illustrate our results using a unique case in prior literature in which a bank's prior information was revealed. In conclusion, the Heckman model cannot be interpreted as a test for private information (or sample selection) when private information takes the form of an omitted variable in the first-stage regression.