Private information and limitations of Heckman's estimator in banking and corporate finance research |
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| Institution: | 1. College of Business, Mississippi State University, Mississippi State, MS 39762, USA;2. Jones College of Business, Middle Tennessee State University, Murfreesboro, TN 37132, USA;1. Cass Business School and Centre for Economic Policy Research (CEPR), London, UK;2. Institute of Finance, University of Lugano, Via Buffi 13, CH-6900 Lugano, Switzerland;3. Department of Finance, Copenhagen Business School, DK-2000 Frederiksberg, Denmark;1. The Smeal College of Business, The Pennsylvania State University, 322 Business Building, University Park, State College, 16801, Pennsylvania, USA;2. Department of Finance, John Molson School of Business, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, P.Q., H3G 1M8, Canada;1. Department of Economics, University of Kiel, Olshausenstr. 40, 24118 Kiel, Germany;2. Banco de España Chair in Computational Economics,University Jaume I, Campus del Riu Sec, 12071 Castellon, Spain;1. Regions Bank, Birmingham, AL, USA;2. Department of Economics, Finance and Legal Studies, Culverhouse College of Commerce & Business Administration, University of Alabama, Tuscaloosa, AL, USA |
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| Abstract: | 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. |
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