An application of the two-stage Bivariate Probit–Tobit model to corporate financing decisions

See the two-stage estimation method introduced by Heckman (1976), Lee (1976) and Amemiya (1978, 1979).

We tried both estimation methods; the results show only marginal differences between the FIML estimator and the two-step procedure. The two-step procedure coefficients are nearly identical with the consistent and efficient coefficients obtained by FIML estimation. All the results reported in this paper use the two-step procedure.

In constructing our data we are following Frank and Goyal (2003), in which firms involved in major mergers (Compustat footnote code AB) are excluded. Also, we exclude firms with missing value of any item in the balance sheet and cash flow statement and a small number of firms that reported format codes 4, 5, or 6. Compustat does not define format codes 4 and 6. Format code 5 is for the Canadian file. The balance sheet and cash flow statement items as a percentage of assets are trimmed to remove the most extreme 0.50% in either tail of the distribution. This serves to remove outliers and the most extremely misrecorded data. Finally, all accounting identities in the financial statements should hold.

To examine the robustness of the two-stage estimators to data errors and outliers, we re-estimate the model by trimming the upper and lower 1% (5%) of each variable used in the analysis to mitigate the impact of data errors and outliers. In addition, to evaluate the impact of data errors and outliers on the marginal effect, two approaches are used. The first is to compute the marginal effect at the sample means of the data. The second approach is to compute marginal effect at each observation and then to calculate the sample average of individual marginal effects to obtain the overall marginal effect. We find no material change to the results when we use different thresholds for trimming the data. Also, to examine the robustness of the model to the time independent assumption, we re-estimate the model year by year; one clear result stands out: \( \rho_{{u_{1} u_{2} }} ,\rho_{{u_{1} \varepsilon }} ,\rho_{{u_{2} \varepsilon }} \) are significantly different from zero in about 85% of the years. Averaging the coefficients of the model across years, as in Fama-McBeth approach, yields similar results. We thank a referee for drawing our attention to these issues.

Green (1996) provides details of how to derive the marginal effects in the Bivariate-Probit model.