In this section, we examine the robustness of results presented in Section 1.3. We investigate deviations from previous findings when applying varying methods. First, we use a log transfor- mation of the TTR. In contrast to the level specification, the TTR is restricted to values greater than zero. As stated in Section 1.3, the resolution bias is an issue of concern. Estimates of the multiple linear regression might be biased due to the overrepresentation of loans with a rather short TTR. If the exact number of missing observations, i.e., loans not completely resolved yet, is known, censored regressions are adaptable to adress the resolution bias. However, as we are not aware of the exact quantity, we apply truncated regressions. The results are compared with the linear model in order to draw conclusions regarding possible distortions in the parameters. Finally, we return to the multiple linear regression but use an alternative measure of the TTR as the dependent variable.
Log transformation
The results regarding the log transformation are displayed in Table 1.A.1 (see Appendix 1.A). Compared to the level specification, we find similar signs for almost all determinants. Dif- ferences arise for the senioritynon senior, the collateralreal estateand the industriesservices andwholesale and retail trade. However, these might be attributable to the modification of the dependent variable and, particularly, to the variation of its distribution.31 Generally, the results seem to be robust regarding the transformation of the TTR as the directions of the coefficients are similar for most of the variables. Changes of the impacts can be explained through the log transformation itself.
Truncated regression
Excluding incompletely resolved loan contracts entails a selection bias. At the time of writing of this paper, the year 2015 marks the present and we do not have any information beyond this point. Loans defaulted in, e.g., 2013 could exhibit a maximum TTR of two years while those which are going to be resolved later on are neglected. Hence, including only resolved loan contracts might yield in distorted parameter estimates. To analyze this bias, we adopt truncated regressions on subsamples on yearly basis. The application on subsets seems necessary as the limiting value of the data has to be unique in the samples. E.g., the limit regarding loans defaulted in 2014 is one year, in 2013 two years, in 2012 three years, and so on. For the reason 31See Appendix 1.A for further information.
of comparability, truncated regressions on yearly basis are compared to their counterparts of the linear regression.32
Generally, the coefficients in both models are almost similar regarding all years. For simplicity, only the subsets with the highest deviations in the parameter estimates are displayed.33 Ta- ble 1.B.1 and 1.B.2 (see Appendix 1.B) contain the results with respect to the years 2008 and 2009, where the coefficients of the year 2008 exhibit slightly higher deviations. Noteworthy, these years mark the summit of the global financial crisis. This indicates that the resolution bias is particularly pronounced during financial turmoil. At first glance, this may be counterintuitive since we would expect the major manifestation in the most recent years. However, the global financial crisis might have entailed a market shakeout. Rather poor debtors have defaulted in crisis years yielding to a better credit quality regarding debtors afterwards. Therefore, short resolution times are more frequent in the recent years and distortions due to longer TTR become less likely.
Comparing the truncated and the linear regression, almost no variations emerge regarding the sign or significance of the coefficients. This gives rise to the conjecture that the resolution bias might not lead to misjudgments regarding the direction of the determinants. In the truncated regression, the absolute values of the coefficients increase compared to the multiple linear model. Therefore, neglecting the resolution bias can lead to an undervaluation of the impacts but not to a misapprehension of the signs. Generally, the deviations are negligible indicating that either the resolution bias does not distort the parameter estimates or its effect is absorbed by the time dummies in the overall data set and the intercepts in the subsamples.
Alternative dependent variable
Besides the application of various models, the TTR is replaced by a different dependent variable inspired by the bond duration. Generally, it is specified by the cash-flow-weighted average of the payment dates and, therefore, expressed in years.34 We will refer to this measure as loan duration: D= 1 P T X t=1 t Ct (1 +r)t ,
wherebyP denotes the present value of the cash flows and is calculated asP =PT t=1
Ct
(1+r)t. The
parameterCt describes the cash flow at timetandrthe discount rate. Generally, only positive
32Comparing regressions of the overall data set with the ones on yearly basis, several deviations among the
parameters arise. See Appendix 1.B for further information.
33The results of the remaining subsets are available from the authors upon request. 34The implied statement of price sensitivity to the interest rate is neglected.
and cash-flow-related transactions enter the loan duration.
Table 1.C.1 (see Appendix 1.C) displays the results of the multiple linear regression with the loan duration as the dependent variable. Compared to the results of Table 1.3, several deviations among the coefficients arise. However, reverse signs are insignificant regarding the TTR or the loan duration.35