Non- and Semi-Parametric Quantile Models for Recovery Rate

This paper proposes a nonparametric quantile regression (NP-QR) and a partially linear additive QR (PLA-QR) for modelling recovery rates (RR). Using Moody's Recovery Database, we uncover two novelties of the NP-QR model. First, the local constant estimation of NP-QR model captures the key empirical feature of RR data being bounded in [0,1] interval. Second, the heterogeneity in the impact of borrower characteristics with clarity can be estimated. For example, we show that the way in which the impact of debt cushion on RR depends on the other characteristics, such as collateralisation and the degree of instrument rank of loans, during various economic conditions. By contrast such heterogeneity is reduced to a single dimension in the parametric regression model. Furthermore, accommodating bimodality and heteroscedastic errors, the NP-QR also provides the heterogeneity of these impacts across the various quantiles of the conditional RR distribution. On the other hand, the idiosyncratic marginal effects of borrower characteristics are estimated using the PLA-QR model over the various quantiles of the conditional RR distribution. For example, for loans with very low risk, we find that the RR is less sensitive to the change in debt cushion at the lower quantiles than that at the upper quantile, particularly when the debt cushion is less than 30%, during economic downturns. The findings of this study have implication for lenders designing an optimum treatment rule for borrowers