Abstract
We consider an observation driven, conditionally Beta distributed model for variables restricted to the
unit interval. The model includes both explanatory variables and autoregressive dependence in the mean
and precision parameters using the mean-precision parametrization of the beta distribution suggested by
Ferrari and Cribari-Neto (2004). Our model is a generalization of the βARMA model proposed in Rocha and
Cribari-Neto (2009), which we generalize to allow for covariates and a ARCH type structure in the precision
parameter. We also highlight some errors in their derivations of the score and information which has implications
for the asymptotic theory. Included simulations suggests that standard asymptotics for estimators and
test statistics apply. In an empirical application to Moody’s monthly US 12-month issuer default rates in the
period 1972 − 2015, we revisit the results of Agosto et al. (2016) in examining the conditional independence
hypothesis of Lando and Nielsen (2010). Empirically we find that; (1) the current default rate influence the
default rate of the following periods even when conditioning on explanatory variables. (2) The 12 month
lag is highly significant in explaining the monthly default rate. (3) There is evidence for volatility clustering
beyond what is accounted for by the inherent mean-precision relationship of the Beta distribution in the
default rate data.
unit interval. The model includes both explanatory variables and autoregressive dependence in the mean
and precision parameters using the mean-precision parametrization of the beta distribution suggested by
Ferrari and Cribari-Neto (2004). Our model is a generalization of the βARMA model proposed in Rocha and
Cribari-Neto (2009), which we generalize to allow for covariates and a ARCH type structure in the precision
parameter. We also highlight some errors in their derivations of the score and information which has implications
for the asymptotic theory. Included simulations suggests that standard asymptotics for estimators and
test statistics apply. In an empirical application to Moody’s monthly US 12-month issuer default rates in the
period 1972 − 2015, we revisit the results of Agosto et al. (2016) in examining the conditional independence
hypothesis of Lando and Nielsen (2010). Empirically we find that; (1) the current default rate influence the
default rate of the following periods even when conditioning on explanatory variables. (2) The 12 month
lag is highly significant in explaining the monthly default rate. (3) There is evidence for volatility clustering
beyond what is accounted for by the inherent mean-precision relationship of the Beta distribution in the
default rate data.
| Originalsprog | Engelsk |
|---|---|
| Antal sider | 30 |
| Status | Udgivet - 2017 |
| Navn | University of Copenhagen. Institute of Economics. Discussion Papers (Online) |
|---|---|
| Nummer | 17-01 |
| ISSN | 1601-2461 |
Emneord
- Det Samfundsvidenskabelige Fakultet
- Beta regression
- credit risk default rates
- contagion
- C12
- C22
- C32
- C50