Rit = β(Xit- Xi )+ (η + β)Xi + λZi + εi + μit ■
(4)
This expression is quite intuitive. δ = η + β can be interpreted as a long-term effect (e. g.
if a country has a permanent high inflation what is the respective effect on the rating),
while β is a short-term effect (e. g. if a country manages to reduce inflation this year by
one point what would be the effect in the rating). This intuitive distinction is useful for
policy purposes as it can tell what a country can do to improve its rating in the short to
medium-term. We will estimate equation (4) by random effects, but we also estimate the
OLS and fixed effects versions. The way we modelled the error term can be considered
successful if the coefficients of Xi are significant and if the Hausman test indicates no
correlation between the regressors and the new error term.
3.3. Ordered response framework
Alternatively we estimate the determinants of sovereign debt ratings in a limited
dependent variable framework. As we mentioned before, the ordered probit is a natural
approach for this type of problem, because the rating is a discrete variable and reflects
an order in terms of probability of default. The setting is the following. Each rating
agency makes a continuous evaluation of a country’s credit-worthiness, embodied in an
unobserved latent variable R*. This latent variable has a linear form and depends on the
same set of variables as before,
Rit = β(Xu — Xi ) + δXi + λZi + εi + μit.
(5)
Because there is a limited number of rating categories, the rating agencies will have
several cut-off points that draw up the boundaries of each rating category. The final
rating will then be given by
Rit
AAA (Aaa)
AA+ (Aa1)
AA (Aa2)
if
if
if
R*>c
it 16
*
c16 >Rit >c15
c15 > Rit* >c14
(6)
< CCC +(Caa1)
if
c1 > Rit*
14