distances is strongly rejected as the thresholds for higher ratings are further apart than
those of the lower ratings. In this case the kink lies at the A rating.
[Insert Figure 2 here]
Finally, for S&P, different distances are found throughout the ratings scale. Looking at
Figure 2, it appears that for lower ratings the relative distance between thresholds of
S&P coincides with that of Moody’s. However, above the investment grade limit, the
distances between thresholds at first decline and then increase, resulting in a slightly
curved ratings schedule that makes the transition to the highest grades most difficult.
4.4. Prediction analysis
Our prediction analysis will focus on two elements: the prediction for the rating of each
individual observation in the sample, as well as the prediction of movements in the
ratings through time.
Prediction with the pooled OLS model was done by rounding the fitted value (which is
continuous) to the closest integer between 1 and 17. For the random effects estimations
we can have two predictions, with or without the country specific effect, εi, and we can
write the corresponding estimated versions of (4) as:
Rit = β ( Xit — X i ) + δX i + λ Zi + ε i, (7 a)
Rit = β(Xit — Xi) + δxi + λZi. (7b)
We can then estimate each country specific effect by taking the time average of the
estimated residual for each country. As a result we can include or exclude this
additional information that comes out of the estimation. In other words, we generate in-
sample and out-of-sample prediction. After the fitted value is computed it is then also
rounded to the closest integer between 1 and 17. The prediction with both ordered probit
and the random effects ordered probit was done by fitting the value of the latent
variable, setting the error term to zero, and then match it up to the cut points do
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