by a dummy variable indicating the past occurrence of a default and by a variable
measuring the number of years since the last default. This variable measures the
recovery of credibility after a default and can be expected to influence positively the
rating score.
3.2. Linear regression framework
A possible starting point for our linear panel model would follow Monfort and Mulder
(2000), Eliasson (2002) or Canuto, Santos and Porto (2004), generalizing a cross section
specification to panel data,
Rit = βXit + λZi+ ai + μtt, (1)
where we have: R - quantitative variable, obtained by a linear or by a non-linear
transformation; Xit is a vector containing time varying variables that includes the time-
varying explanatory variables described above and Zi is a vector of time invariant
variables that include regional dummies.
In (1) the index i (i =1,...,N) denotes the country, the index t (t=1,...,T) indicates the
period and ai stands for the individual effects for each country i (that can either be
modelled as a error term or as N dummies to be estimated). Additionally, it is assumed
that the disturbances μit are independent across countries and across time.
There are three ways to estimate this equation: pooled OLS, fixed effects or random
effects estimation. In normal conditions all estimators are consistent and the ranking of
the three methods in terms of efficiency is clear: a random effects approach is preferable
to the fixed effects, which is preferable to pooled OLS. The question one should ask is
whether the normal conditions are fulfilled. What we mean by normal conditions is
whether or not the country specific error is uncorrelated with the regressors E(ai| Xit,
Zi)=0. If this is the case one should opt for the random effects estimation, while if this
condition does not hold, both the pooled OLS and the random effects estimation give
inconsistent estimates and fixed effects estimation is preferable.
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