The name is absent

In our case, it seems more natural that the country specific effect is correlated with the
regressors.¹ Given this scenario one should be tempted to say that the “fixed effects
estimation” is the best strategy, but that has a problem. Because there is not much
variation of a countries rating over time, the country dummies included in the regression
will capture the country’s average rating, while all the other variables will only capture
movements in the ratings across time. This means that, although statistically correct, a
regression by fixed effects would be seriously striped of meaning.

There are two ways of rescuing a random effects approach under correlation between
the country specific error and the regressors. One is to do the Hausman-Taylor IV
estimation but for that we would have to come up with possible instruments that are not
correlated with ai, which does not seem an easy task. In this paper we will opt for a
different approach that consists on modelling the error term ai. This approach, described
in Wooldridge (2002), is usually applied when estimating non-linear models, as IV
estimation proves to be a Herculean task but, as we shall see, the application to our case
is quite successful. The idea is to give an explicit expression for the correlation between
the error and the regressors, stating that the expected value of the country specific error
is a linear combination of time-averages of the regressors X i . This follows Hajivassiliou
and Ioannides (2006) and Hajivassiliou (2006).

E ( a_i∖ Xt, Z) = η X₁.                           (2)

If we modify our initial equation (1), with a_i= ηXt +ε_i we get

Rt = βXι_t + λZι+ ηXi + ει+ μ_n,                     (3)

whereε_i is an error term by definition uncorrelated with the regressors. In practical
terms, we eliminate the problem by including a time-average of the explanatory
variables as additional time-invariant regressors. We can rewrite (3) as:

¹ This idea can easily be checked by doing some exploratory regressors. We estimated equation (1) using
random effects and performed the Hausman test; the Qui-Square statistisc was in fact very high, and the
null hypothesis of no correlation was rejected with p-values of 0.000.

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