In the empirical section below we use 8 years of quarterly data (32 quarterly
observations) for 18 banks (we only consider the case of a complete panel). With T=32
and N= 18 the asymptotic theory with the (N / T) → 0 condition, becomes the useful
reference.

If we assume that the true model is heterogeneous (different parameters for different
individuals or banks) the estimators are NN consistent for the so-called long-run average
coefficients. Super-consistency is not obtained because the effect of heterogeneity in the
cointegration parameters is to slow down the rate of convergence of the pooled estimator.

If we assume that the underlying model is homogeneous (the same coefficients for all
the individuals) the POLS estimator (which corresponds to the within estimator) is VN T
consistent and has a limiting normal distribution, under the additional assumption of
strictly exogenous regressors, but is consistent (not super-consistent) if the regressors are
correlated with the residuals, because of the persistence of bias effects.

For the case of a homogeneous panel with endogenous regressors the authors suggest
using the Panel Fully-Modified OLS estimator (PFMOLS). This estimator is a simple
generalisation of the well-known Fully-Modified OLS estimator introduced in Phillips and
Hansen (1990) for pure time-series models. The PFMOLS estimator is VNT consistent
and has a normal limit distribution¹⁴.

In addition to POLS and PFMOLS two other estimators were also suggested in the
literature for non-stationary panel data: the corrected OLS (PCOLS) and the dynamic OLS
(PDOLS)¹⁵.

6. Monetary policy and banking sector developments in Portugal during the
nineties

During the second half of the 80’s economic policy in Portugal was driven by the need to
implement the Single Market programme. Fundamental changes in the economic policy
framework as well as in the banking sector occurred in this period. These include

¹⁴ The fully modified OLS is constructed by making corrections for endogeneity and serial correlation to
the OLS estimator. The endogeneity correction use the so called “long-run” covariance matrix defined for the
residuals of the model and the first differences of the regressors, while the serial correlation correction uses
elements from this matrix and also from the so-called “one sided long-run” covariance matrix. The
expressions for the computation of the PFMOLS estimator may be seen in Phillips and Moon (1999) or Kao
and Chiang (2000).

¹⁵ See, for instance, Kao and Chiang (2000).

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