The Global Dimension to Fiscal Sustainability

approach uses principle components and then the Fully Modified estimator of Phillips
and Hansen (1990).

The model is based on the following equation:

y_it =α_i + βx_it +e_it,         i=1,...,N;t=1,...,T .                                 (11)

In this model yit is1×1, β is 1×k is a vector of slope parameters and αi is 1×1 intercept
parameters. Additionally, we have a stationary residual, eit. The nonstationary
variables xit is 1×1 and set out as follows:

x_it = x_it-1 + ε_it                                                                  (12)

As such yit is cointegrated with xit, given the stationarity of the residual. This is the
panel approach adopted in, for example, Pedroni (2004). However, this approach
assumes that the residual terms are cross sectionally independent. We deal with
potential temporal dependence in our panel estimator by adopting a factor model
approach. In the factor model the residual errors are set out as follows:

'

e_it = λ_i F_t +u_it                                                         (13)

Here Ft and λi are the common factor and factor loadings respectively. The error term
uit in equation (13) is the idiosyncratic component of the residual error in equation (6).
The parameters and long-run covariance matrix are estimated recursively, until
convergence is reached, using a Continuously-updated Fully Modified (CupFM)
estimator (see Bai and Kao, 2006, and Westerlund, 2007). According to Monte Carlo
evidence presented in Bai and Kao (2006) OLS has non-negligible bias in comparison
to CupFM.

3.3 Panel Estimation with Nonstationary Factor

Bai, Kao and Ng (2007) provide an estimator of a panel cointegrating model
with cross sectional dependence generated by stochastic trends. This has an advantage

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