The Global Dimension to Fiscal Sustainability

3.1PANIC Panel Unit Root Test

The PANIC approach introduced by Bai and Ng (2004) uses a factor structure
to understand the nature of nonstationarity in large dimensional panels. The Bai and
Ng factor model is set out for the case where only an intercept is included:

y_it =c_i +λ_i'F_t +e_it,                                     (7)

F_t = αF_t-1 + u_t,                                       (8)

e_it = ρ_ie_it-1 +ε_it.                                                (9)

The series y_it is the sum of a cross section specific constant (ci), a common
component λi'Ft and an error, eit, which is the idiosyncratic component. The series y_it
is nonstationary if the common factors are nonstationary (α = 1, in equation (8))
and/or the idiosyncratic component (ρi = 1, in equation (9)) are nonstationary. The
PANIC method allows us to identify whether nonstationarity is pervasive (due to the
common factor) or series specific (due to the individual series). Whether there is a
factor or not is identified by an information criteria, see Bai and Ng (2002). Unlike
Moon and Perron (2004) and Pesaran (2007), the PANIC test does not assume that
only the idiosyncratic component can have a unit root. In the present application, it is
particularly useful that PANIC determines explicitly whether the nonstationarity in a
series is pervasive or variable-specific.

We make use of two test statistics from Bai and Ng (2004). Firstly, an
Augmented Dickey Fuller test on the common factor ( ADFF ) and secondly a Fisher-
type pooled ADF test on the idiosyncratic individual errors ( ADFe^c ( i )). Bai and Ng
(2004) suggest the test statistic on the idiosyncratic element is distributed as standard
normal as follows:

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