Labour Market Flexibility and Regional Unemployment Rate Dynamics: Spain (1980-1995)

- real oil price, real social security benefits, indirect tax rate, and real import price - we
cannot reject the null hypothesis of (trend) stationarity.

Table 3: Unit Root Tests

KPSS_c uses an intercept in the test.

KPSS_c,t uses an intercept and trend in the test.

4.1 Panel Unit Roots

Since it is widely accepted that the use of pooled cross-section and time series data can
generate more powerful unit root tests,²⁷ we examine the stationarity of the regional
variables using panel unit root tests. We apply the simple statistic proposed by Maddala
and Wu (1999) - this is an exact nonparametric test based on Fisher (1932):

N

λ = -2j>Pi ■" X2 (2N),                       (16)

i=1

where pi is the probability value of the ADF unit root test for the ith unit (region).
The Fisher test has the following attractive characteristics. First, since it combines the
significance of N different independent unit root statistics, it does not restrict the au-
toregressive parameter to be homogeneous across i under the alternative of stationarity.
Second, the choice of the lag length and of the inclusion of a time trend in the individual
ADF regressions can be determined separately for each region. Third, the sample sizes of
the individual ADF tests can differ according to data availability for each cross-section.
Finally, it should be noted that the Fisher statistic can be used with any type of unit root
test. Maddala and Wu (1999), using Monte Carlo simulations, conclude that the Fisher
test outperforms both the Levin and Lin (1993) and the Im, Pesaran and Shin (2003)
tests.²⁸

where T is the sample size, St = ^t=ι ¾ is the partial sum of the residuals when the series is regressed
on an intercept (and possibly on a time trend), and s² (κ) is a consistent non-parametric estimate of
the disturbance variance. In particular, s² (κ) is constructed as in Phillips (1987) or Phillips and Perron
(1988) by using a Bartlett window adjustment based on the first κ sample autocovariances as in Newey
and West (1987). KPSS report critical values (c.v.) for the case of (i) a constant in the auxilliary
regression: 1% c.v.=0.74, 2.5% c.v.=0.57, 5% c.v.=0.46, 10% c.v.=0.35, and (ii) both a constant and a
trend: 1% c.v.=0.22, 2.5% c.v.=0.18, 5% c.v.=0.15, 10% c.v.=0.12.

²⁷ See, for example, Levin and Lin (LL) (1993), Im, Pesaran and Shin (2003), Harris and Tzavalis
(1999), Maddala and Wu (1999). Note that the asymptotic properties of tests and estimators proposed
for nonstationary panels depend on how N (the number of cross-section units) and T (the length of the
time series) tend to infinity, see Phillips and Moon (1999).

²⁸ Levin and Lin (LL) proposed asymptotic panel unit root tests which are based on pooled regressions.
The major criticism against the LL tests is that, under the alternative of stationarity, the autoregressive
coefficient is the same across all units (i.e. H1 : ρ₁ = ρ₂ = ... = ρ_N = ρ < 0).

This restrictive assumption is relaxed in the asymptotic test proposed by Im, Pesaran and Shin (IPS).
Like the Fisher test, and in contrast to the LL tests, the IPS test is based on the individual ADF
regressions for each of the N cross-section units. While the Fisher test uses the probability values of the
individual ADF tests, the IPS uses their test statistics. Compared to the Fisher test, the disadvantage
of the IPS test is that it implicitly assumes the same T for all countries and the same lag length for all

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