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

Table 4 reports the Fisher statistics for all the variables used in our structural equa-
tions. The null hypothesis is that the time series has been generated by an I (1) stochastic
process, and the test follows a chi-square distribution with 34 degrees of freedom (the 5%
critical value is 48.32). Note that all the panel unit root test statistics are greater than
the critical value, so the null of a unit root can be rejected at the 5% significance level.

Table 4: Panel Unit Root Tests

Tables 3 and 4 indicate that we can proceed with stationary panel data estimation
techniques.

4.2 Stationary Dynamic Panel Data Model

We estimate the lagged adjustment processes and long-run elasticities of the system of
behavioural equations (14) by using a fixed-effects (FE) model:

A0yit  ⁼  A1yi,t-1 + A2yi,t-2 + B0^xit + B1^xi,t-1 + C0^zt + C1^zt-1 + ^eit^,

eit  =  μi + vit, i = 1,...,N, t = 1,...,T,                                    (17)

The above equation shows that the vector²⁹ of disturbances (eit) follows a one-way error
component model, where vit ~ iid (0, σ²_ν) with Cov (

^eit^, ejt) = 0, for i = j. The vector
of scalars μi represents the effects that are specific to the ith region and are assumed to
remain constant over time. In other words, the FE model assumes that slope coefficients
and variances are identical across regions and only intercepts are allowed to vary.

The FE estimator³⁰ is the most common estimator for dynamic panels. In homogenous
dynamic panels (i.e. models with constant slopes) the FE estimator is consistent as
T → ∞, for fixed N.³¹ Baltagi and Griffin (1997) compare the performance of a large
number of homogenous and heterogeneous estimators and provide evidence in support
of the FE estimator. In particular, they find that (i) individual unit estimates (both
OLS and 2SLS) exhibit substantial variability, whereas pooled estimators provide more
plausible estimates, and (ii) accounting for potential endogeneity is "disappointing as
the 2SLS estimators performed worse than their counterparts assuming all variables are
exogenous."

the individual ADF regressions.

²⁹ This is a 3 × 1 vector representing the labour demand, wage setting, and labour supply equations in
our system.

³⁰ The fixed-effects estimator is also known as the least squares dummy variables (LSDV) estimator, or
the within-group or the analysis of covariance estimator.

³¹ Kiviet (1995) showed that the bias of the FE estimator in a dynamic model of panel data has an
approximation error of O N^-1T^-3/2 . Therefore, the FE estimator is consistent only as T → ∞, while
it is biased and inconsistent when N is large and T is fixed.

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