Thresholds for Employment and Unemployment - a Spatial Analysis of German Regional Labour Markets 1992-2000

kets do not diminish immediately. Instead of estimating unrelated equations in the style
of (3.3) for different periods of time, a spatial SUR analysis is preferred. Contrary to the
familiar SUR model, the system

yii = ^β0 ^+β1 ∙ ^xli ⁺ ∑Y1 j ∙^ω j ^{+ ν}1i

S1

(3.4) y_2i = β₀ +β₁ ∙ x^l_2i +∑γ_2j ∙ω_j +ν_2i

S₂

y_Ti = β₀ +β₁ ∙ x_T^l_i + ∑γ_Tj ∙ω_j +ν_Ti
S_T

is formed by the time periods for all n spatial units ( i=1,2,...,N), see Anselin (1988, pp.
137). The sets S₁, S₂, ..., ST of eigenvectors may be composed of different elements. If
the choice of spatial components for the sets St, t=1,2, ...,T, proves to be successful, the
disturbances νti will be contemporaneous uncorrelated:

(3.5) Cov(ν_ti, Vti) = E(Vt₁-Vt_l) = 0.

Dependencies over time can be modelled by defining the NxN covariance matrix Σ,

(3.6) Σ = E(Vt -V^’s) = σts-IN,

in which σts denotes the covariance between the periods t and s, t≠s, and νt an Nx1 vec-
tor of the disturbances in period t. With this the time-dependent autocorrelation struc-
ture of the spatial SUR system (3.4) is given by the NTxNT covariance matrix

(3.7) Σ* = Σ 0In.

Provided that T < N the covariance matrix Σl can be estimated directly from the data.

As dependencies over time are taken into account, parameters are estimated more effi-
ciently. In previous studies space-time models have been employed where spatial effects
were captured in a restrictive way by first order autoregressive lags, see e.g. Beck and
Katz (2001), Elhorst (2001) and Beck and Gleditsch (2003). Probably due to high com-
putational demands empirical applications of the spatial SUR model are rarely to find.
Exceptions are the works of Florax (1992) and Fingleton (2001). The advantage of Grif-
fith’s approach consists in allowing to set up the model straightforwardly with ordinary
devices taken from regression analysis.

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