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



The unemployment rate (not in logs) is13

ut = lt - nt.                                          (4)

Let us rewrite the labour demand and real wage equations (1)-(2) as

(1 - α1L) nt = -γwt + εtn,                           (5)

(1 - α2L) wt = -δut + εtw ,                            (6)

where L is the lag operator. Substitution of (6) into (5) gives

(1 - α1L) (1 - α2L) nt = γδut + (1 - α2L) εtn - γεtw.               (7)

Next, rewrite the labour supply (3) as

(1 - α1L) (1 - α2L) lt = (1 - α1L) (1 - α2L) εlt.                    (8)

Finally, subtract from (8) the labour demand eq. (7) to get the reduced form unem-
ployment rate equation:14

[γδ + (1 - α1L) (1 - α2L)] ut = - (1 - α2L) εtn + γεtw + (1 - α1L) (1 - α2L) εlt.    (9)

Note that the above equation is dynamically stable since (i) products of polynomials
in
L which satisfy the stability conditions are stable, and (ii) linear combinations of
dynamically stable polynomials in
L are also stable.

Alternatively, the reduced form unemployment rate equation (9) can be written as

ut = φ1ut-1 - φ2ut-2 - β1εtn + β2εtw + β1εlt + θ1εtn-1 - φ1εlt-1 + φ2εlt-2      (10)

where Φ1 = ααi+δ2 ,Φ2 = α+αδ, β 1 = ⅛ ,β2 = ⅛, and θι = ⅛.

The above reparameterisation of the reduced form unemployment rate equation helps
to explain the characteristic features of the chain reaction theory. First, the autoregres-
sive parameters
φ1 and φ2 embody the interactions of the employment and wage setting
adjustment processes (
α1 and α2, respectively).

Second, the coefficients β 1 and β2 are the short-run elasticities and are a function of
the feedback mechanisms that give rise to the spillover effects. When
γ and δ are non
zero, all labour market shocks generate spillover effects. If
δ = 0, i.e. unemployment does
not influence wages, then labour demand and supply shocks do not spillover to wages. If
γ = 0, i.e. labour demand is completely inelastic with respect to wages, then shocks to

13 Since labour force and employment are in logs, we can approximate the unemployment rate by their
difference.

14 The term "reduced form" means that the parameters of the equation are not estimated directly -
they are simply some nonlinear function of the parameters of the underlying labour market system.



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