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

sum of the immediate response (Rt) and persistence (σ) gives the long-run elasticity of
the unemployment rate with respect to x. Thus, the long-run elasticity of the variable is
given by

∞

ʌ + -~σ- =  ∑Rt+j ∙              (13)

^-^          persistence       j=0

short-run elasticity                        ^   - — ^y

long-run elasticity

In other words, the long-run elasticity can be decomposed into the short-run elasticity
and our measure of persistence (11).

Next, we present the structure of the labour market system that we estimate in section
4 and provide an economic rationale for our choice of framework.

3 Structure of the Regional Model

We use a structural vector autoregressive distributed lag model for the Spanish regions to
analyse regional unemployment persistence and explain unemployment rate disparities:¹⁷

A0yit ⁼ A1yi,t-1 + A2yi,t-2 + B0^xit + B1^xi,t-1 + C0^zt + C1^zt-1 + ^eit^,     (14)
where y_it is a vector of endogenous variables, x_it is a vector of regional exogenous variables,
z_t is a vector of national exogenous variables, the A’s, B’s and C’s are coefficient matrices,
and ei_t is a vector of identically independently distributed error terms.

The multi-equation system (14) consists of (i) a labour demand equation, describing
the equilibrium employment (n_it), (ii) a wage setting equation, describing real wage (w_it)
determination, (iii) a labour supply equation, describing the equilibrium size of the labour
force (lit), and (iv) a definition of the unemployment rate (not in logs):¹⁸

^uit ⁼ lit ^{- n}it^∙

According to (14) the regional unemployment rate is determined by (i) local condi-
tions measured by the regional exogenous variables x_it (such as capital stock), and (ii)
nationwide variables z_t (such as oil prices) which are common to all regions. In contrast,
the models in Blanchard and Katz (1992), and Decressin and Fatas (1995) emphasize
regional dynamics as opposed to national dynamics, analysing exclusively the effects of
regional specific shocks.

In our empirical work we split the 17 Spanish regions into two groups depending on
the evolution of the regional unemployment rate relative to the national one. The regions
with a higher (lower) unemployment rate than the national one are referred to as the

¹⁷The dynamic system (14) is stable if, for given values of the exogenous variables, all the roots of the
determinantal equation

∣Ao - AiL - A2L²∣ =0

lie outside the unit circle. Note that the estimated equations in Section 4 below satisfy this condition.

¹⁸ Given then the labour force and employment are in logarithms, this is an approximation.

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