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

7 Total Effects of Actual Shocks

So far we measured (i) the responses of unemployment to hypothetical one-off unit labour
market shocks and (ii) the contributions of the exogenous variables to the evolution of the
unemployment rate during the sample period. To complete our analysis of labour market
dynamics and unemployment reactions to economic shocks, we now seek to answer a
rather different question. How has unemployment responded to the changes that each of
the exogenous variables underwent during our sample?

For ease of exposition suppose the estimated reduced form unemployment rate equa-
tion is given by⁴⁰

uit = ρui,t-1 + czt, t=0,1,2,...,T.                             (19)

In this illustrative model unemployment is dynamically stable (|p| < 1) and depends on
the exogenous variable z . Assuming for simplicity that unemployment is initially at its
steady state, if the exogenous variable remains constant then unemployment will also
remain constant. We can thus say that the changes in the exogenous variable z determine
the trajectory of the unemployment rate.

At each point in time we define the shock in the exogenous variable, 6_t, as the difference
between its value at year t and its value at the base year t = 0:

t

ɛt ≡ Zt - Zo = ^ ∆Zj ,

j=1

where ∆Z_t ≡ Z_t - Z_t-1 is the annual change of the series. In other words, the actual shock
of the exogenous variable at a point in time t, 6_t, is given by the cumulative sum of its
yearly changes. Unemployment is thus driven by a series of actual shocks (6_l,62, ...,6t)
occuring during the sample period.

In line with the analysis in Section 2, the unemployment responses to all shocks during
the sample period are given by the following triangular (T × T ) matrix:

The number of rows refers to the time periods in the sample and the number of colums to
the actual shocks. In particular, the jth column of the above matrix gives the responses
of unemployment to the jth shock at every period in the sample. The tth row of (21)

⁴⁰ This dynamic model without spillovers provides the simplest analytical tool to explain how we com-
pute the total effects of actual shocks. This methodology is then applied to our estimated labour market
model (the results are given in Table 8 below).

23

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