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

Due to labour market conditions like, for example, the unemployment benefit system,
unemployment is presumably of higher persistence than employment. Hence, δ1 is ex-
pected to be lower than the employment intensity (α1) in absolute terms. Like the latter,
δ1 seems to be unstable and has increased in recent times, see Moosa (1997) and Lee
(2000) for some empirical evidence. The stronger response of employment to output
fluctuations may be caused by the productivity slowdown, stronger international compe-
tition, less legal protections of the employed and lower turnover costs, which encourage
firms to reduce labour hoarding in periods of economic downturns. Assuming that po-
tential output growth is roughly constant at least over sufficiently long intervals of time,
the law can be rewritten,

(2.8)   (ut-u*)=δ0+δ1yt ,δ1 <0,

where the trend growth rate can be obtained from the intercept term. However, the gap
specifications (2.7) and (2.8) of Okun’s law are not directly suited for estimation. They
involve unobservable variables, and there is no consensus on the proper procedure on
how to identify them. In fact, a variety of filter techniques and trend decomposition
methods exist, but they can lead to different conclusions. Therefore, the first difference
(FD) specification of Okun’s law,

(2.9)   ∆u_t =γ₀ +γ₁y_t ,γ₁ <0,

may be more favourable for empirical reasons, see Okun (1970) and Prachowny (1993).
In contrast to (2.8), the FD specification relates the change in the actual unemployment
rate to actual output growth.

If actual output growth mets the threshold level (yU), unemployment is equal to its natu-
ral rate, implying that its change is equal to 0. Plugging this condition into (2.8) or (2.9)
shows that the threshold can be derived in terms of the model parameters. Specifically,
the threshold for a drop in unemployment

(2.10a) y u,gap =-δo/ δι

(2.10b) y_U,FD = -γ₀ /γ₁

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