The role of capital accumulation in bargaining models
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Recall that warranted wage was given by w-p=a, but this is assuming that labor was
the only factor of production.
Assume Cobb-Douglas production (in logs)
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The marginal product of labor will give a real (warranted) wage
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which is not affected by the capital stock. If the capital stock falls, this lowers the
warranted wage.
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Let 𝑛̅ be the log of labor stock, so u=𝑛̅ − 𝑛. The unemployment rate that equalizes
the bargained and warranted wage is now
As before, unemployment depends on nominal and real rigidities, but we also get an
effect from change in the capital intensity.
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It is natural to think that the adverse shocks to a, together with the slow adjustment
in real wages (and thus too high levels of unemployment, lowering profits), led to
lower investment and thus a small capital stock. This adds persistence to the effect
of the shocks, possibly explaining why unemployment remained high in the 1980s.
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Expansionary monetary policy should have made the reduction in investment less
severe (due to the low real interest rates). But many countries had a monetary
contraction (in response to the high inflation rates)
Hysteresis
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Another source of persistence that could explain persistent unemployment rates
Captures the idea that temporary rises in unemployment generated by supply and/or
demand shocks had permanent (or at least very persistent) effects.
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In this sense, an increase in short run unemployment can affect the long run
unemployment rate when it persists for a long time, due to labor market rigidities
and the slowness of the adjustment mechanism determined by eg. Trade unions;
discouraged workers, obsolete skills due to long term unemployment, etc.
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In full hysteresis models, there is no equilibrium unemployment in the long run, but
unemployment always reflects past unemployment rates.
The high unemployment in Europe in the 1980s can be explained by hysteresis using an
insider/outsider model.
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Insider/outsider models are a variation on the contract model recognizing that
insiders (those employed/unions) have more privileged positions than the outsiders
(unemployed).
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The implications of this model is that even when there are many unemployed
willing to work for wages lower than existing insider wages, there is an absence of
wage underbidding.
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To incorporate this in a model, we keep the warranted wage the same as before but
assume that 𝑘𝑡 is constant. Instead of the normal wage bargaining equation, assume
that unions will bargain for a wage such that their expected value of employment
next period 𝑛𝑒𝑡 is equal to the number of members in its union, 𝑚𝑡 . The unionmember process is given by
where θ is a measure of how much the union cares about the unemployed (outsiders)
relative to the employed (insiders).
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The wage that makes 𝑛𝑡𝑒 = 𝑚𝑡 can be found using the warranged wage equation in
expectations:
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We still have real and nominal rigidities. In addition, we now get the persistence
effect depending on θ. If we set θ=0, we get unemployment as a random walk (very
persistent).